new latex package calculator (11jun12)

git-svn-id: svn://tug.org/texlive/trunk@27112 c570f23f-e606-0410-a88d-b1316a301751

66 files changed, 6776 insertions, 1 deletions

diff --git a/Master/texmf-dist/doc/latex/calculator/README b/Master/texmf-dist/doc/latex/calculator/README
new file mode 100644
index 00000000000..a117269067e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/README
@@ -0,0 +1,133 @@
+
+The calculator and calculus packages: Use \LaTeX as a scientific calculator.
+
+Robert Fuster, 2012
+
+
+1. Licence
+----------
+This material is subject to the LaTeX Project Public License. 
+
+See http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html 
+for the details of that license.
+
+
+2. About the packages
+---------------------
+
+The calculator and calculus packages define several instructions which allow us 
+to realize algebraic operations and to evaluate elementary functions and derivatives
+in our documents.
+
+My main goal is to define the arithmetic and functional claculations I need in my 
+package "xpicture" (http://www.upv.es/~rfuster/xpicture), but the numeric abilities
+of "calculator" and "calculus" may be useful in other contexts.
+
+2.1 The calculator package
+--------------------------
+
+The operations implemented by the calculator package include
+- arithmetical calculations with  real and integer numbers 
+- two and three dimensional vectors and matrices arithmetics 
+- computation of powers, square roots, trigonometrical, exponential, logarithmic and 
+  hyperbolic functions. 
+
+In addition, some important numbers, such as pi, sqrt(2) or e, are predefined.
+
+Some simple examples:
+
+a) Simplify a fraction: if you type
+
+   \FRACTIONSIMPLIFY{252}{2220}{\num}{\den}
+
+    Then, $\num/\den$ equals to 21/186 
+
+b) Compute elementary functions:
+
+   \LOG{2}{\sol}  ---> \sol equals 0.69315
+
+   \LOG[10]{2}{\sol} ---> \sol equals 0.30103
+
+   \SIN{\numberHALFPI}{\sol} ---> \sol equals 1
+ 
+c) More complex calculations:
+   You can compute the value of sqrt(7.25)cos(pi/7) by typing
+
+   \SQRT{7.25}{\tempa}
+   \DIVIDE{\numberPI}{7}{\tempb}
+   \COS{\tempb}{\tempc}
+   \MULTIPLY{\tempa}{\tempa}{\sol}
+
+   Then, the value 2.42589 is stored in \sol.
+
+d) Vectors and matrices:
+
+   \SCALARPRODUCT(1,2)(2,1){\sol}  ---> \sol equals 4
+
+   \MATRIXPRODUCT(1,1;-1,2)(0,-1;1,1)(\sola,\solb;\solc,\sold)
+        ---> \sola, \solb, \solc, \sold equals 1, 0, 2, 3.
+
+
+2.2. The calculus package
+-------------------------
+
+This package adds to the calculator package several utilities to use and define 
+real functions and their derivatives, including elementary functions, 
+operations with functions, vector-valuated functions polar coordinates.
+When you call a "function", this function ant its derivative are evaluated simultaneously.
+
+Examples:
+
+a) Predefined functions:
+
+   \SINfunction{\numberPI}{\sol}{\Dsol} ---> 
+                     \sol equals to 0 (=sin(pi)), and \Dsol equals -1 (=cos(pi)), 
+                     because cos(t) is the derivative of sin(t).
+
+b) Defining new functions: You can define the function f(t)=exp(2t)cos(t)-t 
+with the following code:
+
+   \SCALEVARIABLEfunction{2}{\EXPfunction}{\functionA}  % A=e^(2t)
+   \MULTIPLY{\functionA}{\COSfunction}{\functionB}      % b=e^(2t)cos(t)
+   \SUBTRACTfunction{\functionB}{\IDENTITYfunction}{\functionF} % My function
+
+Then, \functionF{num}{\sol}{\Dsol} stores f(num) and f'(num) in \sol and \Dsol. 
+
+
+3. Installation and documentation
+---------------------------------
+
+By compiling the source file "calculator.dtx" in the following sequence 
+
+>> pdflatex calculator.dtx
+>> makeindex -s gind.ist -o calculator.ind calculator.idx
+>> makeindex -s gglo.ist -o calculator.gls calculator.glo
+>> pdflatex calculator.dtx
+
+several files will be generated:
+
+ "calculator.sty" and "calculus.sty" (the packages). 
+     Move these two files where LaTeX  search for (typically, in a local texmf tree, 
+     at tex/latex/calculator) and refresh the file database.
+
+ "calculator.pdf" (the user manual)
+
+In addition, many small files, named "calculatorNN.tex" are generated.
+These files contain the source code of all examples included in the manual.
+You can store or discard this files.
+
+---------------------------------------------------
+Robert Fuster
+rfuster@mat.upv.es
+
+Universitat Polit\`ecnica de Val\`encia, 2012/05/19
+---------------------------------------------------
+
+
+
+
+
+   
+
+
+
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator.pdf b/Master/texmf-dist/doc/latex/calculator/calculator.pdf
new file mode 100644
index 00000000000..51d5fdc7f21
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator.pdf
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator1.tex b/Master/texmf-dist/doc/latex/calculator/calculator1.tex
new file mode 100644
index 00000000000..384de7ddb83
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator1.tex
@@ -0,0 +1,16 @@
+%  \tempA=2,5^2
+  \SQUARE{2.5}{\tempA}
+%  \tempB=sqrt(12)
+  \SQUAREROOT{12}{\tempB}
+% \tempC=exp(3,4)
+  \EXP{3.4}{\tempC}
+%  \divisio=\tempA/tempB
+  \DIVIDE{\tempA}{\tempB}{\divisio}
+% \sol=\divisio+\tempC
+  \ADD{\divisio}{\tempC}{\sol}
+\begin{align*}
+\frac{2.5^2}{\sqrt{12}}+\mathrm{e}^{3.4}
+      &= \frac{\tempA}{\tempB}+\tempC \\
+      &= \divisio+\tempC \\
+      &=\sol
+\end{align*}
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator10.tex b/Master/texmf-dist/doc/latex/calculator/calculator10.tex
new file mode 100644
index 00000000000..9f94dd02ada
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator10.tex
@@ -0,0 +1,2 @@
+\LENGTHDIVIDE{1in}{1cm}{\sol}
+One inch equals $\sol$ centimeters.
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator11.tex b/Master/texmf-dist/doc/latex/calculator/calculator11.tex
new file mode 100644
index 00000000000..6864af9ad58
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator11.tex
@@ -0,0 +1,2 @@
+\SQUARE{-1.256}{\sol}
+$(-1.256)^2=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator12.tex b/Master/texmf-dist/doc/latex/calculator/calculator12.tex
new file mode 100644
index 00000000000..2092630e261
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator12.tex
@@ -0,0 +1,2 @@
+\CUBE{-1.256}{\sol}
+$(-1.256)^3=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator13.tex b/Master/texmf-dist/doc/latex/calculator/calculator13.tex
new file mode 100644
index 00000000000..b66337da47e
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator13.tex
@@ -0,0 +1,12 @@
+\POWER{-1.256}{-5}{\sola}
+\POWER{-1.256}{5}{\solb}
+\POWER{-1.256}{0}{\solc}
+\[
+\begin{aligned}
+(-1.256)^{-5}&=\sola
+\\
+(-1.256)^{5}&=\solb
+\\
+(-1.256)^{0}&=\solc
+\end{aligned}
+\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator14.tex b/Master/texmf-dist/doc/latex/calculator/calculator14.tex
new file mode 100644
index 00000000000..cc98a935aec
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator14.tex
@@ -0,0 +1,2 @@
+\ABSVALUE{-1.256}{\sol}
+$\left\vert-1.256\right\vert=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator15.tex b/Master/texmf-dist/doc/latex/calculator/calculator15.tex
new file mode 100644
index 00000000000..45ebda7c91f
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator15.tex
@@ -0,0 +1,4 @@
+\INTEGERPART{1.256}{\sola}
+\INTEGERPART{-1.256}{\solb}
+The integer part of  $1.256$ is $\sola$,
+but the integer part of $-1.256$ is $\solb$.
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator16.tex b/Master/texmf-dist/doc/latex/calculator/calculator16.tex
new file mode 100644
index 00000000000..56fad96daba
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator16.tex
@@ -0,0 +1,2 @@
+\FLOOR{1.256}{\sol}
+The integer part of $1.256$ is $\sol$.
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator17.tex b/Master/texmf-dist/doc/latex/calculator/calculator17.tex
new file mode 100644
index 00000000000..01050f4b105
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator17.tex
@@ -0,0 +1,5 @@
+\FRACTIONALPART{1.256}{\sol}
+\sol
+
+\FRACTIONALPART{-1.256}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator18.tex b/Master/texmf-dist/doc/latex/calculator/calculator18.tex
new file mode 100644
index 00000000000..5b003431148
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator18.tex
@@ -0,0 +1,8 @@
+\TRUNCATE[0]{1.25688}{\sol}
+\sol
+
+\TRUNCATE[2]{1.25688}{\sol}
+\sol
+
+\TRUNCATE[4]{1.25688}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator19.tex b/Master/texmf-dist/doc/latex/calculator/calculator19.tex
new file mode 100644
index 00000000000..d6d05c21da2
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator19.tex
@@ -0,0 +1,8 @@
+\ROUND[0]{1.25688}{\sol}
+\sol
+
+\ROUND[2]{1.25688}{\sol}
+\sol
+
+\ROUND[4]{1.25688}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator2.tex b/Master/texmf-dist/doc/latex/calculator/calculator2.tex
new file mode 100644
index 00000000000..6136ee24cdf
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator2.tex
@@ -0,0 +1,14 @@
+\SQUARE{5}\sol
+The \texttt{\textbackslash sol}
+command contains the square of $5$:
+\[5^2=\sol\]
+\begin{center}
+\SQUAREROOT{5}\sol
+Now, the \texttt{\textbackslash sol}
+command is the square root of $5$:
+\[\sqrt{5}=\sol\]
+\end{center}
+On having gone out of the \texttt{center}
+environment,
+the command recovers its previous value:
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator20.tex b/Master/texmf-dist/doc/latex/calculator/calculator20.tex
new file mode 100644
index 00000000000..c3edaec1594
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator20.tex
@@ -0,0 +1,14 @@
+\INTEGERDIVISION{435}{27}{\sola}{\solb}
+$435=27\times\sola+\solb$
+
+\INTEGERDIVISION{27}{435}{\sola}{\solb}
+$27=435\times\sola+\solb$
+
+\INTEGERDIVISION{-435}{27}{\sola}{\solb}
+$-435=27\times(\sola)+\solb$
+
+\INTEGERDIVISION{435}{-27}{\sola}{\solb}
+$435=-27\times(\sola)+\solb$
+
+\INTEGERDIVISION{-435}{-27}{\sola}{\solb}
+$-435=-27\times\sola+\solb$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator21.tex b/Master/texmf-dist/doc/latex/calculator/calculator21.tex
new file mode 100644
index 00000000000..015b06455a3
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator21.tex
@@ -0,0 +1,8 @@
+\INTEGERQUOTIENT{435}{27}{\sol}
+\sol
+
+\INTEGERQUOTIENT{27}{435}{\sol}
+\sol
+
+\INTEGERQUOTIENT{-43.5}{2.7}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator22.tex b/Master/texmf-dist/doc/latex/calculator/calculator22.tex
new file mode 100644
index 00000000000..cbbc842b31c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator22.tex
@@ -0,0 +1,8 @@
+\MODULO{435}{27}{\sol}
+\[
+435 \equiv \sol \pmod{27}
+\]
+\MODULO{-435}{27}{\sol}
+\[
+-435 \equiv \sol \pmod{27}
+\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator23.tex b/Master/texmf-dist/doc/latex/calculator/calculator23.tex
new file mode 100644
index 00000000000..b2175182b9d
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator23.tex
@@ -0,0 +1,2 @@
+\GCD{435}{27}{\sol}
+$\gcd(435,27)=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator24.tex b/Master/texmf-dist/doc/latex/calculator/calculator24.tex
new file mode 100644
index 00000000000..685027f4f98
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator24.tex
@@ -0,0 +1,3 @@
+\newcommand{\lcm}{\operatorname{lcm}}
+\LCM{435}{27}{\sol}
+$\lcm(435,27)=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator25.tex b/Master/texmf-dist/doc/latex/calculator/calculator25.tex
new file mode 100644
index 00000000000..ed5a5bb26f1
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator25.tex
@@ -0,0 +1,2 @@
+\FRACTIONSIMPLIFY{435}{27}{\sola}{\solb}
+$435/27=\sola/\solb$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator26.tex b/Master/texmf-dist/doc/latex/calculator/calculator26.tex
new file mode 100644
index 00000000000..6df41c19e8a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator26.tex
@@ -0,0 +1,2 @@
+\SQUAREROOT{1.44}{\sol}
+$\sqrt{1.44}=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator27.tex b/Master/texmf-dist/doc/latex/calculator/calculator27.tex
new file mode 100644
index 00000000000..41fd8b4ed82
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator27.tex
@@ -0,0 +1,2 @@
+\EXP{0.5}{\sol}
+$\exp(0.5)=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator28.tex b/Master/texmf-dist/doc/latex/calculator/calculator28.tex
new file mode 100644
index 00000000000..0a8af280fa0
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator28.tex
@@ -0,0 +1,6 @@
+\EXP[10]{1.3}{\sol}
+$10^{1.3}=\sol$
+
+\EXP[2]{0.33333}{\sol}
+$2^{1/3}=\sol$
+
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator29.tex b/Master/texmf-dist/doc/latex/calculator/calculator29.tex
new file mode 100644
index 00000000000..82bf398f848
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator29.tex
@@ -0,0 +1,2 @@
+\LOG{0.5}{\sol}
+$\log 0.5=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator3.tex b/Master/texmf-dist/doc/latex/calculator/calculator3.tex
new file mode 100644
index 00000000000..11f7296ffe2
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator3.tex
@@ -0,0 +1,2 @@
+\COPY{-1.256}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator30.tex b/Master/texmf-dist/doc/latex/calculator/calculator30.tex
new file mode 100644
index 00000000000..ed2bf1e00c5
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator30.tex
@@ -0,0 +1,2 @@
+\LOG[10]{0.5}{\sol}
+$\log_{10} 0.5=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator31.tex b/Master/texmf-dist/doc/latex/calculator/calculator31.tex
new file mode 100644
index 00000000000..e41832e74ce
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator31.tex
@@ -0,0 +1,11 @@
+\SIN{\numberTHIRDPI}{\sol}
+$\sin \pi/3=\sol$
+
+\COS{\numberTHIRDPI}{\sol}
+$\cos \pi/3=\sol$
+
+\TAN{\numberTHIRDPI}{\sol}
+$\tan \pi/3=\sol$
+
+\COT{\numberTHIRDPI}{\sol}
+$\cot \pi/3=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator32.tex b/Master/texmf-dist/doc/latex/calculator/calculator32.tex
new file mode 100644
index 00000000000..cc5a388a759
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator32.tex
@@ -0,0 +1,11 @@
+\DEGREESSIN{60}{\sol}
+$\sin 60^{\textrm o}=\sol$
+
+\DEGREESCOS{60}{\sol}
+$\cos 60^{\textrm o}=\sol$
+
+\DEGREESTAN{60}{\sol}
+$\tan 60^{\textrm o}=\sol$
+
+\DEGREESCOT{60}{\sol}
+$\cot 60^{\textrm o}=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator33.tex b/Master/texmf-dist/doc/latex/calculator/calculator33.tex
new file mode 100644
index 00000000000..9956ce25951
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator33.tex
@@ -0,0 +1,11 @@
+\DEGREESCOS[400]{50}{\sol}
+\sol
+
+\DEGREESCOS{45}{\sol}
+\sol
+
+\COS{\numberQUARTERPI}{\sol}
+\sol
+
+\DEGREESCOS[8]{1}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator34.tex b/Master/texmf-dist/doc/latex/calculator/calculator34.tex
new file mode 100644
index 00000000000..dc73dd1a40d
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator34.tex
@@ -0,0 +1,2 @@
+\DEGtoRAD{60}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator35.tex b/Master/texmf-dist/doc/latex/calculator/calculator35.tex
new file mode 100644
index 00000000000..3125997f51a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator35.tex
@@ -0,0 +1,7 @@
+\MULTIPLY{\numberTWOPI}{10}{\TWENTYPI}
+\ADD{\numberPI}{\TWENTYPI}{\TWENTYONEPI}
+\REDUCERADIANSANGLE{\TWENTYONEPI}{\sol}
+\sol
+
+\REDUCEDEGREESANGLE{3690}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator36.tex b/Master/texmf-dist/doc/latex/calculator/calculator36.tex
new file mode 100644
index 00000000000..cdd27aa2427
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator36.tex
@@ -0,0 +1,11 @@
+\SINH{1.256}{\sol}
+\sol
+
+\COSH{1.256}{\sol}
+\sol
+
+\TANH{1.256}{\sol}
+\sol
+
+\COTH{1.256}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator37.tex b/Master/texmf-dist/doc/latex/calculator/calculator37.tex
new file mode 100644
index 00000000000..848ea112443
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator37.tex
@@ -0,0 +1,5 @@
+\VECTORCOPY(1,-1)(\sola,\solb)
+$(\sola,\solb)$
+
+\VECTORCOPY(1,-1,2)(\sola,\solb,\solc)
+$(\sola,\solb,\solc)$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator38.tex b/Master/texmf-dist/doc/latex/calculator/calculator38.tex
new file mode 100644
index 00000000000..e7d761a1306
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator38.tex
@@ -0,0 +1,5 @@
+\VECTORADD(1,-1,2)(3,5,-1)(\sola,\solb,\solc)
+$(1,-1,2)+(3,5,-1)=(\sola,\solb,\solc)$
+
+\VECTORSUB(1,-1,2)(3,5,-1)(\sola,\solb,\solc)
+$(1,-1,2)-(3,5,-1)=(\sola,\solb,\solc)$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator39.tex b/Master/texmf-dist/doc/latex/calculator/calculator39.tex
new file mode 100644
index 00000000000..9af0c8329a1
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator39.tex
@@ -0,0 +1,6 @@
+\SCALARVECTORPRODUCT{2}(3,5)(\sola,\solb)
+$2(3,5)=(\sola,\solb)$
+
+\SCALARVECTORPRODUCT{2}(3,5,-1)(%
+                       \sola,\solb,\solc)
+$2(3,5,-1)=(\sola,\solb,\solc)$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator4.tex b/Master/texmf-dist/doc/latex/calculator/calculator4.tex
new file mode 100644
index 00000000000..123ab06a45a
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator4.tex
@@ -0,0 +1,2 @@
+\MAX{1.256}{3.214}{\sol}
+\[\max(1.256,3.214)=\sol\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator40.tex b/Master/texmf-dist/doc/latex/calculator/calculator40.tex
new file mode 100644
index 00000000000..4ab16f69418
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator40.tex
@@ -0,0 +1,11 @@
+\SCALARPRODUCT(1,-1)(3,5){\sol}
+$(1,-1)\cdot(3,5)=\sol$
+
+\SCALARPRODUCT(1,-1,2)(3,5,-1){\sol}
+$(1,-1,2)\cdot(3,5,-1)=\sol$
+
+\VECTORNORM(3,4)\sol
+$\left\|(3,4)\right\|=\sol$
+
+\VECTORNORM(1,2,-2)\sol
+$\left\|(1,2,-2)\right\|=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator41.tex b/Master/texmf-dist/doc/latex/calculator/calculator41.tex
new file mode 100644
index 00000000000..045880987a1
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator41.tex
@@ -0,0 +1,5 @@
+\UNITVECTOR(3,4)(\sola,\solb)
+$(\sola,\solb)$
+
+\UNITVECTOR(1,2,-2)(\sola,\solb,\solc)
+$(\sola,\solb,\solc)$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator42.tex b/Master/texmf-dist/doc/latex/calculator/calculator42.tex
new file mode 100644
index 00000000000..c4df209d4ad
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator42.tex
@@ -0,0 +1,5 @@
+\VECTORABSVALUE(3,-4)(\sola,\solb)
+$(\sola,\solb)$
+
+\VECTORABSVALUE(3,-4,-1)(\sola,\solb,\solc)
+$(\sola,\solb,\solc)$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator43.tex b/Master/texmf-dist/doc/latex/calculator/calculator43.tex
new file mode 100644
index 00000000000..a0dd9f85cc5
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator43.tex
@@ -0,0 +1,11 @@
+\MATRIXCOPY(1, -1, 2;
+            3,  0, 5;
+           -1,  1, 4)%
+          (\sola,\solb,\solc;
+           \sold,\sole,\solf;
+           \solg,\solh,\soli)
+$\begin{bmatrix}
+       \sola & \solb & \solc \\
+       \sold & \sole & \solf \\
+       \solg & \solh & \soli
+     \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator44.tex b/Master/texmf-dist/doc/latex/calculator/calculator44.tex
new file mode 100644
index 00000000000..5ee6b5cfa5d
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator44.tex
@@ -0,0 +1,7 @@
+\TRANSPOSEMATRIX(1,-1;3,0)%
+          (\sola,\solb;\solc,\sold)
+$\begin{bmatrix}
+       1 & -1 \\ 3 & 0
+     \end{bmatrix}^T=\begin{bmatrix}
+       \sola & \solb \\ \solc & \sold
+     \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator45.tex b/Master/texmf-dist/doc/latex/calculator/calculator45.tex
new file mode 100644
index 00000000000..c1ed8fc0ac3
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator45.tex
@@ -0,0 +1,21 @@
+\MATRIXADD(1,-1;3,0)(3,5;-3,2)%
+          (\sola,\solb;\solc,\sold)
+$\begin{bmatrix}
+       1 & -1 \\ 3 & 0
+     \end{bmatrix}+
+\begin{bmatrix}
+       3 & 5 \\ -3 & 2
+     \end{bmatrix}=\begin{bmatrix}
+       \sola & \solb \\ \solc & \sold
+     \end{bmatrix}$
+
+\MATRIXSUB(1,-1;3,0)(3,5;-3,2)%
+          (\sola,\solb;\solc,\sold)
+$\begin{bmatrix}
+       1 & -1 \\ 3 & 0
+     \end{bmatrix}-
+\begin{bmatrix}
+       3 & 5 \\ -3 & 2
+     \end{bmatrix}=\begin{bmatrix}
+       \sola & \solb \\ \solc & \sold
+     \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator46.tex b/Master/texmf-dist/doc/latex/calculator/calculator46.tex
new file mode 100644
index 00000000000..c5cf74d4753
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator46.tex
@@ -0,0 +1,14 @@
+\SCALARMATRIXPRODUCT{3}(1,-1,2;
+                        3, 0,5;
+                       -1, 1,4)%
+                      (\sola,\solb,\solc;
+                       \sold,\sole,\solf;
+                       \solg,\solh,\soli)
+$3\begin{bmatrix}
+     1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4
+ \end{bmatrix}
+  =\begin{bmatrix}
+       \sola & \solb & \solc \\
+       \sold & \sole & \solf \\
+       \solg & \solh & \soli
+   \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator47.tex b/Master/texmf-dist/doc/latex/calculator/calculator47.tex
new file mode 100644
index 00000000000..6abe4e7a0b6
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator47.tex
@@ -0,0 +1,11 @@
+\MATRIXVECTORPRODUCT(1,-1;
+                     0, 2)(3,5)(\sola,\solb)
+$\begin{bmatrix}
+     1 & -1 \\ 0 & 2
+ \end{bmatrix}
+ \begin{bmatrix}
+      3 \\ 5
+ \end{bmatrix}
+  =\begin{bmatrix}
+         \sola \\ \solb
+   \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator48.tex b/Master/texmf-dist/doc/latex/calculator/calculator48.tex
new file mode 100644
index 00000000000..c8e2cbeaba1
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator48.tex
@@ -0,0 +1,18 @@
+\MATRIXPRODUCT(1,-1,2;3,0,5;-1,1,4)%
+              (3,5,-1;-3,2,-5;1,-2,3)%
+                (\sola,\solb,\solc;
+                 \sold,\sole,\solf;
+                 \solg,\solh,\soli)
+\begin{multline*}
+\begin{bmatrix}
+       1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4
+     \end{bmatrix}
+\begin{bmatrix}
+       3 & 5 & -1 \\ -3 & 2 & -5 \\ 1 & -2 & 3
+     \end{bmatrix}\\
+=\begin{bmatrix}
+       \sola & \solb & \solc \\
+       \sold & \sole & \solf \\
+       \solg & \solh & \soli
+\end{bmatrix}
+\end{multline*}
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator49.tex b/Master/texmf-dist/doc/latex/calculator/calculator49.tex
new file mode 100644
index 00000000000..16c0b0a8c8b
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator49.tex
@@ -0,0 +1,5 @@
+\DETERMINANT(1,-1,2;3,0,5;-1,1,4){\sol}
+\SpecialUsageIndex{\DETERMINANT}%
+$\begin{vmatrix}
+       1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4
+     \end{vmatrix}=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator5.tex b/Master/texmf-dist/doc/latex/calculator/calculator5.tex
new file mode 100644
index 00000000000..0f410c70277
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator5.tex
@@ -0,0 +1,2 @@
+\MIN{1.256}{3.214}{\sol}
+\sol
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator50.tex b/Master/texmf-dist/doc/latex/calculator/calculator50.tex
new file mode 100644
index 00000000000..7ad03915b39
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator50.tex
@@ -0,0 +1,8 @@
+\INVERSEMATRIX(1,-1;3,5)(%
+            \sola,\solb;\solc,\sold)
+$\begin{bmatrix}
+       1 & -1 \\ 3 & 5
+ \end{bmatrix}^{-1}=
+ \begin{bmatrix}
+       \sola & \solb \\ \solc & \sold
+ \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator51.tex b/Master/texmf-dist/doc/latex/calculator/calculator51.tex
new file mode 100644
index 00000000000..bd69eaf743b
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator51.tex
@@ -0,0 +1,9 @@
+\MATRIXABSVALUE(1,-1,2;3,0,5;-1,1,4)%
+          (\sola,\solb,\solc;
+           \sold,\sole,\solf;
+           \solg,\solh,\soli)
+$\begin{bmatrix}
+       \sola & \solb & \solc \\
+       \sold & \sole & \solf \\
+       \solg & \solh & \soli
+ \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator52.tex b/Master/texmf-dist/doc/latex/calculator/calculator52.tex
new file mode 100644
index 00000000000..1ad53821cf8
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator52.tex
@@ -0,0 +1,15 @@
+\SOLVELINEARSYSTEM(1,-1,2;3,0,5;-1,1,4)%
+                  (-4,4,-2)%
+                  (\sola,\solb,\solc)
+Solving the linear system
+\[
+\begin{bmatrix}
+      1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4
+     \end{bmatrix}\mathsf{X}=\begin{bmatrix}
+      -4\\4\\-2
+     \end{bmatrix}
+\]
+we obtain
+$\mathsf{X}=\begin{bmatrix}
+       \sola \\ \solb\\ \solc
+     \end{bmatrix}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator53.tex b/Master/texmf-dist/doc/latex/calculator/calculator53.tex
new file mode 100644
index 00000000000..2696c2df99c
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator53.tex
@@ -0,0 +1,5 @@
+\SQUAREfunction{3}{\sol}{\Dsol}
+If $f(t)=t^2$, then
+\[
+  f(3)=\sol \mbox{ and } f'(3)=\Dsol
+\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator54.tex b/Master/texmf-dist/doc/latex/calculator/calculator54.tex
new file mode 100644
index 00000000000..4a99aefa2ad
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator54.tex
@@ -0,0 +1,15 @@
+$\begin{array}{cll}
+x & \log x & \log' x \\
+\LOGfunction{1}{\logx}{\Dlogx}
+1 &\logx & \Dlogx\\
+\LOGfunction{2}{\logx}{\Dlogx}
+2 &\logx & \Dlogx\\
+\LOGfunction{3}{\logx}{\Dlogx}
+3 &\logx & \Dlogx\\
+\LOGfunction{4}{\logx}{\Dlogx}
+4 &\logx & \Dlogx\\
+\LOGfunction{5}{\logx}{\Dlogx}
+5 &\logx & \Dlogx\\
+\LOGfunction{6}{\logx}{\Dlogx}
+6 &\logx & \Dlogx
+\end{array}$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator55.tex b/Master/texmf-dist/doc/latex/calculator/calculator55.tex
new file mode 100644
index 00000000000..4a0ab779c75
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator55.tex
@@ -0,0 +1,30 @@
+% exp(-t)
+   \SCALEVARIABLEfunction
+       {-1}{\EXPfunction}
+       {\NEGEXPfunction}
+
+% exp(-t)cos(t)
+   \PRODUCTfunction
+       {\NEGEXPfunction}
+       {\COSfunction}
+       {\NEGEXPCOSfunction}
+
+% 3t^2-2exp(-t)cos(t)
+   \LINEARCOMBINATIONfunction
+       {3}{\SQUAREfunction}
+      {-2}{\NEGEXPCOSfunction}
+      {\myfunction}
+
+\myfunction{5}{\sol}{\Dsol}
+
+If
+\[
+    f(t)=3t^2-2\mathrm{e}^{-t}\cos t
+\]
+then
+\[
+\begin{gathered}
+    f(5)=\sol\\
+    f'(5)=\Dsol
+\end{gathered}
+\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator56.tex b/Master/texmf-dist/doc/latex/calculator/calculator56.tex
new file mode 100644
index 00000000000..f5c10e29574
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator56.tex
@@ -0,0 +1,4 @@
+% \mypoly=1-x^2+x^3
+    \newcpoly{\mypoly}{1}{0}{-1}{1}
+    \mypoly{2}{\sol}{\Dsol}
+$p'(2)=\Dsol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator57.tex b/Master/texmf-dist/doc/latex/calculator/calculator57.tex
new file mode 100644
index 00000000000..9caca3c8c7b
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator57.tex
@@ -0,0 +1,9 @@
+For the $f(t)=(t^2,t^3)$ function we have
+\VECTORfunction
+    {\SQUAREfunction}{\CUBEfunction}{\F}
+
+\F{4}{\solx}{\Dsolx}{\soly}{\Dsoly}
+
+\[
+f(4)=(\solx,\soly), f'(4)=(\Dsolx,\Dsoly)
+\]
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator6.tex b/Master/texmf-dist/doc/latex/calculator/calculator6.tex
new file mode 100644
index 00000000000..663c9a1bff9
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator6.tex
@@ -0,0 +1,2 @@
+\ADD{1.256}{3.214}{\sol}
+$1.256+3.214=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator7.tex b/Master/texmf-dist/doc/latex/calculator/calculator7.tex
new file mode 100644
index 00000000000..6f0d9c2fea7
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator7.tex
@@ -0,0 +1,2 @@
+\SUBTRACT{1.256}{3.214}{\sol}
+$1.256-3.214=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator8.tex b/Master/texmf-dist/doc/latex/calculator/calculator8.tex
new file mode 100644
index 00000000000..de60a332745
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator8.tex
@@ -0,0 +1,2 @@
+\MULTIPLY{1.256}{3.214}{\sol}
+$1.256\times3.214=\sol$
diff --git a/Master/texmf-dist/doc/latex/calculator/calculator9.tex b/Master/texmf-dist/doc/latex/calculator/calculator9.tex
new file mode 100644
index 00000000000..f3c94758d93
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/calculator/calculator9.tex
@@ -0,0 +1,2 @@
+\DIVIDE{1.256}{3.214}{\sol}
+$1.256/3.214=\sol$
diff --git a/Master/texmf-dist/source/latex/calculator/calculator.dtx b/Master/texmf-dist/source/latex/calculator/calculator.dtx
new file mode 100644
index 00000000000..543ed6d3564
--- /dev/null
+++ b/Master/texmf-dist/source/latex/calculator/calculator.dtx
@@ -0,0 +1,4576 @@
+% \iffalse meta-comment
+%<*internal>
+\begingroup
+\input docstrip.tex
+\keepsilent
+\preamble
+------------------------------------------------------------------
+The calculator and calculus packages 
+Copyright (C) 2012 by Robert Fuster <rfuster@mat.upv.es>
+All rights reserved 
+
+This file may be distributed and/or modified under the
+conditions of the LaTeX Project Public License, either version 1.3
+of this license or (at your option) any later version.
+The latest version of this license is in:
+
+    http://www.latex-project.org/lppl.txt
+
+and version 1.3 or later is part of all distributions of LaTeX 
+version 1999/12/01 or later.
+------------------------------------------------------------------
+\endpreamble
+\postamble
+\endpostamble
+\askforoverwritefalse
+
+\generateFile{calculator.sty}{t}{\from{calculator.dtx}{calculator}}
+\generateFile{calculus.sty}{t}{\from{calculator.dtx}{calculus}}
+
+\def\tmpa{plain}
+\ifx\tmpa\fmtname\endgroup\expandafter\bye\fi
+\endgroup
+%</internal>
+%
+% Copyright (C) 2012 by Robert Fuster <rfuster@mat.upv.es>
+% 
+% This file may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.2
+% of this license or (at your option) any later version.
+% The latest version of this license is in:
+%
+%    http://www.latex-project.org/lppl.txt
+%
+% and version 1.2 or later is part of all distributions of LaTeX 
+% version 1999/12/01 or later.
+%
+% \fi
+% \CheckSum{3135}
+% \changes{v1.0}{2012/04/25}{First public version}
+% \changes{v1.0a}{2012/06/10}{calculator.dtx modified to make it autoinstallable.
+%                             calculus.dtx embedded in calculus.dtx}
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\ProvidesFile{calculator.dtx}
+   [2012/06/10 v.1.0a documented calculator package]
+\GetFileInfo{calculator.dtx}
+\usepackage{amsmath}
+\usepackage[lmargin=1.75in,rmargin=1in]{geometry}
+\usepackage{fancyvrb}
+\def\fileversion{1.0a}
+\def\filedate{2012/06/10}
+\usepackage{calculus}
+\title{The \textsf{calculator} and \textsf{calculus} packages%
+      \thanks{This document corresponds to 
+      \textsf{calculator} and \textsf{calculus}~\fileversion, 
+      dated \filedate.}\\
+        Scientific calculations with \LaTeX}
+\author{Robert Fuster\\
+         Universitat Polit\`ecnica de Val\`encia \\
+         \texttt{rfuster@mat.upv.es}}
+\date{\filedate}
+\EnableCrossrefs         
+\CodelineIndex
+\RecordChanges
+
+\newcommand{\TBS}{\textbackslash}
+\newcommand{\Marg}[1]{\textnormal{\marg{#1}}}
+
+\newcounter{exem}\stepcounter{exem}
+\newenvironment{exemple}{%
+\VerbatimEnvironment\begin{VerbatimOut}[gobble=2]{./calculator\theexem.tex}}{%
+\end{VerbatimOut}
+\par\medskip\noindent
+\begin{minipage}{\linewidth}
+\begin{minipage}[t]{0.45\linewidth}
+\setlength{\parindent}{2ex}
+\noindent\textsf{\fbox{Ex. \theexem}}
+\bigskip\par
+\catcode`\%=14
+\input{./calculator\theexem}
+\end{minipage}\hfill
+\begin{minipage}[t]{0.45\linewidth}
+\small
+\VerbatimInput{./calculator\theexem.tex}
+\end{minipage}
+\end{minipage}
+\stepcounter{exem}\par\bigskip\noindent}
+
+\newcommand{\textttit}[1]{\texttt{\textit{#1}}}
+
+\begin{document}
+\maketitle
+  \DocInput{calculator.dtx}
+  \PrintChanges
+  \PrintIndex
+\end{document}
+%</driver>
+%
+% \fi
+%
+
+% \DoNotIndex{\newcommand,\newenvironment,\RequirePackage,\begin,\end}
+% \DoNotIndex{\begingroup,\endgroup,\expandafter,\undefined,\@ifnextchar}
+% \DoNotIndex{\def,\let,\edef,\xdef,\ifx,\ifdim,\ifnum,\else,\fi,\fi,\fi}
+% \DoNotIndex{\@whilenum,\advance,\divide,\do,\newdimen,\number}
+% \DoNotIndex{\noexpand,\ignorespaces,\p@,\z@,\strip@pt}
+% \DoNotIndex{\MessageBreak}
+% 
+% \begin{abstract}
+% The \textsf{calculator} package allows us to use \LaTeX{} as a calculator,
+% with which we can perform many of the common scientific calculations
+% (with the limitation in accuracy imposed by the \TeX{} arithmetic). 
+% 
+% This package introduces several new instructions that allow you to do
+% several calculations with integer and decimal numbers using \LaTeX.
+% Apart from add, multiply or divide, we can calculate powers, square roots,
+% logarithms, trigonometric and hyperbolic functions \ldots
+
+% In addition, the \textsf{calculator} package supports some elementary calculations with
+% vectors 
+% in two and three dimensions and square $2\times2$ and $3\times3$ matrices. 
+% \smallskip
+
+% The
+% \textsf{calculus} package adds to the \textsf{calculator} package
+% several utilities to use and define various functions and their derivatives,
+% including elementary functions, operations with functions, 
+% polar coordinates and vector-valued real functions.
+% \end{abstract}
+% 
+% \tableofcontents
+% 
+% \section{Introduction}
+% The \textsf{calculator} package defines some instructions which allow
+% us to realize algebraic operations 
+% (and to evaluate elementary functions) in our documents.
+% The operations implemented by the \textsf{calculator} package
+% include routines of assignment of variables, 
+% arithmetical calculations with real and integer numbers,
+% two and three dimensional vector and matrix arithmetics 
+% and the computation of square roots, 
+% trigonometrical, exponential, logarithmic and hyperbolic functions. 
+% In addition, some important numbers, such as $\sqrt2$, $\pi$ or $\mathrm e$,
+% are predefined.
+% 
+% The name of all these commands is spelled in capital letters
+% (with very few exceptions: % the commands \cs{DEGtoRAD} and \cs{RADtoDEG}
+% and the control sequences that define special numbers, as 
+% \cs{numberPI})
+% and, in general, they all need one or more mandatory arguments, 
+% the first one(s) of which is(are) number(s) and the last one(s) is(are)
+% the name(s) of the command(s) where 
+% the results will be stored.\footnote{%
+% Logically, the control sequences that represent special numbers
+% (as \cs{numberPI}) does not need any argument.}
+% The new commands defined in this way work in any \LaTeX{} mode.  
+% 
+% 
+% By example, this instruction 
+% \begin{verbatim}
+%    \MAX{3}{5}{\solution}
+% \end{verbatim}
+% stores |5| in the command \cs{solution}. In a similar way, 
+% \begin{verbatim}
+%    \FRACTIONSIMPLIFY{10}{12}{\numerator}{\denominator}
+% \end{verbatim}
+% defines \cs{numerator} and \cs{denominator} as |5| i |6|, respectively.
+% 
+% The \emph{data} arguments should not be necessarily explicit numbers; 
+% it may also consist in commands the value of which is a number.
+% This allows us to chain several calculations, since in the following
+% example:
+% \begin{exemple}
+% %  \tempA=2,5^2
+%   \SQUARE{2.5}{\tempA}
+% %  \tempB=sqrt(12)
+%   \SQUAREROOT{12}{\tempB}
+% % \tempC=exp(3,4)
+%   \EXP{3.4}{\tempC}
+% %  \divisio=\tempA/tempB
+%   \DIVIDE{\tempA}{\tempB}{\divisio}
+% % \sol=\divisio+\tempC
+%   \ADD{\divisio}{\tempC}{\sol}
+% \begin{align*}
+% \frac{2.5^2}{\sqrt{12}}+\mathrm{e}^{3.4}
+%       &= \frac{\tempA}{\tempB}+\tempC \\
+%       &= \divisio+\tempC \\
+%       &=\sol
+% \end{align*}
+% \end{exemple}
+% Observe that, in this example, we have followed exactly the same steps 
+% that we would do to calculate
+% $\frac{2.5^2}{\sqrt{12}}+\mathrm{e}^{3.4}$ with a standard calculator: 
+% We would calculate the square, the root and the exponential and, 
+% finally, we would divide and add the results.
+% 
+% It does not matter if the arguments \emph{results} are or not predefined. 
+% But these commands act as declarations, so that its scope is local 
+% in environments and groups.
+% \begin{exemple}
+% \SQUARE{5}\sol
+% The \texttt{\textbackslash sol} 
+% command contains the square of $5$: 
+% \[5^2=\sol\]
+% \begin{center}
+% \SQUAREROOT{5}\sol
+% Now, the \texttt{\textbackslash sol}
+% command is the square root of $5$:
+% \[\sqrt{5}=\sol\]
+% \end{center}
+% On having gone out of the \texttt{center} 
+% environment, 
+% the command recovers its previous value:
+% \sol
+% \end{exemple}
+% 
+% The \textsf{calculus} package 
+% goes a step further and allows us to define and use in a user-friendly 
+% manner various functions and their derivatives.
+%  
+% For exemple, using the
+% \textsf{calculus} package, you can define the $f(t)=t^2e^t-\cos 2t$ function
+% as follows:
+% \begin{Verbatim}
+%    \PRODUCTfunction{\SQUAREfunction}{\EXPfunction}{\tempfunctionA}
+%    \SCALEVARIABLEfunction{2}{\COSfunction}{\tempfunctionB}
+%    \SUBTRACTfunction{\tempfunctionA}{\tempfunctionB}{\Ffunction}
+% \end{Verbatim}
+% 
+% Then you cau compute any value of the new function |\Ffunction|
+% and its derivative: typing
+% \begin{quote}
+%    |\Ffunction|\marg{num}\marg{\cs{sol}}\marg{\cs{Dsol}}
+% \end{quote} 
+% the values of $f(\textit{num})$ and $f'(\textit{num})$ will be stored in
+% \textttit{\cs{sol}} and \textttit{\cs{Dsol}}.
+%
+% \part{The \textsf{calculator} package}
+% \section{Predefined numbers}
+% The \textsf{calculator} package predefines the following numbers:
+% \SpecialUsageIndex{\numberPI}
+% \SpecialUsageIndex{\numberHALFPI}
+% \SpecialUsageIndex{\numberTHREEHALFPI}
+% \SpecialUsageIndex{\numberTHIRDPI}
+% \SpecialUsageIndex{\numberQUARTERPI}
+% \SpecialUsageIndex{\numberFIFTHPI}
+% \SpecialUsageIndex{\numberSIXTHPI}
+% \SpecialUsageIndex{\numberTWOPI}
+% \SpecialUsageIndex{\numberE} 
+% \SpecialUsageIndex{\numberINVE}
+% \SpecialUsageIndex{\numberETWO}
+% \SpecialUsageIndex{\numberINVETWO}
+% \SpecialUsageIndex{\numberLOGTEN}
+% \SpecialUsageIndex{\numberGOLD}
+% \SpecialUsageIndex{\numberINVGOLD} 
+% \SpecialUsageIndex{\numberSQRTTWO} 
+% \SpecialUsageIndex{\numberSQRTTHREE}
+% \SpecialUsageIndex{\numberSQRTFIVE}
+% \SpecialUsageIndex{\numberCOSXXX}
+% \SpecialUsageIndex{\numberCOSXLV} 
+% \begin{center}
+% \begin{tabular}{llll}
+% \ttfamily \cs{numberPI} & $\numberPI\approx\pi$ &
+% \ttfamily \cs{numberHALFPI} & $\numberHALFPI\approx\pi/2$ \\
+% \ttfamily \cs{numberTHREEHALFPI} & $\numberTHREEHALFPI\approx3\pi/2$ &
+% \ttfamily \cs{numberTHIRDPI} & $\numberTHIRDPI\approx\pi/3$ \\
+% \ttfamily \cs{numberQUARTERPI} & $\numberQUARTERPI\approx\pi/4$ &
+% \ttfamily \cs{numberFIFTHPI} & $\numberFIFTHPI\approx\pi/5$ \\
+% \ttfamily \cs{numberSIXTHPI} & $\numberSIXTHPI\approx\pi/6$ &
+% \ttfamily \cs{numberTWOPI} & $\numberTWOPI\approx2\pi$ \\
+% \hline
+% \ttfamily \cs{numberE} & $\numberE\approx\mathrm e$ &
+% \ttfamily \cs{numberINVE} & $\numberINVE\approx1/\mathrm e$ \\
+% \ttfamily \cs{numberETWO} & $\numberETWO\approx\mathrm e^2$ &
+% \ttfamily \cs{numberINVETWO} & $\numberINVETWO\approx1/\mathrm e^2$ \\
+% \hline
+% \ttfamily \cs{numberLOGTEN} & $\numberLOGTEN\approx\log 10$
+%  \\
+% \hline
+% \ttfamily \cs{numberGOLD} & $\numberGOLD\approx\phi$ &
+% \ttfamily \cs{numberINVGOLD} & $\numberINVGOLD\approx1/\phi$ \\
+% \hline
+% \ttfamily \cs{numberSQRTTWO} & $\numberSQRTTWO\approx\sqrt2$ &
+% \ttfamily \cs{numberSQRTTHREE} & $\numberSQRTTHREE\approx\sqrt3$ \\
+% \ttfamily \cs{numberSQRTFIVE} & $\numberSQRTFIVE\approx\sqrt5$  \\
+% \hline
+% \ttfamily \cs{numberCOSXXX} & $\numberCOSXXX\approx\cos{\pi/6}$ &
+% \ttfamily \cs{numberCOSXLV} & $\numberCOSXLV\approx\cos{\pi/4}$ 
+% \end{tabular}
+% \end{center}
+% \section{Operations with numbers}
+% \subsection{Assignments and comparisons}
+% The first command we describe here is used to store a number
+% in a control sequence.
+% The other two commands in this section determine the maximum and minimum
+% of a pair of numbers.
+% \begin{description}
+% \item[\cs{COPY}\marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\COPY}% 
+% stores the number \textttit{num} to the command \textttit{\TBS cmd}.
+% \begin{exemple}
+% \COPY{-1.256}{\sol}
+% \sol
+% \end{exemple}
+% \item[\cs{MAX}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\MAX}%
+% stores in \textttit{\TBS cmd} the maximum of the numbers \textttit{num1}
+% and \textttit{num2}.
+% \begin{exemple}
+% \MAX{1.256}{3.214}{\sol} 
+% \[\max(1.256,3.214)=\sol\]
+% \end{exemple}
+% \item[\cs{MIN}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\MIN}%
+% stores in \textttit{\TBS cmd} the minimum of \textttit{num1} and
+% \textttit{num2}.
+% \begin{exemple}
+% \MIN{1.256}{3.214}{\sol}
+% \sol
+% \end{exemple}
+% \end{description}
+% \subsection{Real arithmetic}
+% \subsubsection{The four basic operations}
+% The following commands calculate the four arithmetical basic operations.
+% \begin{description}
+% \item[\cs{ADD}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\ADD}%
+% Sum of numbers \textttit{num1} and \textttit{num2}.
+% \begin{exemple}
+% \ADD{1.256}{3.214}{\sol}
+% $1.256+3.214=\sol$
+% \end{exemple}
+% 
+% \item[\cs{SUBTRACT}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\SUBTRACT}% 
+% Difference \textttit{num1}-\textttit{num2}.
+% \begin{exemple}
+% \SUBTRACT{1.256}{3.214}{\sol}
+% $1.256-3.214=\sol$
+% \end{exemple}
+% 
+% \item[\cs{MULTIPLY}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\MULTIPLY}%
+% Product \textttit{num1}$\times$\textttit{num2}.
+% \begin{exemple}
+% \MULTIPLY{1.256}{3.214}{\sol}
+% $1.256\times3.214=\sol$
+% \end{exemple}
+% 
+% \item[\cs{DIVIDE}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\DIVIDE}%
+% Quotient 
+% \textttit{num1}/\textttit{num2}.\footnote{This command uses a modified 
+% version of the division algorithm of Claudio Beccari.}
+% \begin{exemple}
+% \DIVIDE{1.256}{3.214}{\sol}
+% $1.256/3.214=\sol$
+% \end{exemple}
+% 
+% In addition, the \cs{LENGTHDIVIDE} command divides two lengths
+% and returns a number.
+% \item[\cs{LENGTHDIVIDE}\marg{length1}\marg{length2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\LENGTHDIVIDE}\mbox{}
+% \begin{exemple}
+% \LENGTHDIVIDE{1in}{1cm}{\sol}
+% One inch equals $\sol$ centimeters.
+% \end{exemple}
+% \end{description}
+% \subsubsection{Powers with integer exponent}
+% \begin{description}
+% \item[\cs{SQUARE}\marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\SQUARE}%
+% Square of the  number \textttit{num}.
+% \begin{exemple}
+% \SQUARE{-1.256}{\sol}
+% $(-1.256)^2=\sol$
+% \end{exemple}
+% \item[\cs{CUBE}\marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\CUBE}%
+% Cube of \textttit{num}.
+% \begin{exemple}
+% \CUBE{-1.256}{\sol}
+% $(-1.256)^3=\sol$
+% \end{exemple}
+% \item[\cs{POWER}\marg{num}\marg{exp}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\POWER}% 
+% The \textttit{exp} power of \textttit{num}. 
+% 
+% The exponent, \textttit{exp}, must be an integer
+% (if you want to calculate powers
+% with non integer exponents, use the \cs{EXP} command).
+% \begin{exemple}
+% \POWER{-1.256}{-5}{\sola} 
+% \POWER{-1.256}{5}{\solb}
+% \POWER{-1.256}{0}{\solc}
+% \[
+% \begin{aligned}
+% (-1.256)^{-5}&=\sola
+% \\
+% (-1.256)^{5}&=\solb
+% \\
+% (-1.256)^{0}&=\solc
+% \end{aligned}
+% \]
+% \end{exemple}
+% \end{description}
+% 
+% \subsubsection{Absolute value, integer part and fractional part}
+% \begin{description}
+% \item[\cs{ABSVALUE}\marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\ABSVALUE}% 
+% Absolute value of  \textttit{num}.
+% \begin{exemple}
+% \ABSVALUE{-1.256}{\sol}
+% $\left\vert-1.256\right\vert=\sol$
+% \end{exemple}
+% \item[\cs{INTEGERPART}\marg{num}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\INTEGERPART}%
+% Integer part of  \textttit{num}.\footnote{The integer part of $x$
+% is the largest integer that is less than or equal to $x$.}
+% \begin{exemple}
+% \INTEGERPART{1.256}{\sola}
+% \INTEGERPART{-1.256}{\solb}
+% The integer part of  $1.256$ is $\sola$,
+% but the integer part of $-1.256$ is $\solb$.
+% \end{exemple}
+% \item[\cs{FLOOR}]\SpecialUsageIndex{\FLOOR}%
+% is an alias of \cs{INTEGERPART}. 
+% \begin{exemple}
+% \FLOOR{1.256}{\sol}
+% The integer part of $1.256$ is $\sol$.
+% \end{exemple}
+% \item[\cs{FRACTIONALPART}\marg{num}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\FRACTIONALPART}% 
+% Fractional part of \textttit{num}.
+% \begin{exemple}
+% \FRACTIONALPART{1.256}{\sol}
+% \sol
+% 
+% \FRACTIONALPART{-1.256}{\sol}
+% \sol
+% \end{exemple}
+% \end{description}
+% \subsubsection{Truncation and rounding}
+% \begin{description}
+% \item[\cs{TRUNCATE}\oarg{n}\marg{num}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\TRUNCATE}% 
+% truncates the number \textttit{num} to \textttit{n} decimal places.
+% \item[\cs{ROUND}{[\textttit{n}]}\marg{num}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\ROUND}%
+% rounds the number \textttit{num} to \textttit{n} decimal places.
+%
+% The optional argument \textttit{n} may be \texttt{0}, \texttt{1},
+% \texttt{2}, \texttt{3} or \texttt{4} (the default is \texttt{2}).\footnote{% 
+% Note than \cs{TRUNCATE[0]} is equivalent to \cs{INTEGERPART}
+% only for non-negative numbers.}
+% \begin{exemple}
+% \TRUNCATE[0]{1.25688}{\sol}
+% \sol
+% 
+% \TRUNCATE[2]{1.25688}{\sol}
+% \sol
+%
+% \TRUNCATE[4]{1.25688}{\sol}
+% \sol
+% \end{exemple}
+% \begin{exemple}
+% \ROUND[0]{1.25688}{\sol}
+% \sol
+%
+% \ROUND[2]{1.25688}{\sol}
+% \sol
+%
+% \ROUND[4]{1.25688}{\sol}
+% \sol
+% \end{exemple}
+% \end{description}
+% 
+% \subsection{Integers}
+% The operations described here are subject 
+% to the same restrictions as those referring to decimal numbers. 
+% In particular, although \TeX{} does not have this restriction
+% in its integer arithmetic, 
+% the largest integer that can be used is 16383.
+% \subsubsection{Integer division, quotient and remainder}
+% \begin{description}
+% \item
+% [\cs{INTEGERDIVISION}\marg{num1}\marg{num2}\marg{\cs{cmd1}}\marg{\cs{cmd2}}]
+% \SpecialUsageIndex{\INTEGERDIVISION}%
+% stores in the \textttit{\TBS cmd1} and 
+%  \textttit{\TBS cmd2} commands the quotient and the remainder of the
+%  integer division of the two integers 
+% \textttit{num1} and \textttit{num2}. 
+% The remainder is a non-negative number smaller than the divisor.\footnote{% 
+% The scientific computing systems (such as Matlab. Scilab or Mathematica) 
+% do not always return a non-negative residue
+% ---especially when the divisor is negative---. 
+% However, the most reasonable definition of integer quotient is this one:
+% \emph{the quotient of the division $D/d$ is the largest number $q$
+% for which $dq \leq D$}. 
+% With this definition, the remainder $r=D-qd$ is a non-negative number.}
+% \begin{exemple}
+% \INTEGERDIVISION{435}{27}{\sola}{\solb}
+% $435=27\times\sola+\solb$
+% 
+% \INTEGERDIVISION{27}{435}{\sola}{\solb}
+% $27=435\times\sola+\solb$
+% 
+% \INTEGERDIVISION{-435}{27}{\sola}{\solb}
+% $-435=27\times(\sola)+\solb$
+% 
+% \INTEGERDIVISION{435}{-27}{\sola}{\solb}
+% $435=-27\times(\sola)+\solb$
+% 
+% \INTEGERDIVISION{-435}{-27}{\sola}{\solb}
+% $-435=-27\times\sola+\solb$
+% \end{exemple}
+% \item[\cs{INTEGERQUOTIENT}\marg{num1}\marg{num2}\marg{\cs{cmd}}]
+% \SpecialUsageIndex{\INTEGERQUOTIENT}%
+% Integer part of the quotient of 
+% \textttit{num1} and \textttit{num2}. These two numbers are not necessarily
+% integers.
+% \begin{exemple}
+% \INTEGERQUOTIENT{435}{27}{\sol}
+% \sol
+% 
+% \INTEGERQUOTIENT{27}{435}{\sol}
+% \sol
+% 
+% \INTEGERQUOTIENT{-43.5}{2.7}{\sol}
+% \sol
+% \end{exemple}
+% \item[\cs{MODULO}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\MODULO}%
+% Remainder of the integer division of 
+% \textttit{num1} and \textttit{num2}.
+% \begin{exemple}
+% \MODULO{435}{27}{\sol}
+% \[
+% 435 \equiv \sol \pmod{27}
+% \]
+% \MODULO{-435}{27}{\sol}
+% \[
+% -435 \equiv \sol \pmod{27}
+% \]
+% \end{exemple}
+% \end{description}
+% \subsubsection{Greatest common divisor and least common multiple}
+% \begin{description}
+% \item
+% [\cs{GCD}\marg{num1}\marg{num2}\marg{\cs{cmd}}]\SpecialUsageIndex{\GCD}%
+% Greatest common divisor of the integers
+% \textttit{num1} and \textttit{num2}.
+% \begin{exemple}
+% \GCD{435}{27}{\sol}
+% $\gcd(435,27)=\sol$
+% \end{exemple}
+% \item[\cs{LCM}\marg{num1}\marg{num2}\marg{\cs{cmd}}]%
+% \SpecialUsageIndex{\LCM}%
+% Least common multiple of \textttit{num1} and \textttit{num2}.
+% \begin{exemple}
+% \newcommand{\lcm}{\operatorname{lcm}}
+% \LCM{435}{27}{\sol}
+% $\lcm(435,27)=\sol$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Simplifying fractions}
+% \begin{description}
+% \item[\cs{FRACTIONSIMPLIFY}\marg{num1}\marg{num2}\marg{\cs{cmd1}}% 
+%          \marg{\cs{cmd2}}]\SpecialUsageIndex{\FRACTIONSIMPLIFY}%
+% stores in the \TBS\textttit{cmd1} and \textttit{\TBS cmd2} commands
+% the numerator and denominator of the irreducible fraction equivalent to
+% \textttit{num1}/\textttit{num2}.
+% \begin{exemple}
+% \FRACTIONSIMPLIFY{435}{27}{\sola}{\solb}
+% $435/27=\sola/\solb$
+% \end{exemple}
+% \end{description}
+% \subsection{Elementary functions}
+% \subsubsection{Square roots}
+% \begin{description}
+% \item[\cs{SQUAREROOT}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\SQUAREROOT}%
+% Square root of the number \textttit{num}.
+% \begin{exemple}
+% \SQUAREROOT{1.44}{\sol}
+% $\sqrt{1.44}=\sol$
+% \end{exemple}
+% If the argument \textttit{num} is negative, the package returns
+% a warning message.
+% \end{description}
+% Instead of \cs{SQUAREROOT}, you can use the alias \cs{SQRT}.%
+% \SpecialUsageIndex{\SQRT}
+% 
+% \subsubsection{Exponential and logarithm}
+% The \cs{EXP} and \cs{LOG} commands compute, by default, 
+% exponentials and logarithms of the natural base $\mathrm{e}$. 
+% They admit, however, an optional argument to choose another base.
+% \begin{description}
+% \item[\cs{EXP}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\EXP}% 
+% Exponential of the number \textttit{num}.
+% \begin{exemple}
+% \EXP{0.5}{\sol}
+% $\exp(0.5)=\sol$
+% \end{exemple}
+% The argument \textttit{num} must be in the interval $[-9.704,9.704]$.%
+% \footnote{$9.704$ is the logarithm of $16383$, 
+% the largest number that supports the \TeX's arithmetic.}
+% 
+% Moreover, the \cs{EXP} command accepts an optional argument, 
+% to compute expressions such as $a^x$: 
+% \item[\cs{EXP}% 
+% \oarg{num1}\marg{num2}\marg{\cs{cmd}}]\SpecialUsageIndex{\EXP}% 
+% Exponential with base \textttit{num1} of \textttit{num2}.
+% \textttit{num1} must be a positive number.
+% \begin{exemple}
+% \EXP[10]{1.3}{\sol}
+% $10^{1.3}=\sol$
+% 
+% \EXP[2]{0.33333}{\sol}
+% $2^{1/3}=\sol$
+% 
+% \end{exemple}
+% \item[\cs{LOG}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\LOG}%
+% logarithm of the number \textttit{num}.
+% \begin{exemple}
+% \LOG{0.5}{\sol}
+% $\log 0.5=\sol$
+% \end{exemple}
+% \item[\cs{LOG}% 
+% \oarg{num1}\marg{num2}\marg{\cs{cmd}}]\SpecialUsageIndex{\LOG}% 
+% Logarithm in base \textttit{num1} of \textttit{num2}.
+% \begin{exemple}
+% \LOG[10]{0.5}{\sol}
+% $\log_{10} 0.5=\sol$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Trigonometric functions}
+% The arguments, in functions \cs{SIN}, \cs{COS}, \ldots,
+% are measured in radians. 
+% If you measure angles in degrees (sexagesimal or not), use the
+%  \cs{DEGREESSIN}, \cs{DEGREESCOS}, \dots\ commands. 
+% \begin{description}
+% \item[\cs{SIN}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\SIN}%
+% Sine of \textttit{num}.
+% 
+% \item[\cs{COS}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\COS}% 
+% Cosine of \textttit{num}.
+% 
+% \item[\cs{TAN}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\TAN}% 
+% Tangent of \textttit{num}.
+% 
+% \item[\cs{COT}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\COT}% 
+% Cotangent of \textttit{num}.
+% \begin{exemple}
+% \SIN{\numberTHIRDPI}{\sol}
+% $\sin \pi/3=\sol$
+% 
+% \COS{\numberTHIRDPI}{\sol}
+% $\cos \pi/3=\sol$
+% 
+% \TAN{\numberTHIRDPI}{\sol}
+% $\tan \pi/3=\sol$
+% 
+% \COT{\numberTHIRDPI}{\sol}
+% $\cot \pi/3=\sol$
+% \end{exemple}
+% 
+% \item[\cs{DEGREESSIN}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\DEGREESSIN}% 
+% Sine of \textttit{num} sexagesimal degrees.
+% 
+% \item[\cs{DEGREESCOS}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\DEGREESCOS}%
+% Cosine of \textttit{num} sexagesimal degrees.
+% 
+% \item[\cs{DEGREESTAN}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\DEGREESTAN}% 
+% Tangent of \textttit{num}  sexagesimal degrees.
+% 
+% \item[\cs{DEGREESCOT}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\DEGREESCOT}%
+% Cotangent of  \textttit{num}  sexagesimal degrees.
+% 
+% \begin{exemple}
+% \DEGREESSIN{60}{\sol}
+% $\sin 60^{\textrm o}=\sol$
+% 
+% \DEGREESCOS{60}{\sol}
+% $\cos 60^{\textrm o}=\sol$
+% 
+% \DEGREESTAN{60}{\sol}
+% $\tan 60^{\textrm o}=\sol$
+% 
+% \DEGREESCOT{60}{\sol}
+% $\cot 60^{\textrm o}=\sol$
+% \end{exemple}
+% \end{description}
+% 
+% The latter commands support an optional argument 
+% that allows us to divide the circle
+% in an arbitrary number of \emph{degrees} (not necessarily $360$).
+% \begin{description}
+% \item[\cs{DEGREESSIN}% 
+% \oarg{degrees}\marg{num}\marg{\cs{cmd}}] \mbox{}
+% \item[\cs{DEGREESCOS}% 
+% \oarg{degrees}\marg{num}\marg{\cs{cmd}}] \mbox{}
+% \item[\cs{DEGREESTAN}% 
+% \oarg{degrees}\marg{num}\marg{\cs{cmd}}] \mbox{}
+% \item[\cs{DEGREESCOT}% 
+% \oarg{degrees}\marg{num}\marg{\cs{cmd}}] \mbox{}
+% \end{description}
+% 
+% By example, |\DEGREESCOS[400]{50}| computes the cosine of 50 gradians
+% (a right angle has $100$ gradians, the whole circle has 400 gradians),
+% which are equivalent to 45 (sexagesimal) degrees or 
+% $\pi/4$ radians. Or to 1 \emph{degree},
+% if we divide the circle into 8 parts!
+% \begin{exemple}
+% \DEGREESCOS[400]{50}{\sol}
+% \sol
+% 
+% \DEGREESCOS{45}{\sol}
+% \sol
+% 
+% \COS{\numberQUARTERPI}{\sol}
+% \sol
+% 
+% \DEGREESCOS[8]{1}{\sol}
+% \sol
+% \end{exemple}
+% 
+% Moreover, we have a couple od commands  
+% to convert between radians and degrees,
+% \begin{description}
+% \item[\cs{DEGtoRAD}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\DEGtoRAD}% 
+% Equivalence in radians
+% of  \textttit{num} sexagesimal degrees.
+% \item[\cs{RADtoDEG}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\RADtoDEG}%
+% Equivalence in sexagesimal degrees
+% of \textttit{num} radians.
+% \begin{exemple}
+% \DEGtoRAD{60}{\sol}
+% \sol
+% \end{exemple}
+% \end{description}
+% and two other commands to reduce arguments to basic intervals:
+% \begin{description}
+% \item[\cs{REDUCERADIANSANGLE}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\REDUCERADIANSANGLE}%
+% Reduces the arc \textttit{num} to the interval $]-\pi,\pi]$.
+% 
+% \item[\cs{REDUCEDEGREESANGLE}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\REDUCEDEGREESANGLE}%
+% Reduces the angle \textttit{num} to the interval $]-180,180]$.
+% \begin{exemple}
+% \MULTIPLY{\numberTWOPI}{10}{\TWENTYPI}
+% \ADD{\numberPI}{\TWENTYPI}{\TWENTYONEPI}
+% \REDUCERADIANSANGLE{\TWENTYONEPI}{\sol}
+% \sol
+% 
+% \REDUCEDEGREESANGLE{3690}{\sol}
+% \sol
+% \end{exemple}
+% 
+% 
+% \end{description}
+% 
+% \subsubsection{Hyperbolic functions}
+% \begin{description}
+% \item[\cs{SINH}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\SINH}%
+% stores in \textttit{\TBS cmd} 
+% the hyperbolic sine of \textttit{num}.
+% 
+% \item[\cs{COSH}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\COSH}% 
+% Hyperbolic cosine of  \textttit{num}.
+% 
+% \item[\cs{TANH}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\TANH}% 
+% Hyperbolic tangent of \textttit{num}.
+% 
+% \item[\cs{COTH}% 
+% \marg{num}\marg{\cs{cmd}}]\SpecialUsageIndex{\COTH}% 
+% Hyperbolic cotangent of \textttit{num}.
+% 
+% \begin{exemple}
+% \SINH{1.256}{\sol}
+% \sol
+% 
+% \COSH{1.256}{\sol}
+% \sol
+% 
+% \TANH{1.256}{\sol}
+% \sol
+% 
+% \COTH{1.256}{\sol}
+% \sol
+% \end{exemple}
+% \end{description}
+% \section{Matrix arithmetic}
+% The \textsf{calculator} package defines the commands described below 
+% to operate on vectors and matrices.
+% We only work with two or three-dimensional vectors and 
+% $2\times2$ and $3\times3$ matrices. 
+% Vectors are represented in the form
+% |(a1,a2)| or |(a1,a2,a3);|\footnote{But they are \emph{column} vectors.} 
+% and, in the case of matrices, columns are separated \emph{\`a la matlab}
+% by semicolons: |(a11,a12;a21,a22)|
+% or |(a11,a12,a13;a21,a22,a23;a31,a32,a33)|.
+% \subsection{Vector operations}
+% \subsubsection{Assignments}
+% \begin{description}
+% \item[\cs{VECTORCOPY}\parg{x,y}\parg{\TBS cmd1,\TBS cmd2}]%
+% \SpecialUsageIndex{\VECTORCOPY}%
+% copy the entries of vector \parg{x,y} to the
+% \textttit{\TBS cmd1} and \textttit{\TBS cmd2} commands.
+% \item[\cs{VECTORCOPY}\parg{x,y,z}\parg{\TBS cmd1,\TBS cmd2,\TBS cmd3}]
+% copy the entries of vector (\textttit{x},\textttit{y},\textttit{z}) to the
+%  \textttit{\TBS cmd1}, \textttit{\TBS cmd2} and
+% \textttit{\TBS cmd3} commands.
+% \begin{exemple}
+% \VECTORCOPY(1,-1)(\sola,\solb)
+% $(\sola,\solb)$
+% 
+% \VECTORCOPY(1,-1,2)(\sola,\solb,\solc)
+% $(\sola,\solb,\solc)$
+% \end{exemple}
+% \end{description}
+% 
+% \subsubsection{Vector addition and subtraction}
+% \begin{description}
+% \item[\cs{VECTORADD}\parg{x1,y1}\parg{x2,y2}\parg{\TBS cmd1,\TBS cmd2}]
+% \SpecialUsageIndex{\VECTORADD}
+% 
+% \item[\cs{VECTORADD}\parg{x1,y1,z1}\parg{x2,y2,z2}%
+% \parg{\TBS cmd1,\TBS cmd2,\TBS cmd3}]
+% \SpecialUsageIndex{\VECTORADD}
+% 
+% \item[\cs{VECTORSUB}\parg{x1,y1}\parg{x2,y2}\parg{\TBS cmd1,\TBS cmd2}]
+% \SpecialUsageIndex{\VECTORSUB}
+% 
+% \item[\cs{VECTORSUB}\parg{x1,y1,z1}\parg{x2,y2,z2}%
+% \parg{\TBS cmd1,\TBS cmd2,\TBS cmd3}]\mbox{}
+% \SpecialUsageIndex{\VECTORSUB}
+% 
+% \begin{exemple}
+% \VECTORADD(1,-1,2)(3,5,-1)(\sola,\solb,\solc)
+% $(1,-1,2)+(3,5,-1)=(\sola,\solb,\solc)$
+% 
+% \VECTORSUB(1,-1,2)(3,5,-1)(\sola,\solb,\solc)
+% $(1,-1,2)-(3,5,-1)=(\sola,\solb,\solc)$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Scalar-vector product}
+% \begin{description}
+% \item[\cs{SCALARVECTORPRODUCT}\marg{num}\parg{x,y}%
+% \parg{\cs{cmd1},\cs{cmd2}}]\mbox{}
+% \SpecialUsageIndex{\SCALARVECTORPRODUCT}
+% 
+% \item[\cs{SCALARVECTORPRODUCT}\marg{num}\parg{x,y,z}%
+% \parg{\cs{cmd1},\cs{cmd2},\cs{cmd3}}]\mbox{}
+% \SpecialUsageIndex{\SCALARVECTORPRODUCT}
+% \begin{exemple}
+% \SCALARVECTORPRODUCT{2}(3,5)(\sola,\solb)
+% $2(3,5)=(\sola,\solb)$
+% 
+% \SCALARVECTORPRODUCT{2}(3,5,-1)(%
+%                        \sola,\solb,\solc)
+% $2(3,5,-1)=(\sola,\solb,\solc)$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Scalar product and euclidean norm}
+% \begin{description}
+% \item[\cs{SCALARPRODUCT}\parg{x1,y1}\parg{x2,y2}\marg{\cs{cmd}}]
+% \SpecialUsageIndex{\SCALARPRODUCT}%
+% 
+% \item[\cs{SCALARPRODUCT}\parg{x1,y1,z1}\parg{x2,y2,z2}\marg{\cs{cmd}}]
+% \SpecialUsageIndex{\SCALARPRODUCT}%
+% 
+% \item[\cs{VECTORNORM}\parg{x,y}\marg{\cs{cmd}}]\mbox{}
+% \SpecialUsageIndex{\VECTORNORM}%
+% 
+% \item[\cs{VECTORNORM}\parg{x,y,z}\marg{\cs{cmd}}]\mbox{}
+% \SpecialUsageIndex{\VECTORNORM}%
+% \begin{exemple}
+% \SCALARPRODUCT(1,-1)(3,5){\sol}
+% $(1,-1)\cdot(3,5)=\sol$
+% 
+% \SCALARPRODUCT(1,-1,2)(3,5,-1){\sol}
+% $(1,-1,2)\cdot(3,5,-1)=\sol$
+% 
+% \VECTORNORM(3,4)\sol
+% $\left\|(3,4)\right\|=\sol$
+% 
+% \VECTORNORM(1,2,-2)\sol
+% $\left\|(1,2,-2)\right\|=\sol$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Unit vector parallel to a given vector (normalized vector)}
+% \begin{description}
+% \item[\cs{UNITVECTOR}\parg{x,y}\parg{\TBS cmd1,\TBS cmd2}]
+% \SpecialUsageIndex{\UNITVECTOR}%
+% 
+% \item[\cs{UNITVECTOR}\parg{x,y,z}\parg{\TBS cmd1,\TBS cmd2,\TBS cmd3}]
+% \mbox{}\SpecialUsageIndex{\UNITVECTOR}
+% \begin{exemple}
+% \UNITVECTOR(3,4)(\sola,\solb)
+% $(\sola,\solb)$
+% 
+% \UNITVECTOR(1,2,-2)(\sola,\solb,\solc)
+% $(\sola,\solb,\solc)$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Absolute value (in each entry of a given vector)}
+% \begin{description}
+% \item[\cs{VECTORABSVALUE}\parg{x,y}\parg{\TBS cmd1,\TBS cmd2}]
+% \SpecialUsageIndex{\VECTORABSVALUE}%
+% 
+% \item[\cs{VECTORABSVALUE}\parg{x,y,z}\parg{\TBS cmd1,\TBS cmd2,\TBS cmd3}]
+% \mbox{} \SpecialUsageIndex{\VECTORABSVALUE}
+% \begin{exemple}
+% \VECTORABSVALUE(3,-4)(\sola,\solb)
+% $(\sola,\solb)$
+% 
+% \VECTORABSVALUE(3,-4,-1)(\sola,\solb,\solc)
+% $(\sola,\solb,\solc)$
+% \end{exemple}
+% \end{description}
+% \subsection{Matrix operations}
+% \subsubsection{Assignments}
+% \begin{description}
+% \item[\cs{MATRIXCOPY}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\MATRIXCOPY}%
+% 
+% \noindent
+% Use this command to store the matrix $\begin{bmatrix}
+% a11 & a12 \\ a21 & 22
+% \end{bmatrix}$ in \textttit{\TBS cmm11}, \textttit{\TBS cmm12}, 
+% \textttit{\TBS cmm21}, \textttit{\TBS cmm22}.
+% The analogous $3\times3$ version is
+% \item[\cs{MATRIXCOPY}% 
+% \parg{a11,a12,a13; \textup{[\dots]} ,a33}% 
+% \parg{\cs{cmd11},\cs{cmd12},\cs{cmd13};% 
+%     \textup{[\dots]} ,\cs{cmd33}}]\mbox{}
+% \SpecialUsageIndex{\MATRIXCOPY}%
+% \begin{exemple}
+% \MATRIXCOPY(1, -1, 2;
+%             3,  0, 5;
+%            -1,  1, 4)% 
+%           (\sola,\solb,\solc;
+%            \sold,\sole,\solf;
+%            \solg,\solh,\soli)
+% $\begin{bmatrix}
+%        \sola & \solb & \solc \\ 
+%        \sold & \sole & \solf \\
+%        \solg & \solh & \soli
+%      \end{bmatrix}$
+% \end{exemple}
+% \end{description}
+% 
+% 
+% Henceforth, we will present only the syntax for commands 
+% operating with $2\times2$ matrices. 
+% In all cases, the syntax is similar if we work with $3\times3$ matrices.
+% In the examples, we will work with either $2\times2$ or $3\times3$ matrices.
+% \subsubsection{Transposed matrix}
+% \begin{description}
+% \item[\cs{TRANSPOSEMATRIX}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\TRANSPOSEMATRIX}%
+% \begin{exemple}
+% \TRANSPOSEMATRIX(1,-1;3,0)% 
+%           (\sola,\solb;\solc,\sold)
+% $\begin{bmatrix}
+%        1 & -1 \\ 3 & 0
+%      \end{bmatrix}^T=\begin{bmatrix}
+%        \sola & \solb \\ \solc & \sold
+%      \end{bmatrix}$
+% \end{exemple}
+% \end{description}
+% 
+% 
+% \subsubsection{Matrix addition and subtraction}
+% \begin{description}
+% \item[\cs{MATRIXADD}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{b11,b12;b21,b22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]
+% \SpecialUsageIndex{\MATRIXADD}%
+% 
+% \item[\cs{MATRIXSUB}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{b11,b12;b21,b22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\MATRIXSUB}%
+% 
+% \begin{exemple}
+% \MATRIXADD(1,-1;3,0)(3,5;-3,2)% 
+%           (\sola,\solb;\solc,\sold)
+% $\begin{bmatrix}
+%        1 & -1 \\ 3 & 0
+%      \end{bmatrix}+
+% \begin{bmatrix}
+%        3 & 5 \\ -3 & 2
+%      \end{bmatrix}=\begin{bmatrix}
+%        \sola & \solb \\ \solc & \sold
+%      \end{bmatrix}$
+% 
+% \MATRIXSUB(1,-1;3,0)(3,5;-3,2)% 
+%           (\sola,\solb;\solc,\sold)
+% $\begin{bmatrix}
+%        1 & -1 \\ 3 & 0
+%      \end{bmatrix}-
+% \begin{bmatrix}
+%        3 & 5 \\ -3 & 2
+%      \end{bmatrix}=\begin{bmatrix}
+%        \sola & \solb \\ \solc & \sold
+%      \end{bmatrix}$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Scalar-matrix product}
+% \begin{description}
+% \item[\cs{SCALARMATRIXPRODUCT}\marg{num}% 
+% \parg{a11,a12;a21,a22}% 
+%              \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\SCALARMATRIXPRODUCT}%
+% 
+% \begin{exemple}
+% \SCALARMATRIXPRODUCT{3}(1,-1,2;
+%                         3, 0,5;
+%                        -1, 1,4)% 
+%                       (\sola,\solb,\solc;
+%                        \sold,\sole,\solf;
+%                        \solg,\solh,\soli)
+% $3\begin{bmatrix}
+%      1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4 
+%  \end{bmatrix}  
+%   =\begin{bmatrix}
+%        \sola & \solb & \solc \\ 
+%        \sold & \sole & \solf \\
+%        \solg & \solh & \soli
+%    \end{bmatrix}$  
+% \end{exemple}
+% \end{description}
+% \subsubsection{Matriu-vector product}
+% \begin{description}
+% \item[\cs{MATRIXVECTORPRODUCT}% 
+% \parg{a11,a12;a21,a22}\parg{x,y}% 
+% \parg{\cs{cmd1},\cs{cmd2}}]\mbox{}
+% \SpecialUsageIndex{\MATRIXVECTORPRODUCT}%
+% \begin{exemple}
+% \MATRIXVECTORPRODUCT(1,-1;
+%                      0, 2)(3,5)(\sola,\solb)
+% $\begin{bmatrix}
+%      1 & -1 \\ 0 & 2
+%  \end{bmatrix}
+%  \begin{bmatrix}
+%       3 \\ 5
+%  \end{bmatrix}  
+%   =\begin{bmatrix}
+%          \sola \\ \solb
+%    \end{bmatrix}$ 
+% \end{exemple}
+% \end{description}
+% \subsubsection{Product of two square matrices}
+% \begin{description}
+% \item[\cs{MATRIXPRODUCT}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{b11,b12;b21,b22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]
+% \mbox{}
+% \SpecialUsageIndex{\MATRIXPRODUCT}%
+% \begin{exemple}
+% \MATRIXPRODUCT(1,-1,2;3,0,5;-1,1,4)% 
+%               (3,5,-1;-3,2,-5;1,-2,3)% 
+%                 (\sola,\solb,\solc;
+%                  \sold,\sole,\solf;
+%                  \solg,\solh,\soli)
+% \begin{multline*}
+% \begin{bmatrix}
+%        1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4 
+%      \end{bmatrix}
+% \begin{bmatrix}
+%        3 & 5 & -1 \\ -3 & 2 & -5 \\ 1 & -2 & 3
+%      \end{bmatrix}\\
+% =\begin{bmatrix}
+%        \sola & \solb & \solc \\ 
+%        \sold & \sole & \solf \\
+%        \solg & \solh & \soli
+% \end{bmatrix}
+% \end{multline*}     
+% \end{exemple}
+% \end{description}
+% \subsubsection{Determinant}
+% \begin{description}
+% \item[\cs{DETERMINANT}% 
+% \parg{a11,a12;a21,a22}
+% \marg{\cs{cmd}}]\mbox{}
+% \begin{exemple}
+% \DETERMINANT(1,-1,2;3,0,5;-1,1,4){\sol}
+% \SpecialUsageIndex{\DETERMINANT}%
+% $\begin{vmatrix}
+%        1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4 
+%      \end{vmatrix}=\sol$
+% \end{exemple}
+% \end{description}
+% \subsubsection{Inverse matrix}
+% \begin{description}
+% \item[\cs{INVERSEMATRIX}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\INVERSEMATRIX}%
+% \begin{exemple}
+% \INVERSEMATRIX(1,-1;3,5)(%
+%             \sola,\solb;\solc,\sold)
+% $\begin{bmatrix}
+%        1 & -1 \\ 3 & 5
+%  \end{bmatrix}^{-1}=
+%  \begin{bmatrix}
+%        \sola & \solb \\ \solc & \sold
+%  \end{bmatrix}$
+% \end{exemple}
+% 
+% If the given matrix is singular, the \textsf{calculator} package returns
+% a warning message 
+% and the  \textttit{\cs{cmd11}}, \ldots, commands are marqued as undefined.
+% \end{description}
+% \subsubsection{Absolute value (in each entry)}
+% \begin{description}
+% \item[\cs{MATRIXABSVALUE}% 
+% \parg{a11,a12;a21,a22}% 
+% \parg{\cs{cmd11},\cs{cmd12};\cs{cmd21},\cs{cmd22}}]\mbox{}
+% \SpecialUsageIndex{\MATRIXABSVALUE}%
+% 
+% \begin{exemple}
+% \MATRIXABSVALUE(1,-1,2;3,0,5;-1,1,4)% 
+%           (\sola,\solb,\solc;
+%            \sold,\sole,\solf;
+%            \solg,\solh,\soli)
+% $\begin{bmatrix}
+%        \sola & \solb & \solc \\ 
+%        \sold & \sole & \solf \\
+%        \solg & \solh & \soli
+%  \end{bmatrix}$     
+% \end{exemple}
+% \end{description}
+% \subsubsection{Solving a linear system}
+% \begin{description}
+% \item[\cs{SOLVELINEARSYSTEM}% 
+% \parg{a11,a12;a21,a22}\parg{b1,b2}\parg{\cs{cmd1},\cs{cmd2}}]
+% \SpecialUsageIndex{\SOLVELINEARSYSTEM}%
+% solves the linear system 
+% $\begin{pmatrix}
+%  \textttit{a11}&\textttit{a12}\\
+%  \textttit{a21}&\textttit{a22}
+% \end{pmatrix}
+% \begin{pmatrix} 
+%  \textttit{x}\\
+%  \textttit{y}\end{pmatrix}
+% =\begin{pmatrix}
+%   \textttit{b1}\\
+%   \textttit{b2}
+% \end{pmatrix}$
+% and stores the solution in (\textttit{\cs{cmd1}},\textttit{\cs{cmd2}}).
+% \begin{exemple}
+% \SOLVELINEARSYSTEM(1,-1,2;3,0,5;-1,1,4)% 
+%                   (-4,4,-2)% 
+%                   (\sola,\solb,\solc)
+% Solving the linear system     
+% \[
+% \begin{bmatrix}
+%       1 & -1 & 2 \\ 3 & 0 & 5 \\ -1 & 1 & 4
+%      \end{bmatrix}\mathsf{X}=\begin{bmatrix}
+%       -4\\4\\-2
+%      \end{bmatrix}
+% \]     
+% we obtain 
+% $\mathsf{X}=\begin{bmatrix}
+%        \sola \\ \solb\\ \solc
+%      \end{bmatrix}$         
+% \end{exemple}
+% If the given matrix is singular, the package \textsf{calculator}
+% returns a warning message. 
+% When system is indeterminate, in the bi-dimensional case
+% one of the solutions is computed; 
+% if the system is incompatible,
+% then the  \verb+\sola+, \dots, commands are marqued as undefined. 
+% For three equations systems, only determinate systems are solved.\footnote{% 
+% This is the only command that does not behave the same way with 
+% $2\times2$ and $3\times3$ matrices.}
+% \end{description}
+% 
+% \part{The \textsf{calculus} package}
+% \section{What is a \emph{function}?}
+% From the point of view of this package, a \emph {function} $f$ is a pair of
+% formulae: the first one calculates $f(t)$; the other, $f'(t)$. 
+% Therefore, any function is applied using three arguments: 
+% the value of the variable $t$,
+% and two command names where $f(t)$ and $f'(t)$ will be stored. 
+% For example, 
+% \begin{quote}
+% \cs{SQUAREfunction}\Marg{num}\Marg{\TBS sol}\Marg{\TBS Dsol}
+% \end{quote}
+% computes $f(t)=t^2$ and $f'(t)=2t$ (where $t=$\textit{num}), 
+% and stores the results in the commands 
+% \textit{\TBS sol} and \textit{\TBS Dsol}.\footnote%
+% {Do not spect any control about the existence or differentiability
+%  of the function; if the function or the derivative
+% are not well defined, a \TeX{} error will occur.}
+%
+% \begin{exemple}
+% \SQUAREfunction{3}{\sol}{\Dsol}
+% If $f(t)=t^2$, then
+% \[
+%   f(3)=\sol \mbox{ and } f'(3)=\Dsol
+% \]
+% \end{exemple}
+% \medskip
+% 
+% \noindent
+% For all functions defined here, you must use the following syntax:
+% \begin{quote}
+% \textttit{\TBS functionname}\Marg{num}\Marg{\TBS cmd1}\Marg{\TBS cmd2}
+% \end{quote}
+% being \textit{num} a number (or a command whose value is a number), 
+% and \verb+\+\textit{cmd1} and \verb+\+\textit{cmd2} two control sequence 
+% names where the values of the function and its derivative (in this number) 
+% will be stored.
+% \medskip
+% 
+% The key difference between this \emph{functions} and the instructions
+% defined in the \textsf{calculator} package 
+% is the inclusion of the derivative; for example, the |\SQUARE{3}{\sol}|
+% instruction computes, only,
+% the square power of number $3$, while |\SQUAREfunction{3}{\sol}{\Dsol}|
+% finds, also, the corresponding derivative.
+% \section{Predefined functions}
+% The \textsf{calculus} package 
+% predefines the most commonly used elementary functions, 
+% and includes several utilities for defining new ones.
+% The predefined functions are the following:
+% \SpecialUsageIndex{\ZEROfunction}
+% \SpecialUsageIndex{ONEfunction}
+% \SpecialUsageIndex{IDENTITYfunction} 
+% \SpecialUsageIndex{RECIPROCALfunction} 
+% \SpecialUsageIndex{SQUAREfunction}
+% \SpecialUsageIndex{CUBEfunction} 
+% \SpecialUsageIndex{SQRTfunction} 
+% \SpecialUsageIndex{EXPfunction}  
+% \SpecialUsageIndex{LOGfunction} 
+% \SpecialUsageIndex{COSfunction}  
+% \SpecialUsageIndex{SINfunction}  
+% \SpecialUsageIndex{TANfunction} 
+% \SpecialUsageIndex{COTfunction}
+% \SpecialUsageIndex{COSHfunction}
+% \SpecialUsageIndex{SINHfunction} 
+% \SpecialUsageIndex{TANHfunction}  
+% \SpecialUsageIndex{COTHfunction} 
+% \SpecialUsageIndex{HEAVISIDEfunction}
+% \begin{center}
+% \begin{tabular}{llll}
+% \ttfamily \cs{ZEROfunction} & $f(t)=0$ & 
+% \ttfamily \cs{ONEfunction}  & $f(t)=1$    \\
+% \ttfamily \cs{IDENTITYfunction}  & $f(t)=t$ &
+% \ttfamily \cs{RECIPROCALfunction}  & $f(t)=1/t$ \\
+% \ttfamily \cs{SQUAREfunction}  & $f(t)=t^2$ &
+% \ttfamily \cs{CUBEfunction}  & $f(t)=t^3$ \\
+% \ttfamily \cs{SQRTfunction}  & $f(t)=\sqrt t$ \\
+% \ttfamily \cs{EXPfunction}  & $f(t)=\exp t$ &
+% \ttfamily \cs{LOGfunction} & $f(t)=\log t$ \\
+% \ttfamily \cs{COSfunction}  & $f(t)=\cos t$ &
+% \ttfamily \cs{SINfunction}  & $f(t)=\sin t$ \\
+% \ttfamily \cs{TANfunction}  & $f(t)=\tan t$ &
+% \ttfamily \cs{COTfunction}  & $f(t)=\cot t$ \\
+% \ttfamily \cs{COSHfunction}  & $f(t)=\cosh t$ &
+% \ttfamily \cs{SINHfunction}  & $f(t)=\sinh t$ \\
+% \ttfamily \cs{TANHfunction}  & $f(t)=\tanh t$ &
+% \ttfamily \cs{COTHfunction}  & $f(t)=\coth t$ \\
+% \ttfamily \cs{HEAVISIDEfunction} & $f(t)=\begin{cases}
+%                     0 & \text{si $t<0$} \\
+%                     1 & \text{si $t\geq0$}
+%                     \end{cases}$
+% \end{tabular}
+% \end{center}
+% 
+% In the following example, we use the |\LOGfunction| function to compute 
+% a table of the $\log$ function and its derivative.
+% \begin{exemple}
+% $\begin{array}{cll}
+% x & \log x & \log' x \\
+% \LOGfunction{1}{\logx}{\Dlogx}
+% 1 &\logx & \Dlogx\\
+% \LOGfunction{2}{\logx}{\Dlogx}
+% 2 &\logx & \Dlogx\\
+% \LOGfunction{3}{\logx}{\Dlogx}
+% 3 &\logx & \Dlogx\\
+% \LOGfunction{4}{\logx}{\Dlogx}
+% 4 &\logx & \Dlogx\\
+% \LOGfunction{5}{\logx}{\Dlogx}
+% 5 &\logx & \Dlogx\\
+% \LOGfunction{6}{\logx}{\Dlogx}
+% 6 &\logx & \Dlogx
+% \end{array}$
+% \end{exemple}
+% 
+% \section{Operations with functions}
+% We can define new functions using the following \emph{operations}
+% (the last argument is the name of the new function):
+% \begin{description}
+% \item[\cs{CONSTANTfunction}\Marg{num}\Marg{\TBS Function}]%
+% \SpecialUsageIndex{\CONSTANTfunction}
+% defines \textit{\TBS Function} as the constant function \textit{num}.
+% 
+%  Example. Definition of the $F(t)=5$ function:
+% 
+% |\CONSTANTfunction{5}{\F}|  
+% 
+% \item[\cs{SUMfunction}\Marg{\TBS function1}\Marg{\TBS function2}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\SUMfunction}
+% defines \textit{\TBS Function} as the sum of functions 
+% \textit{\TBS function1} and \textit{\TBS function2}.
+% 
+% Example. Definition of the $F(t)=t^2+t^3$ function:
+% 
+% |\SUMfunction{\SQUAREfunction}{\CUBEfunction}{\F}|
+% 
+% \item[\cs{SUBTRACTfunction}\Marg{\TBS function1}\Marg{\TBS function2}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\SUBTRACTfunction}
+% defines \textit{\TBS Function} as the difference of functions 
+% \textit{\TBS function1} and \textit{\TBS function2}.
+% 		
+% Example. Definition of the $F(t)=t^2-t^3$ function:
+% 
+% |\SUBTRACTfunction{\SQUAREfunction}{\CUBEfunction}{\F}|
+% 
+% \item[\cs{PRODUCTfunction}\Marg{\TBS function1}\Marg{\TBS function2}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\PRODUCTfunction}
+% defines \textit{\TBS Function} as the product of functions
+% \textit{\TBS function1} and \textit{\TBS function2}
+% 
+% Example. Definition of the $F(t)=\mathrm e^t\cos t$ function:
+% 
+% |\PRODUCTfunction{\EXPfunction}{\COSfunction}{\F}|
+% 
+% \item[\cs{QUOTIENTfunction}\Marg{\TBS function1}\Marg{\TBS function2}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\QUOTIENTfunction}
+% defines \textit{\TBS Function} as the quotient of functions
+% \textit{\TBS function1} and \textit{\TBS function2}.
+% 
+% Example. Definition of the $F(t)=\mathrm e^t/\cos t$ function:
+% 
+% |\QUOTIENTfunction{\EXPfunction}{\COSfunction}{\F}| 
+% 
+% \item[\cs{COMPOSITIONfunction}\Marg{\TBS function1}\Marg{\TBS function2}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\COMPOSITIONfunction}
+% defines \textit{\TBS Function} as the composition of functions
+% \textit{\TBS function1} and \textit{\TBS function2}.
+% 
+% Example. Definition of the $F(t)=\mathrm e^{\cos t}$ function:
+% 
+% |\COMPOSITIONfunction{\EXPfunction}{\COSfunction}{\F}| 
+% 
+% (note than |\COMPOSITIONfunction{f}{g}{\F}| means |\F|$=f\circ g$).
+%
+% \item[\cs{SCALEfunction}\Marg{num}\Marg{\TBS function}\Marg{\TBS Function}]%
+% \SpecialUsageIndex{\SCALEfunction}
+% defines \textit{\TBS Function} as the product of number \textit{num}
+% and function \textit{\TBS function}.
+% 
+% Example. Definition of the $F(t)=3{\cos t}$ function:
+% 
+% |\SCALEfunction{3}{\COSfunction}{\F}|
+% 
+% \item[\cs{SCALEVARIABLEfunction}\Marg{num}\Marg{\TBS function}%
+% \Marg{\TBS Function}]\SpecialUsageIndex{\SCALEVARIABLEfunction}
+% scales the variable by factor \textit{num} and then applies the function
+% \textit{\TBS function}.
+% 
+% Example. Definition of the $F(t)=\cos 3t$ function:
+% 
+% |\SCALEVARIABLEfunction{3}{\COSfunction}{\F}|
+% 
+% \item[\cs{POWERfunction}\Marg{\TBS function}\Marg{num}\Marg{\TBS Function}]%
+% \SpecialUsageIndex{\POWERfunction}
+% defines \textit{\TBS Function} as the power of function 
+% \textit{\TBS function} to the exponent \textit{num} (a positive integer).
+% Example. Definition of the $F(t)=t^5$ function:
+% 
+% |\POWERfunction{\IDENTITYfunction}{5}{\F}|
+% 
+% \item[\cs{LINEARCOMBINATIONfunction}\Marg{num1}\Marg{\TBS function1}%
+% \Marg{num2}\Marg{\TBS function2}\Marg{\TBS Function}]
+% \SpecialUsageIndex{\LINEARCOMBINATIONfunction}
+% defines \textit{\TBS Function} as the linear combination of functions
+% \textit{\TBS function1} and \textit{\TBS function2}
+% multiplied, respectively, by numbers \textit{num1} and \textit{num2}.
+% 
+% Example. Definition of the $F(t)=2t-3\cos t$ function:
+% 
+% |\LINEARCOMBINATIONfunction{2}{\IDENTITYfunction}{-3}{\COSfunction}{\F}| 
+% \end{description}
+% 
+% By combining properly this operations and the predefined functions, 
+% many elementary functions can be defined.
+% 
+% \begin{exemple}
+% % exp(-t)
+%    \SCALEVARIABLEfunction
+%        {-1}{\EXPfunction}
+%        {\NEGEXPfunction}  
+%
+% % exp(-t)cos(t)                              
+%    \PRODUCTfunction
+%        {\NEGEXPfunction}
+%        {\COSfunction}
+%        {\NEGEXPCOSfunction}
+%
+% % 3t^2-2exp(-t)cos(t)                             
+%    \LINEARCOMBINATIONfunction
+%        {3}{\SQUAREfunction}
+%       {-2}{\NEGEXPCOSfunction}
+%       {\myfunction} 
+%
+% \myfunction{5}{\sol}{\Dsol}
+% 
+% If 
+% \[
+%     f(t)=3t^2-2\mathrm{e}^{-t}\cos t 
+% \]
+% then   
+% \[
+% \begin{gathered}
+%     f(5)=\sol\\
+%     f'(5)=\Dsol
+% \end{gathered}
+% \]
+% \end{exemple}
+% 
+% \section{Polynomial functions}
+% Although polynomial functions can be defined using linear combinations
+% of power functions, 
+% to facilitate our work, the \textsf{calculus} package includes the
+% following commands to define more easily the polynomials of 
+% 1, 2, and 3 degrees:
+% |\newlpoly| (new \emph{linear} polynomial), |\newqpoly|
+% (new \emph{quadratic} polynomial), 
+% and |\newcpoly| (new \emph{cubic} polynomial):
+% \begin{description}
+% \item[\cs{newlpoly}\Marg{\TBS Function}\Marg{a}\Marg{b}]%
+% \SpecialUsageIndex{\newlpoly}
+% stores the 
+% $p(t)=\texttt{\textit{a}}+\texttt{\textit{b}}t$ 
+% function in the  \cs{\textit{Function}} command.
+% \item[\cs{newqpoly}\Marg{\TBS Function}%
+% \Marg{a}\Marg{b}\Marg{c}]\SpecialUsageIndex{\newqpoly} 
+% stores the 
+% $p(t)=\texttt{\textit{a}}+\texttt{\textit{b}}t+\texttt{\textit{c}}t^2$ 
+% function in the   \cs{\textit{Function}} command.
+% \item[\cs{newcpoly}\Marg{\TBS Function}\Marg{a}\Marg{b}\Marg{c}\Marg{d}]%
+% \SpecialUsageIndex{\newcpoly} 
+% stores the
+% $p(t)=\texttt{\textit{a}}+\texttt{\textit{b}}t+
+%         \texttt{\textit{c}}t^2+\texttt{\textit{d}}t^3$
+% function in the \cs{\textit{Function}} command.
+% \end{description}
+% \begin{exemple}
+% % \mypoly=1-x^2+x^3
+%     \newcpoly{\mypoly}{1}{0}{-1}{1}
+%     \mypoly{2}{\sol}{\Dsol}
+% $p'(2)=\Dsol$
+% \end{exemple}
+% These declarations behave similarly to to the declaration  
+% |\newcommand|:
+% If the name you want to assign to the new function is that of 
+% an already defined command, the \textsf{calculus} package returns
+% an error message and do not redefines this command.
+% To obtain any alternative behavior, our package includes
+% three other sets of declarations:
+% 
+% \begin{description}
+% \item[\cs{renewlpoly}, \cs{renewqpoly}, \cs{renewcpoly}]%
+% \SpecialUsageIndex{\renewlpoly}%
+% \SpecialUsageIndex{\renewqpoly}%
+% \SpecialUsageIndex{\renewcpoly} 
+% redefine the already existing command \cs{\textit{Function}}. 
+% If this command does not exist, then 
+% it is not defined and an error message occurs.
+% \item[\cs{ensurelpoly}, \cs{ensureqpoly}, \cs{ensurecpoly}]%
+% \SpecialUsageIndex{\ensurelpoly}%
+% \SpecialUsageIndex{\ensureqpoly}%
+% \SpecialUsageIndex{\ensurecpoly} 
+% define a new function. 
+% If the command \cs{\textit{Function}}  already exists, 
+% it is not redefined.
+% \item[\cs{forcelpoly}, \cs{forceqpoly}, \cs{forcecpoly}]%
+% \SpecialUsageIndex{\forcelpoly}%
+% \SpecialUsageIndex{\forceqpoly}%
+% \SpecialUsageIndex{\forcecpoly} 
+% define a new function. 
+% If the command \cs{\textit{Function}} already exists, 
+% it is redefined.
+% \end{description}
+% \section{Vector-valued functions (or parametrically defined curves)}
+% The instruction 
+% \begin{quote}\SpecialUsageIndex{\PARAMETRICfunction}
+% |\PARAMETRICfunction|\Marg{\TBS Xfunction}\Marg{\TBS Yfunction}%
+% \Marg{\TBS myvectorfunction}
+% \end{quote}
+% defines the new vector-valued function $f(t)=(x(t),y(t))$. 
+% 
+% The first and second arguments are a pair of functions already defined and, 
+% the third, the name of the new function we define.
+% Once we have defined them, the new vector functions requires five arguments:
+% \begin{quote}
+% \textttit{\TBS myvectorfunction}\Marg{num}\Marg{\TBS cmd1}%
+% \Marg{\TBS cmd2}\Marg{\TBS cmd3}\Marg{\TBS cmd4}
+% \end{quote}
+% where
+% \begin{itemize}
+% \item \textit{num} is a number $t$, 
+% \item \textit{\TBS cmd1} and \textit{\TBS cmd2} are two command names
+% where the values of the $x(t)$ function and its derivative $x'(t)$
+%  will be stored, and
+% \item \textit{\TBS cmd3} and \textit{\TBS cmd4} will store 
+%  $y(t)$ and $y'(t)$.
+% \end{itemize}
+% In short, in this context, a vector function is a pair of scalar functions.
+%
+% Instead of |\PARAMETRICfunction| we can use the alias |\VECTORfunction|.%
+% \SpecialUsageIndex{\VECTORfunction}
+% 
+% \begin{exemple}
+% For the $f(t)=(t^2,t^3)$ function we have
+% \VECTORfunction
+%     {\SQUAREfunction}{\CUBEfunction}{\F}
+%
+% \F{4}{\solx}{\Dsolx}{\soly}{\Dsoly}
+% 
+% \[
+% f(4)=(\solx,\soly), f'(4)=(\Dsolx,\Dsoly)
+% \]
+% \end{exemple}
+% 
+% \section{Vector-valued functions in polar coordinates}
+% The following instruction:
+% \begin{quote}\SpecialUsageIndex{\POLARfunction}
+% |\POLARfunction|\Marg{\TBS rfunction}\Marg{\TBS Polarfunction}
+% \end{quote}
+% declares the vector function $f(\phi)=(r(\phi)\cos \phi,r(\phi)\sin \phi)$. 
+% The first argument is the  
+% $r=r(\phi)$ function, (an already defined function).
+% For example, we can define the \emph{Archimedean spiral} $r(\phi)=0{,}5\phi$,
+% as follows:
+% \begin{Verbatim}[gobble=2]
+%    \SCALEfunction{0.5}{\IDENTITYfunction}{\rfunction}
+%    \POLARfunction{\rfunction}{\archimedes}
+% \end{Verbatim}
+% \section{Low-level instructions}
+% Probably, many users of the package will not be interested
+% in the implementation of the commands this package includes.
+% If this is your case, you can ignore this section.
+% \subsection{The \cs{newfunction} declaration and its variants}
+% All the functions predefined by this package use the |\newfunction|
+% declaration.
+% This control sequence works as follows:
+% \begin{description}
+% \item[\cs{newfunction}\Marg{\TBS Function}\Marg{Instructions to compute 
+%                           \cs{y} and \cs{Dy} from \cs{t}}]
+% \end{description}
+% where the second argument is the list of the instructions you need to run
+% to calculate the value of the function |\y|
+% and the derivative |\Dy| in the |\t| point.
+% 
+% For example, if you want to define the $f(t)=t^2+\mathrm e^t\cos t$ function,
+% whose derivative is
+% $f'(t)=2t+\mathrm e^t(\cos t-\sin t)$,
+% using the high-level instructions we defined earlier,
+% you can write the following instructions:
+% \begin{Verbatim}[gobble=2]
+%    \PRODUCTfunction{\EXPfunction}{\COSfunction}{\ffunction}
+%    \SUMfunction{\SQUAREfunction}{\ffunction}{\Ffunction}
+% \end{Verbatim}
+% 
+% But you can also define this function using the \cs{newfunction}
+% command as follows: 
+% \begin{Verbatim}[gobble=2]
+%    \newfunction{\Ffunction}{%
+%       \SQUARE{\t}{\tempA}               % A=t^2
+%       \EXP{\t}{\tempB}                  % B=e^t
+%       \COS{\t}{\tempC}                  % C=cos(t)
+%       \SIN{\t}{\tempD}                  % D=sin(t)
+%       \MULTIPLY{2}{\t}{\tempE}          % E=2t
+%       \MULTIPLY{\tempB}{\tempC}{\tempC} % C=e^t cos(t)
+%       \MULTIPLY{\tempB}{\tempD}{\tempD} % D=e^t sin(t)
+%       \ADD{\tempA}{\tempC}{\y}            % y=t^2 + e^t cos(t)  
+%       \ADD{\tempE}{\tempC}{\tempC}      % C=t^2 + e^t cos(t)   
+%       \SUBTRACT{\tempC}{\tempD}{\Dy}      % y'=t^2 + e^t cos(t) - e^t sin(t)
+%    }
+% \end{Verbatim}
+% 
+% It must be said, however, that the |\newfunction| declaration
+% behaves similarly to |\newcommand| or |\newlpoly|:
+% If the name you want to assign to the new function is that of an already
+% defined command, % the \textsf{calculus} package returns an error message
+% and does not redefines this command.
+% To obtain any alternative behavior, our package includes three other
+% versions of the |\newfunction| declarations: the 
+% |\renewfunction|, |\ensurefunction| and |\forcefunction| declarations. 
+% Each of these declarations behaves differently:
+% \begin{description}
+% \item[\cs{newfunction}]\SpecialUsageIndex{\newfunction}
+% defines a new function. If the command \cs{\textit{Function}} already exists, 
+% it is not redefined and an error message occurs.
+% \item[\cs{renewfunction}]\SpecialUsageIndex{\renewfunction}
+% redefines the already existing command 
+% \cs{\textit{Function}}. 
+% If this command does not exists, then it is not defined
+% and an error message occurs.
+% \item[\cs{ensurefunction}]\SpecialUsageIndex{\ensurefunction}
+% defines a new function. 
+% If the command \cs{\textit{Function}}  already exists, 
+% it is not redefined.
+% \item[\cs{forcefunction}]\SpecialUsageIndex{\forcefunction}
+% defines a new function. 
+% If the command \cs{\textit{Function}}  already exists, 
+% it is redefined.
+% \end{description}
+% \subsection{Vector functions and polar coordinates}
+% You can (re)define a vector function $f(t)=(x(t),y(t))$ using the
+% |\newvectorfunction|%
+% \SpecialUsageIndex{\newvectorfunction}%
+% \SpecialUsageIndex{\renewvectorfunction}%
+% \SpecialUsageIndex{\ensurevectorfunction}%
+% \SpecialUsageIndex{\forcevectorfunction}
+% declaration or any
+% of its variants  |\renewvectorfunction|, |\ensurevectorfunction|
+% and |\forcevectorfunction|:
+% \begin{description}
+% \item[\cs{newvectorfunction}\Marg{\TBS Function}\Marg{Instructions to compute 
+%                          \cs{x}, \cs{Dx}, \cs{y} and \cs{Dy} from \cs{t}}]
+% \end{description}
+% 
+% For example, you can define the function $f(t)=(t^2,t^3)$ 
+% in the following way:
+% \begin{Verbatim}[gobble=2]
+%    \newvectorfunction{\F}{%
+%       \SQUARE{\t}{\x}         % x=t^2
+%       \MULTIPLY{2}{\t}{\Dx}   % x'=2t
+%       \CUBE{\t}{\y}           % y=t^3
+%       \MULTIPLY{3}{\x}{\Dy}   % y'=3t^2
+%    }
+% \end{Verbatim}
+
+% \SpecialUsageIndex{\newpolarfunction}%
+% \SpecialUsageIndex{\renewpolarfunction}%
+% \SpecialUsageIndex{\ensurepolarfunction}%
+% \SpecialUsageIndex{\forcepolarfunction}%
+% Finally, to define the $r=r(\phi)$ function, in polar coordinates,
+% we have the declarations
+% |\newpolarfunction|,
+% |\renewpolarfunction|, |\ensurepolarfunction| and |\forcepolarfunction|.
+% \begin{description}
+% \item[\cs{newpolarfunction}\Marg{\TBS Function}\Marg{Instructions to compute 
+%                          \cs{r} and \cs{Dr} from \cs{t}}]
+% \end{description}
+% 
+% For example, you can define the \emph{cardioide} curve $r(\phi)=1+\cos \phi$,
+% using high level instructions,
+% \begin{Verbatim}[gobble=2]
+%    \SUMfunction{\ONEfunction}{\COSfunction}{\ffunction} % y=1 + cos t 
+%    \POLARfunction{\ffunction}{\cardioide}
+% \end{Verbatim}
+% or, with the |\newpolarfunction| declaration,
+% \begin{Verbatim}[gobble=2]
+%    \newpolarfunction{\cardioide}{%
+%       \COS{\t}{\r}
+%       \ADD{1}{\r}{\r}         % r=1+cos t
+%       \SIN{\t}{\Dr}
+%       \MULTIPLY{-1}{\Dr}{\Dr} % r'=-sin t
+%    }
+% \end{Verbatim}
+%
+% \StopEventually{}
+%
+% \section{Implementation (\textsf{calculator})}
+%    \begin{macrocode}
+%<*calculator>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{calculator}[2012/06/10 v.1.0a]
+%    \end{macrocode}
+% \subsection{Internal lengths and special nmbers}
+% \cs{cctr@lengtha} and \cs{cctr@lengthb}
+% will be used in internal calculations and comparisons.
+%    \begin{macrocode}
+\newdimen\cctr@lengtha
+\newdimen\cctr@lengthb
+%    \end{macrocode}
+% \begin{macro}{\cctr@epsilon}
+% \cs{cctr@epsilon} will store the closest to zero length 
+% in the \TeX{} arithmetic: one scaled point 
+% ($1\,\mathsf{sp}=1/65536\,\mathsf{pt}$).
+% This means the smallest positive number will be 
+% $0.00002\approx1/65536=1/2^{16}$.
+%    \begin{macrocode}
+\newdimen\cctr@epsilon
+\cctr@epsilon=1sp
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\cctr@logmaxnum}
+% The largest \TeX{} number is $16383.99998\approx2^{14}$;
+% \cs{cctr@logmaxnum} is the logarithm of this number,
+% $9.704\approx\log16384$.
+%    \begin{macrocode}
+\def\cctr@logmaxnum{9.704}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Warning messages}
+%    \begin{macrocode}
+\def\cctr@Warndivzero#1#2{%
+      \PackageWarning{calculator}%
+        {Division by 0.\MessageBreak 
+         I can't define #1/#2}}   
+         
+\def\cctr@Warnnogcd{%
+      \PackageWarning{calculator}%
+        {gcd(0,0) is not well defined}}     
+                 
+\def\cctr@Warnnoposrad#1{%
+      \PackageWarning{calculator}%
+                    {The argument in square root\MessageBreak
+                     must be non negative\MessageBreak
+                     I can't define sqrt(#1)}}
+
+\def\cctr@Warnnointexp#1#2{%
+      \PackageWarning{calculator}%
+                    {The exponent in power function\MessageBreak
+                     must be an integer\MessageBreak
+                     I can't define #1^#2}}
+
+\def\cctr@Warnsingmatrix#1#2#3#4{%
+      \PackageWarning{calculator}%
+        {Matrix (#1 #2 ; #3 #4) is singular\MessageBreak   
+         Its inverse is not defined}}
+
+\def\cctr@WarnsingTDmatrix#1#2#3#4#5#6#7#8#9{%
+      \PackageWarning{calculator}%
+        {Matrix (#1 #2 #3; #4 #5 #6; #7 #8 #9) is singular\MessageBreak   
+         Its inverse is not defined}}
+
+\def\cctr@WarnIncLinSys{\PackageWarning{xpicture}{%
+      Incompatible linear system}}
+
+\def\cctr@WarnIncTDLinSys{\PackageWarning{xpicture}{%
+      Incompatible or indeterminate linear system\MessageBreak
+      For 3x3 systems I can solve only determinate systems}}
+
+\def\cctr@WarnIndLinSys{\PackageWarning{xpicture}{%
+      Indeterminate linear system.\MessageBreak
+      I will choose one of the infinite solutions}}
+
+\def\cctr@WarnZeroLinSys{\PackageWarning{xpicture}{%
+      0x=0 linear system. Every vector is a solution!\MessageBreak
+      I will choose the (0,0) solution}}
+
+\def\cctr@Warninftan#1{%
+             \PackageWarning{calculator}{%
+                    Undefined tangent.\MessageBreak
+                           The cosine of #1 is zero and, then,\MessageBreak
+                           the tangent of #1 is not defined}}
+
+\def\cctr@Warninfcotan#1{%
+             \PackageWarning{calculator}{%
+                    Undefined cotangent.\MessageBreak
+                           The sine of #1 is zero and, then,\MessageBreak
+                           the cotangent of #1 is not defined}} 
+
+\def\cctr@Warninfexp#1{%
+             \PackageWarning{calculator}{%
+                    The absolute value of the variable\MessageBreak
+                    in the exponential function must be less than 
+                    \cctr@logmaxnum\MessageBreak
+                   (the logarithm of the max number I know)\MessageBreak
+                    I can't define exp(#1)}} 
+
+\def\cctr@Warninfexpb#1#2{%
+             \PackageWarning{calculator}{%
+                    The base\MessageBreak
+                    in the exponential function must be positive.
+                    \MessageBreak
+                    I can't define #1^(#2)}} 
+
+\def\cctr@Warninflog#1{%
+             \PackageWarning{calculator}{%
+                    The value of the variable\MessageBreak
+                    in the logarithm function must be positive\MessageBreak
+                    I can't define log(#1)}} 
+%    \end{macrocode}
+% \subsection{Operations with numbers}
+% \subsubsection*{Assignements and comparisons}
+% \begin{macro}{\COPY}
+% \cs{COPY}\marg{\#1}\marg{\#2} 
+% defines the \textit{\#2} command as the number \textit{\#1}.
+%    \begin{macrocode}
+\def\COPY#1#2{\edef#2{#1}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\GLOBALCOPY}
+% Global version of \cs{COPY}. 
+% The new defined command \textit{\#2} is not changed outside groups.
+%    \begin{macrocode}
+\def\GLOBALCOPY#1#2{\xdef#2{#1}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@OUTPUTSOL}
+% \cs{@OUTPUTSOL}\marg{\#1}: an internal macro to save solutions 
+% when a group is closed.
+% 
+% The global c.s. \cs{cctr@outa} preserves solutions.
+% Whenever we use any temporary parameters in the definition
+% of an instruction, 
+% we use a group to ensure the local character of those parameters. 
+% The instruction \cs{@OUTPUTSOL} is a bypass to export the solution.
+%    \begin{macrocode}
+\def\@OUTPUTSOL#1{\GLOBALCOPY{#1}{\cctr@outa}\endgroup\COPY{\cctr@outa}{#1}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@OUTPUTSOLS}
+% Analogous to \cs{@OUTPUTSOL}, preserving a pair of solutions. 
+%    \begin{macrocode}
+\def\@OUTPUTSOLS#1#2{\GLOBALCOPY{#1}{\cctr@outa}
+                     \GLOBALCOPY{#2}{\cctr@outb}\endgroup
+                     \COPY{\cctr@outa}{#1}\COPY{\cctr@outb}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\MAX}
+% \cs{MAX}\marg{\#1}\marg{\#2}\marg{\#3} 
+% defines the \textit{\#3} command as the maximum of numbers
+% \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}
+\def\MAX#1#2#3{%
+   \ifdim #1\p@ < #2\p@
+      \COPY{#2}{#3}\else\COPY{#1}{#3}\fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\MIN}
+% \cs{MIN}\marg{\#1}\marg{\#2}\marg{\#3} 
+% defines the \textit{\#3} command as the minimum of numbers
+% \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}
+\def\MIN#1#2#3{%
+   \ifdim #1\p@ > #2\p@
+      \COPY{#2}{#3}\else\COPY{#1}{#3}\fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{Real arithmetic}
+% \begin{macro}{\ABSVALUE}
+% \cs{ABSVALUE}\marg{\#1}\marg{\#2} 
+% defines the \textit{\#2} command as the 
+% absolute value of number \textit{\#1}.
+%    \begin{macrocode}      
+\def\ABSVALUE#1#2{%
+    \ifdim #1\p@<\z@
+          \MULTIPLY{-1}{#1}{#2}\else\COPY{#1}{#2}\fi}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Product, sum and difference}
+% \begin{macro}{\MULTIPLY}
+% \cs{MULTIPLY}\marg{\#1}\marg{\#2}\marg{\#3} 
+% defines the \textit{\#3} command as the 
+% product of numbers \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}
+\def\MULTIPLY#1#2#3{\cctr@lengtha=#1\p@
+       \cctr@lengtha=#2\cctr@lengtha
+       \edef#3{\expandafter\strip@pt\cctr@lengtha}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ADD}
+% \cs{ADD}\marg{\#1}\marg{\#2}\marg{\#3} 
+% defines the \textit{\#3} command as the 
+% sum of numbers \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}
+\def\ADD#1#2#3{\cctr@lengtha=#1\p@
+       \cctr@lengthb=#2\p@
+       \advance\cctr@lengtha by \cctr@lengthb
+       \edef#3{\expandafter\strip@pt\cctr@lengtha}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SUBTRACT}
+% \cs{SUBTRACT}\marg{\#1}\marg{\#2}\marg{\#3} 
+% defines the \textit{\#3} command as the 
+% difference of numbers \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}
+\def\SUBTRACT#1#2#3{\ADD{#1}{-#2}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Divisions}
+% We define several kinds of \emph{divisions}: the quotient of
+% two real numbers, the integer quotient, and the quotient of
+% two lengths.
+% The basic algorithm is a lightly modified version of the Beccari's division.
+% \begin{macro}{\DIVIDE}
+% \cs{DIVIDE}\marg{\#1}\marg{\#2}\marg{\#3}
+% defines the \textit{\#3} command as the 
+% quotient of numbers \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode}           
+\def\DIVIDE#1#2#3{%
+     \begingroup
+%    \end{macrocode}
+% Absolute values of dividend and divisor
+%    \begin{macrocode} 
+       \ABSVALUE{#1}{\cctr@tempD}                 
+       \ABSVALUE{#2}{\cctr@tempd}
+%    \end{macrocode}
+% The sign of quotient
+%    \begin{macrocode}        
+       \ifdim#1\p@<\z@\ifdim#2\p@>\z@\COPY{-1}{\cctr@sign}
+          \else\COPY{1}{\cctr@sign}\fi
+       \else\ifdim#2\p@>\z@\COPY{1}{\cctr@sign}
+               \else\COPY{-1}{\cctr@sign}\fi
+            \fi
+%    \end{macrocode}
+% Integer part of quotient
+%    \begin{macrocode}             
+       \@DIVIDE{\cctr@tempD}{\cctr@tempd}{\cctr@tempq}{\cctr@tempr}
+       \COPY{\cctr@tempq.}{\cctr@Q}
+%    \end{macrocode}
+% Fractional part up to five decimal places.
+%    \cs{cctr@ndec} is the number of decimal places already computed.
+%    \begin{macrocode}        
+       \COPY{0}{\cctr@ndec}
+       \@whilenum \cctr@ndec<5 \do{%
+%    \end{macrocode}       
+% Each decimal place is calculated by multiplying by 10 the last remainder
+% and dividing it by the divisor. 
+% But when the remainder is greater than 1638.3, an overflow occurs, because 
+% 16383.99998 is the greatest number. 
+% So, instead, we multiply the divisor by 0.1. 
+%    \begin{macrocode}
+           \ifdim\cctr@tempr\p@<1638\p@
+              \MULTIPLY{\cctr@tempr}{10}{\cctr@tempD}
+           \else
+              \COPY{\cctr@tempr}{\cctr@tempD}
+              \MULTIPLY{\cctr@tempd}{0.1}{\cctr@tempd}
+           \fi
+           \@DIVIDE{\cctr@tempD}{\cctr@tempd}{\cctr@tempq}{\cctr@tempr}
+           \COPY{\cctr@Q\cctr@tempq}{\cctr@Q}            
+           \ADD{1}{\cctr@ndec}{\cctr@ndec}}%
+%    \end{macrocode}
+% Adjust the sign and return the solution.
+%    \begin{macrocode}            
+       \MULTIPLY{\cctr@sign}{\cctr@Q}{#3}
+       \@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@DIVIDE}
+% The \cs{@DIVIDE}\parg{\#1} \parg{\#2}\parg{\#3}\parg{\#4}
+% command computes $\textit{\#1}/\textit{\#2}$ and
+% returns an integer quotient (\textit{\#3}) and a real remainder
+% (\textit{\#4}).
+%    \begin{macrocode} 
+  \def\@DIVIDE#1#2#3#4{% 
+       \@INTEGERDIVIDE{#1}{#2}{#3}
+       \MULTIPLY{#2}{#3}{#4}
+       \SUBTRACT{#1}{#4}{#4}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@INTEGERDIVIDE}
+% \cs{@INTEGERDIVIDE} divides two numbers (not necessarily integer) 
+% and returns an integer 
+% (this is the integer quotient only for nonnegative integers).
+%    \begin{macrocode} 
+\def\@INTEGERDIVIDE#1#2#3{%
+       \cctr@lengtha=#1\p@
+       \cctr@lengthb=#2\p@
+       \ifdim\cctr@lengthb=\z@
+          \let#3\undefined
+          \cctr@Warndivzero#1#2%  
+       \else
+          \divide\cctr@lengtha\cctr@lengthb
+          \COPY{\number\cctr@lengtha}{#3}
+       \fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\LENGTHDIVIDE}
+% The quotient of two lengths must be a number (not a length).
+% For example, one inch over one centimeter equals $2.54$.
+% \cs{LENGTHDIVIDE}\marg{\#1}\marg{\#2}\marg{\#3}
+% stores in \textit{\#3} the quotient of the  lenghts 
+% \textit{\#1} and \textit{\#2}.
+%    \begin{macrocode} 
+\def\LENGTHDIVIDE#1#2#3{%
+       \begingroup
+       \cctr@lengtha=#1
+       \cctr@lengthb=#2
+       \edef\cctr@tempa{\expandafter\strip@pt\cctr@lengtha}%
+       \edef\cctr@tempb{\expandafter\strip@pt\cctr@lengthb}%
+       \DIVIDE{\cctr@tempa}{\cctr@tempb}{#3}
+       \@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Powers}
+% \begin{macro}{\SQUARE}
+% \cs{SQUARE}\marg{\#1}\marg{\#2}
+% stores \textit{\#1} squared in \textit{\#2}.
+%    \begin{macrocode} 
+\def\SQUARE#1#2{\MULTIPLY{#1}{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\CUBE}
+% \cs{CUBE}\marg{\#1}\marg{\#2}
+% stores \textit{\#1} cubed in \textit{\#2}.
+%    \begin{macrocode} 
+\def\CUBE#1#2{\MULTIPLY{#1}{#1}{#2}\MULTIPLY{#2}{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\POWER}
+% \cs{POWER}\marg{\#1}\marg{\#2}\marg{\#3}
+% stores in \textit{\#3} the power $\textit{\#1}^{\textit{\#2}}$
+%    \begin{macrocode} 
+\def\POWER#1#2#3{%
+       \begingroup       
+       \INTEGERPART{#2}{\cctr@tempexp}
+       \ifdim \cctr@tempexp\p@<#2\p@ 
+         \cctr@Warnnointexp{#1}{#2}
+         \let#3\undefined     
+       \else
+%    \end{macrocode}        
+% This ensures that power will be defined only if the exponent is an integer.
+%    \begin{macrocode}        
+          \@POWER{#1}{#2}{#3}\fi\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+%    \begin{macrocode}
+\def\@POWER#1#2#3{%
+      \begingroup
+      \ifdim #2\p@<\z@
+%    \end{macrocode}        
+% For negative exponents, $a^n=(1/a)^{-n}$.
+%    \begin{macrocode} 
+             \DIVIDE{1}{#1}{\cctr@tempb}
+             \MULTIPLY{-1}{#2}{\cctr@tempc}
+             \@POWER{\cctr@tempb}{\cctr@tempc}{#3}
+          \else
+             \COPY{0}{\cctr@tempa}
+             \COPY{1}{#3}
+             \@whilenum \cctr@tempa<#2 \do {%
+                \MULTIPLY{#1}{#3}{#3}
+                \ADD{1}{\cctr@tempa}{\cctr@tempa}}%
+       \fi\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+
+% \subsubsection*{Integer arithmetic and related things}
+% \begin{macro}{\INTEGERDIVISION}
+% \cs{INTEGERDIVISION}\marg{\#1}\marg{\#2}\marg{\#3}\marg{\#4}
+% computes the division $\textit{\#1}/\textit{\#2}$ and returns
+% an integer quotient and a positive remainder.
+%    \begin{macrocode} 
+\def\INTEGERDIVISION#1#2#3#4{% 
+       \begingroup                
+       \ABSVALUE{#2}{\cctr@tempd}
+       \@DIVIDE{#1}{#2}{#3}{#4}
+       \ifdim #4\p@<\z@ 
+          \ifdim #1\p@<\z@ 
+             \ifdim #2\p@<\z@ 
+                \ADD{#3}{1}{#3}
+             \else
+                \SUBTRACT{#3}{1}{#3}
+             \fi
+             \ADD{#4}{\cctr@tempd}{#4}
+       \fi\fi\@OUTPUTSOLS{#3}{#4}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\MODULO}
+% \cs{MODULO}\marg{\#1}\marg{\#2}\marg{\#3}
+% returns the remainder of division $\textit{\#1}/\textit{\#2}$.
+%    \begin{macrocode} 
+\def\MODULO#1#2#3{%
+       \begingroup
+       \INTEGERDIVISION{#1}{#2}{\cctr@temp}{#3}\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\INTEGERQUOTIENT}
+% \cs{INTEGERQUOTIENT}\marg{\#1}\marg{\#2}\marg{\#3}
+% returns the integer quotient of division 
+% $\textit{\#1}/\textit{\#2}$.
+%    \begin{macrocode}       
+\def\INTEGERQUOTIENT#1#2#3{%
+       \begingroup
+       \INTEGERDIVISION{#1}{#2}{#3}{\cctr@temp}\@OUTPUTSOL{#3}}      
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\INTEGERPART}
+% \cs{INTEGERPART}\marg{\#1}\marg{\#2}
+% returns the integer part of \textit{\#2}. 
+%    \begin{macrocode}
+\def\@@INTEGERPART#1.#2.#3)#4{\ifnum #11=1 \COPY{0}{#4} 
+                              \else \COPY{#1}{#4}\fi}
+\def\@INTEGERPART#1#2{\expandafter\@@INTEGERPART#1..){#2}}             
+\def\INTEGERPART#1#2{\begingroup
+                     \ifdim #1\p@<\z@
+                        \MULTIPLY{-1}{#1}{\cctr@temp}
+                        \INTEGERPART{\cctr@temp}{#2}
+                        \ifdim #2\p@<\cctr@temp\p@
+                           \SUBTRACT{-#2}{1}{#2}
+                        \else \COPY{-#2}{#2}
+                        \fi
+                     \else
+                        \@INTEGERPART{#1}{#2}
+                     \fi\@OUTPUTSOL{#2}}      
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\FLOOR}
+% \cs{FLOOR} is an alias for \cs{INTEGERPART}.
+%    \begin{macrocode}       
+\let\FLOOR\INTEGERPART
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\FRACTIONALPART}
+% \cs{FRACTIONALPART}\marg{\#1}\marg{\#2}
+% returns the fractional part of  
+% \textit{\#2}.
+%    \begin{macrocode}
+\def\@@FRACTIONALPART#1.#2.#3)#4{\ifnum #2=11  \COPY{0}{#4} 
+                                \else \COPY{0.#2}{#4}\fi}
+\def\@FRACTIONALPART#1#2{\expandafter\@@FRACTIONALPART#1..){#2}}
+\def\FRACTIONALPART#1#2{\begingroup
+                     \ifdim #1\p@<\z@
+                        \INTEGERPART{#1}{\cctr@tempA}
+                        \SUBTRACT{#1}{\cctr@tempA}{#2}
+                     \else
+                        \@FRACTIONALPART{#1}{#2}
+                     \fi\@OUTPUTSOL{#2}} 
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TRUNCATE}
+% \cs{TRUNCATE}\oarg{\#1}\marg{\#2}\marg{\#3}
+% truncates \textit{\#2} to \textit{\#1} (0, 1, 2 (default), 3 or 4) digits.
+%    \begin{macrocode}
+\def\TRUNCATE{\@ifnextchar[\@@TRUNCATE\@TRUNCATE}
+\def\@TRUNCATE#1#2{\@@TRUNCATE[2]{#1}{#2}}
+\def\@@TRUNCATE[#1]#2#3{%
+    \begingroup 
+    \INTEGERPART{#2}{\cctr@tempa}
+    \ifdim \cctr@tempa\p@ = #2\p@      
+       \expandafter\@@@TRUNCATE#2.00000)[#1]{#3}
+    \else
+       \expandafter\@@@TRUNCATE#200000.)[#1]{#3}
+    \fi
+    \@OUTPUTSOL{#3}}  
+\def\@@@TRUNCATE#1.#2#3#4#5#6.#7)[#8]#9{%
+    \ifcase #8
+       \COPY{#1}{#9}
+    \or\COPY{#1.#2}{#9}
+    \or\COPY{#1.#2#3}{#9}
+    \or\COPY{#1.#2#3#4}{#9}
+    \or\COPY{#1.#2#3#4#5}{#9}
+    \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ROUND}
+% \cs{ROUND}\oarg{\#1}\marg{\#2}\marg{\#3}
+% rounds \textit{\#2} to \textit{\#1}  (0, 1, 2 (default), 3 or 4) digits.
+%    \begin{macrocode}       
+\def\ROUND{\@ifnextchar[\@@ROUND\@ROUND}
+\def\@ROUND#1#2{\@@ROUND[2]{#1}{#2}}
+\def\@@ROUND[#1]#2#3{%
+       \begingroup
+       \ifdim#2\p@<\z@
+           \MULTIPLY{-1}{#2}{\cctr@temp}
+           \@@ROUND[#1]{\cctr@temp}{#3}\COPY{-#3}{#3}
+       \else
+          \@@TRUNCATE[#1]{#2}{\cctr@tempe}
+          \SUBTRACT{#2}{\cctr@tempe}{\cctr@tempc}
+          \POWER{10}{#1}{\cctr@tempb}
+          \MULTIPLY{\cctr@tempb}{\cctr@tempc}{\cctr@tempc}
+          \ifdim\cctr@tempc\p@<0.5\p@           
+          \else 
+             \DIVIDE{1}{\cctr@tempb}{\cctr@tempb}
+             \ADD{\cctr@tempe}{\cctr@tempb}{\cctr@tempe}
+          \fi
+          \@@TRUNCATE[#1]{\cctr@tempe}{#3}
+       \fi
+       \@OUTPUTSOL{#3}} 
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\GCD}	
+% \cs{GCD}\marg{\#1}\marg{\#2}\marg{\#3}
+% Greatest common divisor, using the Euclidean algorithm
+%    \begin{macrocode}
+\def\GCD#1#2#3{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa}
+       \ABSVALUE{#2}{\cctr@tempb}
+       \MAX{\cctr@tempa}{\cctr@tempb}{\cctr@tempc}
+       \MIN{\cctr@tempa}{\cctr@tempb}{\cctr@tempa}
+       \COPY{\cctr@tempc}{\cctr@tempb}
+       \ifnum \cctr@tempa = 0 
+          \ifnum \cctr@tempb = 0
+             \cctr@Warnnogcd
+             \let#3\undefined
+          \else
+          \COPY{\cctr@tempb}{#3}
+          \fi
+       \else
+%    \end{macrocode}
+% Euclidean algorithm: if $c\equiv b \pmod{a}$ then $\gcd(b,a)=\gcd(a,c)$. 
+% Iterating this property, we obtain  $\gcd(b,a)$ as the last nonzero residual.
+%    \begin{macrocode}       
+          \@whilenum \cctr@tempa > \z@ \do {%
+             \COPY{\cctr@tempa}{#3}%
+             \MODULO{\cctr@tempb}{\cctr@tempa}{\cctr@tempc}%
+             \COPY\cctr@tempa\cctr@tempb%
+             \COPY\cctr@tempc\cctr@tempa}
+       \fi\ignorespaces\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\LCM}
+% \cs{LCM}\marg{\#1}\marg{\#2}\marg{\#3}
+% Least common multiple.
+%    \begin{macrocode}
+\def\LCM#1#2#3{%
+       \GCD{#1}{#2}{#3}%
+       \ifx #3\undefined \COPY{0}{#3} 
+       \else
+          \DIVIDE{#1}{#3}{#3}
+          \MULTIPLY{#2}{#3}{#3}
+          \ABSVALUE{#3}{#3}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\FRACTIONSIMPLIFY}	
+% \cs{FRACTIONSIMPLIFY}\marg{\#1}\marg{\#2}\marg{\#3}\marg{\#4}
+% Fraction simplification: $\textit{\#3}/\textit{\#4}$ is the irreducible 
+% fraction equivalent to  $\textit{\#1}/\textit{\#2}$.
+%    \begin{macrocode}
+\def\FRACTIONSIMPLIFY#1#2#3#4{%
+       \ifnum #1=\z@
+          \COPY{0}{#3}\COPY{1}{#4}
+       \else
+          \GCD{#1}{#2}{#3}%
+          \DIVIDE{#2}{#3}{#4}
+          \DIVIDE{#1}{#3}{#3}
+          \ifnum #4<0 \MULTIPLY{-1}{#4}{#4}\MULTIPLY{-1}{#3}{#3}\fi
+       \fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{Elementary functions}
+% \paragraph*{Square roots}
+% \begin{macro}{\SQUAREROOT}	
+% \cs{SQUAREROOT}\marg{\#1}\marg{\#2}
+% defines \textit{\#2} as the square root of \textit{\#1}, 
+% using the Newton's method: $x_{n+1}=x_n-(x_n^2-\textit{\#1})/(2x_n)$.
+%    \begin{macrocode}        
+\def\SQUAREROOT#1#2{%
+       \begingroup
+       \ifdim #1\p@ = \z@ 
+         \COPY{0}{#2}
+       \else    
+         \ifdim #1\p@ < \z@   
+             \let#2\undefined
+             \cctr@Warnnoposrad{#1}%
+          \else
+%    \end{macrocode}
+%  We take \textit{\#1} as the initial approximation.
+%    \begin{macrocode}    
+             \COPY{#1}{#2}
+%    \end{macrocode}
+% \cs{cctr@lengthb} will be the difference of two successive iterations.
+%
+% We start with |\cctr@lengthb=5\p@| to ensure almost one iteration.
+%    \begin{macrocode}  
+             \cctr@lengthb=5\p@
+%    \end{macrocode}
+% Successive iterations
+%    \begin{macrocode} 
+             \@whilenum \cctr@lengthb>\cctr@epsilon \do {% 
+%    \end{macrocode}
+% Copy the actual approximation to \cs{cctr@tempw}
+%    \begin{macrocode}             
+                \COPY{#2}{\cctr@tempw}
+                \DIVIDE{#1}{\cctr@tempw}{\cctr@tempz}
+                \ADD{\cctr@tempw}{\cctr@tempz}{\cctr@tempz}
+                \DIVIDE{\cctr@tempz}{2}{\cctr@tempz}
+%    \end{macrocode}
+% Now,  \cs{cctr@tempz} is the new approximation.
+%    \begin{macrocode}                 
+                \COPY{\cctr@tempz}{#2}
+%    \end{macrocode}
+% Finally, we store in \cs{cctr@lengthb} the difference
+% of the two last approximations, finishing the loop.
+%    \begin{macrocode}                 
+                \SUBTRACT{#2}{\cctr@tempw}{\cctr@tempw}
+                \cctr@lengthb=\cctr@tempw\p@%
+                \ifnum 
+                   \cctr@lengthb<\z@ \cctr@lengthb=-\cctr@lengthb
+                \fi}               
+       \fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SQRT}	
+% \cs{SQRT} is an alias for \cs{SQUAREROOT}.
+%    \begin{macrocode} 
+\let\SQRT\SQUAREROOT
+%    \end{macrocode}
+% \end{macro}
+% \paragraph{Trigonometric functions}
+% For a variable close enough to zero, the sine and tangent functions 
+% are computed using some continued fractions.
+% Then, all trigonometric functions are derived from well-known formulas. 
+% \begin{macro}{\SIN}
+% \cs{SIN}\marg{\#1}\marg{\#2}. Sine of \textit{\#1}.
+%    \begin{macrocode}
+\def\SIN#1#2{%
+    \begingroup
+%    \end{macrocode}
+% Exact sine for $t\in\{\pi/2,-\pi/2,3\pi/2\}$
+%   \begin{macrocode}  
+    \ifdim #1\p@=-\numberHALFPI\p@ \COPY{-1}{#2}
+    \else   
+         \ifdim #1\p@=\numberHALFPI\p@ \COPY{1}{#2} 
+         \else      
+              \ifdim #1\p@=\numberTHREEHALFPI\p@ \COPY{-1}{#2}
+               \else 
+%    \end{macrocode}
+% If $\left\vert t \right\vert>\pi/2$, change $t$ to a smaller value.
+%   \begin{macrocode}           
+                   \ifdim#1\p@<-\numberHALFPI\p@ 
+                      \ADD{#1}{\numberTWOPI}{\cctr@tempb} 
+                      \SIN{\cctr@tempb}{#2}
+                   \else
+                      \ifdim #1\p@<\numberHALFPI\p@
+%    \end{macrocode}
+% Compute the sine.
+%   \begin{macrocode}                       
+                         \@BASICSINE{#1}{#2} 
+                      \else 
+                         \ifdim #1\p@<\numberTHREEHALFPI\p@ 
+                           \SUBTRACT{\numberPI}{#1}{\cctr@tempb}
+                           \SIN{\cctr@tempb}{#2}
+                        \else 
+                          \SUBTRACT{#1}{\numberTWOPI}{\cctr@tempb}
+                          \SIN{\cctr@tempb}{#2}
+  \fi\fi\fi\fi\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@BASICSINE}
+% \cs{@BASICSINE}\marg{\#1}\marg{\#2} applies this approximation:
+% \[
+% \sin x = \frac{x}{
+%  1+\displaystyle\frac{x^2}{
+%  2\cdot3-x^2+\displaystyle\frac{2\cdot3x^2}{
+%  4\cdot5-x^2+\displaystyle\frac{4\cdot5x^2}{
+%  6\cdot7-x^2+\cdots
+% }          
+% }          
+% }          
+% }
+% \]
+%    \begin{macrocode}
+\def\@BASICSINE#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa} 
+%    \end{macrocode}       
+% Exact sine of zero
+%    \begin{macrocode}
+          \ifdim\cctr@tempa\p@=\z@ \COPY{0}{#2}
+          \else
+%    \end{macrocode}       
+% For $t$ very close to zero, $\sin t\approx t$.
+%    \begin{macrocode}            
+             \ifdim \cctr@tempa\p@<0.009\p@\COPY{#1}{#2}
+             \else  
+%    \end{macrocode}       
+% Compute the continued fraction.
+%    \begin{macrocode}                  
+                \SQUARE{#1}{\cctr@tempa}
+                \DIVIDE{\cctr@tempa}{42}{#2}       
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{\cctr@tempa}{#2}
+                \DIVIDE{#2}{20}{#2}
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{\cctr@tempa}{#2}
+                \DIVIDE{#2}{6}{#2}
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{#1}{#2}
+          \fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COS}
+% \cs{COS}\marg{\#1}\marg{\#2}. Cosine of \textit{\#1}: $\cos t=\sin(t+\pi/2)$.
+%    \begin{macrocode}
+\def\COS#1#2{%
+        \begingroup
+        \ADD{\numberHALFPI}{#1}{\cctr@tempc}
+        \SIN{\cctr@tempc}{#2}\@OUTPUTSOL{#2}}  
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TAN}
+% \cs{TAN}\marg{\#1}\marg{\#2}. Tangent of \textit{\#1}.
+%    \begin{macrocode}       
+\def\TAN#1#2{%
+          \begingroup
+%    \end{macrocode}       
+% Tangent is infinite for $t=\pm\pi/2$
+%    \begin{macrocode}             
+          \ifdim #1\p@=-\numberHALFPI\p@
+             \cctr@Warninftan{#1}
+             \let#2\undefined                 
+          \else
+             \ifdim #1\p@=\numberHALFPI\p@
+                 \cctr@Warninftan{#1}
+                 \let#2\undefined
+             \else
+%    \end{macrocode}
+% If $\left\vert t \right\vert>\pi/2$, change $t$ to a smaller value.
+%   \begin{macrocode}              
+                \ifdim #1\p@<-\numberHALFPI\p@
+                   \ADD{#1}{\numberPI}{\cctr@tempb} 
+                   \TAN{\cctr@tempb}{#2} 
+                \else
+                   \ifdim #1\p@<\numberHALFPI\p@
+%    \end{macrocode}
+% Compute the tangent.
+%   \begin{macrocode}                    
+                      \@BASICTAN{#1}{#2}
+                   \else
+                      \SUBTRACT{#1}{\numberPI}{\cctr@tempb}
+                      \TAN{\cctr@tempb}{#2}
+          \fi\fi\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@BASICTAN}
+% \cs{@BASICTAN}\marg{\#1}\marg{\#2} applies this approximation:
+% \[
+% \tan x = \frac{1}{
+%  \displaystyle\frac{1}{x}-\displaystyle\frac{1}{
+%  \displaystyle\frac{3}{x}-\displaystyle\frac{1}{
+%  \displaystyle\frac{5}{x}-\displaystyle\frac{1}{
+%  \displaystyle\frac{7}{x}-\displaystyle\frac{1}{
+%  \displaystyle\frac{9}{x}-\displaystyle\frac{1}{
+%  \displaystyle\frac{11}{x}-
+%  \cdots
+% }         
+% }          
+% }          
+% }          
+% }
+% }
+% \]
+%    \begin{macrocode}
+\def\@BASICTAN#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa}
+%    \end{macrocode}       
+% Exact tangent of zero.
+%    \begin{macrocode}         
+          \ifdim\cctr@tempa\p@=\z@ \COPY{0}{#2}
+          \else
+%    \end{macrocode}       
+% For $t$ very close to zero, $\tan t\approx t$.
+%    \begin{macrocode}              
+             \ifdim\cctr@tempa\p@<0.04\p@
+                \COPY{#1}{#2}
+             \else
+%    \end{macrocode}       
+% Compute the continued fraction.
+%    \begin{macrocode}             
+                \DIVIDE{#1}{11}{#2}
+                \DIVIDE{9}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{7}{#1}{\cctr@tempa}   
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{5}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{3}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{1}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+          \fi\fi\@OUTPUTSOL{#2}}        
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COT}
+% \cs{COT}\marg{\#1}\marg{\#2}. Cotangent of \textit{\#1}: 
+% If $\cos t=0$ then $\cot t=0$; if $\tan t=0$ then $\cot t=\infty$.
+% Otherwise, $\cot t=1/\tan t$.
+%    \begin{macrocode}
+\def\COT#1#2{%
+        \begingroup
+        \COS{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \COPY{0}{#2}
+        \else        
+        \TAN{#1}{#2}
+        \ifdim #2\p@ = \z@         
+        \cctr@Warninfcotan{#1}
+        \let#2\undefined                              
+        \else
+        \DIVIDE{1}{#2}{#2}
+        \fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\DEGtoRAD}
+% \cs{DEGtoRAD}\marg{\#1}\marg{\#2}. Convert degrees to radians.
+%    \begin{macrocode}
+\def\DEGtoRAD#1#2{\DIVIDE{#1}{57.29578}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\RADtoDEG}
+% \cs{RADtoDEG}\marg{\#1}\marg{\#2}. Convert radians to degrees.
+%    \begin{macrocode}
+\def\RADtoDEG#1#2{\MULTIPLY{#1}{57.29578}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\REDUCERADIANSANGLE}
+% Reduces to the trigonometrically equivalent arc in $]{-}\pi,\pi]$. 
+%    \begin{macrocode}
+\def\REDUCERADIANSANGLE#1#2{%
+         \COPY{#1}{#2}
+         \ifdim #1\p@ < -\numberPI\p@
+                 \ADD{#1}{\numberTWOPI}{#2}
+                 \REDUCERADIANSANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ >  \numberPI\p@
+                 \SUBTRACT{#1}{\numberTWOPI}{#2}
+                 \REDUCERADIANSANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ = -180\p@ \COPY{\numberPI}{#2} \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\REDUCEDEGREESANGLE}
+% Reduces to the trigonometrically equivalent angle in $]{-}180,180]$. 
+%    \begin{macrocode}
+\def\REDUCEDEGREESANGLE#1#2{%
+         \COPY{#1}{#2}
+         \ifdim #1\p@ < -180\p@
+                 \ADD{#1}{360}{#2}
+                 \REDUCEDEGREESANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ >  180\p@
+                 \SUBTRACT{#1}{360}{#2}
+                 \REDUCEDEGREESANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ = -180\p@ \COPY{180}{#2} \fi}
+%    \end{macrocode}
+% \end{macro}
+% \subparagraph*{Trigonometric functions in degrees}
+% Four next commands compute trigonometric functions
+% in \emph{degrees}. By default, a circle has $360$
+% degrees, but we can use an arbitrary number of divisions
+% using the optional argument of these commands.
+% \begin{macro}{\DEGREESSIN}
+% \cs{DEGREESSIN}\oarg{\#1}\marg{\#2}\marg{\#3}.
+% Sine of \textit{\#2} \emph{degrees}.
+%    \begin{macrocode}
+\def\DEGREESSIN{\@ifnextchar[\@@DEGREESSIN\@DEGREESSIN}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\DEGREESCOS}
+% \cs{DEGREESCOS}\oarg{\#1}\marg{\#2}\marg{\#3}.
+% Cosine of \textit{\#2} \emph{degrees}.
+%    \begin{macrocode}                      
+\def\DEGREESCOS{\@ifnextchar[\@@DEGREESCOS\@DEGREESCOS}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\DEGREESTAN}
+% \cs{DEGREESTAN}\oarg{\#1}\marg{\#2}\marg{\#3}.
+% Tangent of \textit{\#2} \emph{degrees}.
+%    \begin{macrocode} 
+\def\DEGREESTAN{\@ifnextchar[\@@DEGREESTAN\@DEGREESTAN}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\DEGREESCOT}
+% \cs{DEGREESCOT}\oarg{\#1}\marg{\#2}\marg{\#3}.
+% Cotangent of \textit{\#2} \emph{degrees}.
+%    \begin{macrocode} 
+\def\DEGREESCOT{\@ifnextchar[\@@DEGREESCOT\@DEGREESCOT}                       
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@DEGREESSIN}
+% \cs{@DEGREESSIN} computes the sine in sexagesimal \emph{degrees}.
+%    \begin{macrocode} 
+\def\@DEGREESSIN#1#2{%
+    \begingroup
+    \ifdim #1\p@=-90\p@ \COPY{-1}{#2} 
+    \else
+         \ifdim #1\p@=90\p@ \COPY{1}{#2} 
+         \else      
+                  \ifdim #1\p@=270\p@ \COPY{-1}{#2} 
+         \else  
+           \ifdim#1\p@<-90\p@ 
+                \ADD{#1}{360}{\cctr@tempb}           
+                \DEGREESSIN{\cctr@tempb}{#2}
+           \else
+              \ifdim #1\p@<90\p@
+                    \DEGtoRAD{#1}{\cctr@tempb}
+                    \@BASICSINE{\cctr@tempb}{#2}    
+                  \else 
+                       \ifdim #1\p@<270\p@ 
+                         \SUBTRACT{180}{#1}{\cctr@tempb}
+                          \DEGREESSIN{\cctr@tempb}{#2}
+                         \else 
+                              \SUBTRACT{#1}{360}{\cctr@tempb}
+                              \DEGREESSIN{\cctr@tempb}{#2}
+  \fi\fi\fi\fi\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@DEGREESCOS}
+% \cs{@DEGREESCOS} computes the cosine in sexagesimal \emph{degrees}.
+%    \begin{macrocode}
+\def\@DEGREESCOS#1#2{%
+        \begingroup
+        \ADD{90}{#1}{\cctr@tempc}
+        \DEGREESSIN{\cctr@tempc}{#2}\@OUTPUTSOL{#2}}  
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@DEGREESTAN}
+% \cs{@DEGREESTAN} computes the tangent in sexagesimal \emph{degrees}.
+%    \begin{macrocode}
+\def\@DEGREESTAN#1#2{%
+          \begingroup
+          \ifdim #1\p@=-90\p@
+          \cctr@Warninftan{#1}
+          \let#2\undefined                 
+          \else
+            \ifdim #1\p@=90\p@
+            \cctr@Warninftan{#1}
+            \let#2\undefined
+          \else
+          \ifdim #1\p@<-90\p@
+            \ADD{#1}{180}{\cctr@tempb} \DEGREESTAN{\cctr@tempb}{#2} 
+          \else
+              \ifdim #1\p@<90\p@
+                   \DEGtoRAD{#1}{\cctr@tempb}
+                   \@BASICTAN{\cctr@tempb}{#2}
+                 \else
+                     \SUBTRACT{#1}{180}{\cctr@tempb}
+                     \DEGREESTAN{\cctr@tempb}{#2}
+   \fi\fi\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@DEGREESCOT}
+% \cs{@DEGREESCOT} computes the cotangent in sexagesimal \emph{degrees}.
+%    \begin{macrocode}
+\def\@DEGREESCOT#1#2{%
+        \begingroup
+        \DEGREESCOS{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \COPY{0}{#2}
+        \else        
+        \DEGREESTAN{#1}{#2}
+        \ifdim #2\p@ = \z@         
+        \cctr@Warninfcotan{#1}
+        \let#2\undefined                              
+        \else
+        \DIVIDE{1}{#2}{#2}
+        \fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% For an arbitrary number of \emph{degrees}, we normalise
+% to $360$ degrees and, then, call the former functions. 
+% \begin{macro}{\@@DEGREESSIN}
+% \cs{@@DEGREESSIN} computes the sine. 
+% A circle has \textit{\#1} \emph{degrees}.
+%    \begin{macrocode}
+\def\@@DEGREESSIN[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \@DEGREESSIN{\@DEGREES}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@DEGREESCOS}
+% \cs{@@DEGREESCOS} computes the sine. 
+% A circle has \textit{\#1} \emph{degrees}.
+%    \begin{macrocode}                         
+\def\@@DEGREESCOS[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESCOS{\@DEGREES}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@DEGREESTAN}
+% \cs{@@DEGREESTAN} computes the sine. 
+% A circle has \textit{\#1} \emph{degrees}.
+%    \begin{macrocode} 
+\def\@@DEGREESTAN[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESTAN{\@DEGREES}{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@DEGREESCOT}
+% \cs{@@DEGREESCOT} computes the sine. 
+% A circle has \textit{\#1} \emph{degrees}.
+%    \begin{macrocode} 
+\def\@@DEGREESCOT[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESCOT{\@DEGREES}{#3}}                         
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@CONVERTDEG}
+% \cs{@CONVERTDEG} normalises to sexagesimal degrees.
+%    \begin{macrocode} 
+\def\@CONVERTDEG#1#2{\DIVIDE{#2}{#1}{\@DEGREES}
+        \MULTIPLY{\@DEGREES}{360}{\@DEGREES}}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Exponential functions}
+% \begin{macro}{\EXP}
+% \cs{EXP}\oarg{\#1}\marg{\#2}\marg{\#3} computes 
+% the exponential $\textit{\#3}=\textit{\#1}^{\textit{\#2}}$. 
+% Default for \textit{\#1} is number $\mathrm e$.
+%    \begin{macrocode}
+\def\EXP{\@ifnextchar[\@@EXP\@EXP}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@EXP} \cs{@@EXP}\oarg{\textit{\#1}}\marg{\#2}\marg{\#3} 
+% computes $\textit{\#3}=\textit{\#1}^{\textit{\#2}}$
+%    \begin{macrocode}
+\def\@@EXP[#1]#2#3{%
+      \begingroup
+%    \end{macrocode}
+% \#1 must be a positive number.
+%    \begin{macrocode}      
+      \ifdim #1\p@<\cctr@epsilon
+          \cctr@Warninfexpb{#1}{#2}
+          \let#3\undefined
+      \else
+%    \end{macrocode}
+% $a^b=\exp(b\log a)$.
+%    \begin{macrocode}       
+          \LOG{#1}{\cctr@log}
+          \MULTIPLY{#2}{\cctr@log}{\cctr@log}
+          \@EXP{\cctr@log}{#3}
+      \fi\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@EXP} \cs{@EXP}\marg{\#1}\marg{\#2} 
+% computes $\textit{\#3}=\mathrm{e}^{\textit{\#2}}$
+%    \begin{macrocode}
+\def\@EXP#1#2{%
+      \begingroup
+      \ABSVALUE{#1}{\cctr@absval}
+%    \end{macrocode}
+% If $\left\vert t\right\vert$ is greater than \cs{cctr@logmaxnum}
+% then $\exp t$ is too large.
+%    \begin{macrocode}      
+      \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+              \cctr@Warninfexp{#1}
+             \let#2\undefined
+      \else
+          \ifdim #1\p@ < \z@  
+%    \end{macrocode}          
+% We call \cs{@BASICEXP} when $t\in [{-}6,3]$. 
+% Otherwise we use the equality $\exp t=\left(\exp t/2\right)^2$.
+%    \begin{macrocode}
+            \ifdim #1\p@ > -6.00002\p@                   
+               \@BASICEXP{#1}{#2}
+            \else 
+               \DIVIDE{#1}{2}{\cctr@expt}
+               \@EXP{\cctr@expt}{\cctr@expy}
+               \SQUARE{\cctr@expy}{#2}
+            \fi
+          \else
+               \ifdim #1\p@ < 3.00002\p@        
+                  \@BASICEXP{#1}{#2}
+               \else 
+                  \DIVIDE{#1}{2}{\cctr@expt}
+                  \@EXP{\cctr@expt}{\cctr@expy}
+                  \SQUARE{\cctr@expy}{#2}
+               \fi
+\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@BASICEXP}
+% \cs{@BASICEXP}\marg{\#1}\marg{\#2} applies this approximation:
+% \[
+% \exp x \approx 1+\frac{2x}{
+%  2-x+\displaystyle\frac{x^2/6}{
+%  1+\displaystyle\frac{x^2/60}{
+%  1+\displaystyle\frac{x^2/140}{
+%  1+\displaystyle\frac{x^2/256}{
+%  1+\displaystyle\frac{x^2}{396
+% }         
+% }          
+% }          
+% }          
+% }
+% }
+% \]
+%    \begin{macrocode}
+\def\@BASICEXP#1#2{% 
+       \begingroup
+       \SQUARE{#1}\cctr@tempa
+       \DIVIDE{\cctr@tempa}{396}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{256}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{140}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{60}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{6}{#2}
+       \ADD{2}{#2}{#2}
+       \SUBTRACT{#2}{#1}{#2}
+       \DIVIDE{#1}{#2}{#2}
+       \MULTIPLY{2}{#2}{#2}
+       \ADD{1}{#2}{#2}\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Hyperbolic functions}
+% \begin{macro}{\COSH}
+% \cs{COSH}. Hyperbolic cosine: $\cosh t=(\exp t+\exp(-t))/2$.
+%    \begin{macrocode}
+\def\COSH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \EXP{#1}{\cctr@expx}
+          \MULTIPLY{-1}{#1}{\cctr@minust}
+          \EXP{\cctr@minust}{\cctr@expminusx}
+          \ADD{\cctr@expx}{\cctr@expminusx}{#2}
+          \DIVIDE{#2}{2}{#2}
+       \fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SINH}
+% \cs{SINH}. Hyperbolic sine: $\sinh t=(\exp t-\exp(-t))/2$.
+%    \begin{macrocode}
+\def\SINH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \EXP{#1}{\cctr@expx}
+          \MULTIPLY{-1}{#1}{\cctr@minust}
+          \EXP{\cctr@minust}{\cctr@expminusx}
+          \SUBTRACT{\cctr@expx}{\cctr@expminusx}{#2}
+          \DIVIDE{#2}{2}{#2}
+       \fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TANH}
+% \cs{TANH}. Hyperbolic tangent: $\tanh t=\sinh t/{\cosh t}$.
+%    \begin{macrocode}
+\def\TANH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \SINH{#1}{\cctr@tanhnum}
+          \COSH{#1}{\cctr@tanhden}
+          \DIVIDE{\cctr@tanhnum}{\cctr@tanhden}{#2}
+       \fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COTH}
+% \cs{COTH}. Hyperbolic cotangent $\coth t=\cosh t/{\sinh t}$.
+%    \begin{macrocode}
+\def\COTH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \SINH{#1}{\cctr@tanhden}
+          \COSH{#1}{\cctr@tanhnum}
+          \DIVIDE\cctr@tanhnum\cctr@tanhden{#2}
+       \fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \paragraph*{Logarithm}
+% \begin{macro}{\LOG}
+% \cs{LOG}\oarg{\#1}\marg{\#2}\marg{\#3} computes 
+% the logarithm $\textit{\#3}=\log_{\textit{\#1}}{\textit{\#2}}$. 
+% Default for \textit{\#1} is number $\mathrm e$.
+%    \begin{macrocode}
+\def\LOG{\@ifnextchar[\@@LOG\@LOG}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@LOG} \cs{@LOG}\marg{\textit{\#1}}\marg{\#2} 
+% computes $\textit{\#2}=\log\textit{\#1}$
+%    \begin{macrocode}
+\def\@LOG#1#2{%
+       \begingroup
+%    \end{macrocode} 
+% The argument $t$ must be positive.
+%    \begin{macrocode}       
+       \ifdim #1\p@<\cctr@epsilon
+          \cctr@Warninflog{#1}
+          \let#2\undefined
+       \else
+       \ifdim #1\p@ > \numberETWO\p@
+%    \end{macrocode} 
+% If $t>\mathrm{e}^2$, $\log t=\log\mathrm{e}+\log(t/{\mathrm{e}})=1+\log(t/{\mathrm{e}})$
+%    \begin{macrocode}          
+          \DIVIDE{#1}{\numberE}{\cctr@ae}
+          \@LOG{\cctr@ae}{#2}
+          \ADD{1}{#2}{#2}
+       \else
+          \ifdim #1\p@ < 1\p@      
+%    \end{macrocode} 
+% If $t<1$, $\log t=\log(1/\mathrm{e})+\log(t\mathrm{e})=-1+\log(t\mathrm{e})$
+%    \begin{macrocode}          
+             \MULTIPLY{\numberE}{#1}{\cctr@ae}
+             \LOG{\cctr@ae}{#2}
+             \SUBTRACT{#2}{1}{#2}
+          \else
+%    \end{macrocode} 
+% For $t\in[1,\mathrm{e}^2]$ we call \cs{@@BASICLOG}.
+%    \begin{macrocode}            
+             \@BASICLOG{#1}{#2}
+\fi\fi\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@@LOG} \cs{@@LOG}\oarg{\textit{\#1}}\marg{\#2}\marg{\#3} 
+% computes $\textit{\#3}=\log_\textit{\#1}\textit{\#2}
+% =\log(\textit{\#2})/\log(\textit{\#1})$
+%    \begin{macrocode}
+\def\@@LOG[#1]#2#3{\begingroup
+       \@LOG{#1}{\cctr@loga}
+       \@LOG{#2}{\cctr@logx}
+       \DIVIDE{\cctr@logx}{\cctr@loga}{#3}\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@BASICLOG} \cs{@BASICLOG}\marg{\textit{\#1}}\marg{\#2}
+% applies the Newton's method to calculate $x=\log t$:
+% \[x_{n+1}=x_n+\frac{t}{\mathrm{e}^{x_n}}-1\]
+%    \begin{macrocode}         
+\def\@BASICLOG#1#2{\begingroup 
+%  We take $\textit{\#1}-1$ as the initial approximation.
+%    \begin{macrocode}    
+             \SUBTRACT{#1}{1}{\cctr@tempw}
+%    \end{macrocode}
+%
+% We start with |\cctr@lengthb=5\p@| to ensure almost one iteration.
+%    \begin{macrocode}  
+             \cctr@lengthb=5\p@%
+             \cctr@lengtha=\cctr@epsilon%
+%    \end{macrocode}
+% Successive iterations
+%    \begin{macrocode} 
+       \@whilenum \cctr@lengthb>\cctr@lengtha \do {%
+           \COPY{\cctr@tempw}{\cctr@tempoldw}
+           \EXP{\cctr@tempw}{\cctr@tempxw}
+           \DIVIDE{#1}{\cctr@tempxw}{\cctr@tempxw}
+           \ADD{\cctr@tempw}{\cctr@tempxw}{\cctr@tempw}
+           \SUBTRACT{\cctr@tempw}{1}{\cctr@tempw}
+           \SUBTRACT{\cctr@tempw}{\cctr@tempoldw}{\cctr@tempdif}
+           \cctr@lengthb=\cctr@tempdif\p@%
+           \ifnum 
+              \cctr@lengthb<\z@ \cctr@lengthb=-\cctr@lengthb
+           \fi}%
+       \COPY{\cctr@tempw}{#2}\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Matrix arithmetics}
+% \subsubsection*{Vector operations}
+% \begin{macro}{\VECTORSIZE}
+% The \emph{size} of a vector is $2$ or $3$.
+% \cs{VECTORSIZE}\parg{\#1}\marg{\#2} stores in \textit{\#2} the 
+% size of \parg{\#1}. 
+%
+% Almost all vector commands needs to know the vector size.
+%    \begin{macrocode}
+\def\VECTORSIZE(#1)#2{\expandafter\@VECTORSIZE(#1,,){#2}}
+\def\@VECTORSIZE(#1,#2,#3,#4)#5{\ifx$#3$\COPY{2}{#5}
+                                \else\COPY{3}{#5}\fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORCOPY}	
+% \cs{VECTORCOPY}\parg{\#1,\#2}\parg{\#3,\#4}
+% stores \textit{\#1} and \textit{\#2} 
+% in \textit{\#3} and \textit{\#4}. 
+% 
+% \noindent\cs{VECTORCOPY}\parg{\#1,\#2,\#3}\parg{\#4,\#5\#6}
+% stores \textit{\#1}, \textit{\#2} and \textit{\#3} 
+% in \textit{\#4} and \textit{\#5} and \textit{\#6}. 
+%    \begin{macrocode}
+\def\@@VECTORCOPY(#1,#2)(#3,#4){%
+    \COPY{#1}{#3}\COPY{#2}{#4}}       
+    
+\def\@@@VECTORCOPY(#1,#2,#3)(#4,#5,#6){%
+    \COPY{#1}{#4}\COPY{#2}{#5}\COPY{#3}{#6}}    
+
+\def\VECTORCOPY(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORCOPY(#1)(#2)
+        \else \@@@VECTORCOPY(#1)(#2)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORGLOBALCOPY}	
+% \cs{VECTORGLOBALCOPY} is the global version of \cs{VECTORCOPY}  
+%    \begin{macrocode}
+\def\@@VECTORGLOBALCOPY(#1,#2)(#3,#4){%
+    \GLOBALCOPY{#1}{#3}\GLOBALCOPY{#2}{#4}}       
+    
+\def\@@@VECTORGLOBALCOPY(#1,#2,#3)(#4,#5,#6){%
+    \GLOBALCOPY{#1}{#4}\GLOBALCOPY{#2}{#5}\GLOBALCOPY{#3}{#6}}    
+
+\def\VECTORGLOBALCOPY(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORGLOBALCOPY(#1)(#2)
+        \else \@@@VECTORGLOBALCOPY(#1)(#2)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@OUTPUTVECTOR}
+%    \begin{macrocode}
+\def\@@OUTPUTVECTOR(#1,#2){%
+    \VECTORGLOBALCOPY(#1,#2)(\cctr@outa,\cctr@outb)
+    \endgroup\VECTORCOPY(\cctr@outa,\cctr@outb)(#1,#2)}
+    
+\def\@@@OUTPUTVECTOR(#1,#2,#3){%
+    \VECTORGLOBALCOPY(#1,#2,#3)(\cctr@outa,\cctr@outb,\cctr@outc)
+    \endgroup\VECTORCOPY(\cctr@outa,\cctr@outb,\cctr@outc)(#1,#2,#3)}
+
+\def\@OUTPUTVECTOR(#1){\VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@OUTPUTVECTOR(#1)
+        \else \@@@OUTPUTVECTOR(#1)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SCALARPRODUCT}	
+% Scalar product of two vectors.
+%    \begin{macrocode}
+\def\@@SCALARPRODUCT(#1,#2)(#3,#4)#5{%
+       \MULTIPLY{#1}{#3}{#5}
+       \MULTIPLY{#2}{#4}\cctr@tempa
+       \ADD{#5}{\cctr@tempa}{#5}}
+
+\def\@@@SCALARPRODUCT(#1,#2,#3)(#4,#5,#6)#7{%
+       \MULTIPLY{#1}{#4}{#7}
+       \MULTIPLY{#2}{#5}\cctr@tempa
+       \ADD{#7}{\cctr@tempa}{#7}       
+       \MULTIPLY{#3}{#6}\cctr@tempa
+       \ADD{#7}{\cctr@tempa}{#7}}
+       
+\def\SCALARPRODUCT(#1)(#2)#3{%
+        \begingroup
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARPRODUCT(#1)(#2){#3}
+        \else \@@@SCALARPRODUCT(#1)(#2){#3}\fi\@OUTPUTSOL{#3}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORADD}	
+% Sum of two vectors.
+%    \begin{macrocode}
+\def\@@VECTORADD(#1,#2)(#3,#4)(#5,#6){%
+       \ADD{#1}{#3}{#5}
+       \ADD{#2}{#4}{#6}}
+
+\def\@@@VECTORADD(#1,#2,#3)(#4,#5,#6)(#7,#8,#9){%
+       \ADD{#1}{#4}{#7}
+       \ADD{#2}{#5}{#8}
+       \ADD{#3}{#6}{#9}}
+                         
+\def\VECTORADD(#1)(#2)(#3){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORADD(#1)(#2)(#3)
+        \else \@@@VECTORADD(#1)(#2)(#3)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORSUB}	
+% Difference of two vectors.
+%    \begin{macrocode}                       
+\def\@@VECTORSUB(#1,#2)(#3,#4)(#5,#6){%
+       \VECTORADD(#1,#2)(-#3,-#4)(#5,#6)}
+       
+\def\@@@VECTORSUB(#1,#2,#3)(#4,#5,#6)(#7,#8,#9){%
+       \VECTORADD(#1,#2,#3)(-#4,-#5,-#6)(#7,#8,#9)}
+       
+\def\VECTORSUB(#1)(#2)(#3){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORSUB(#1)(#2)(#3)
+        \else \@@@VECTORSUB(#1)(#2)(#3)\fi}              
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORABSVALUE}	
+% Absolute value of a each entry of a vector.
+%    \begin{macrocode}
+\def\@@VECTORABSVALUE(#1,#2)(#3,#4){%
+       \ABSVALUE{#1}{#3}\ABSVALUE{#2}{#4}}
+
+\def\@@@VECTORABSVALUE(#1,#2,#3)(#4,#5,#6){%
+       \ABSVALUE{#1}{#4}\ABSVALUE{#2}{#5}\ABSVALUE{#3}{#6}}
+       
+\def\VECTORABSVALUE(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORABSVALUE(#1)(#2)
+        \else \@@@VECTORABSVALUE(#1)(#2)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SCALARVECTORPRODUCT}	
+% Scalar-vector product.
+%    \begin{macrocode}
+\def\@@SCALARVECTORPRODUCT#1(#2,#3)(#4,#5){%
+       \MULTIPLY{#1}{#2}{#4}
+       \MULTIPLY{#1}{#3}{#5}}
+       
+\def\@@@SCALARVECTORPRODUCT#1(#2,#3,#4)(#5,#6,#7){%
+       \MULTIPLY{#1}{#2}{#5}
+       \MULTIPLY{#1}{#3}{#6}
+       \MULTIPLY{#1}{#4}{#7}}
+       
+\def\SCALARVECTORPRODUCT#1(#2)(#3){%
+        \VECTORSIZE(#2){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARVECTORPRODUCT{#1}(#2)(#3)
+        \else \@@@SCALARVECTORPRODUCT{#1}(#2)(#3)\fi}        
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\VECTORNORM}	
+% Euclidean norm of a vector.
+%    \begin{macrocode}
+\def\VECTORNORM(#1)#2{%
+       \begingroup
+       \SCALARPRODUCT(#1)(#1){\cctr@temp}
+       \SQUAREROOT{\cctr@temp}{#2}\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\UNITVECTOR}	
+% Unitary vector parallel to a given vector.
+%    \begin{macrocode}
+\def\UNITVECTOR(#1)(#2){%
+       \begingroup
+       \VECTORNORM(#1){\cctr@tempa}
+       \DIVIDE{1}{\cctr@tempa}{\cctr@tempa}
+       \SCALARVECTORPRODUCT{\cctr@tempa}(#1)(#2)\@OUTPUTVECTOR(#2)}
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{Matrix operations}
+% Here, we need to define some internal macros 
+% to simulate commands with more than nine arguments. 
+% \begin{macro}{\@TDMATRIXCOPY}
+% This command copies a $3\times3$ matrix to the commands
+% \cs{cctr@solAA}, \cs{cctr@solAB}, \dots, \cs{cctr@solCC}.
+%    \begin{macrocode}        
+\def\@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \COPY{#1}{\cctr@solAA}
+       \COPY{#2}{\cctr@solAB}
+       \COPY{#3}{\cctr@solAC}
+       \COPY{#4}{\cctr@solBA}
+       \COPY{#5}{\cctr@solBB}
+       \COPY{#6}{\cctr@solBC}
+       \COPY{#7}{\cctr@solCA}
+       \COPY{#8}{\cctr@solCB}
+       \COPY{#9}{\cctr@solCC}}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\@TDMATRIXSOL}
+% This command copies  the commands
+% \cs{cctr@solAA}, \cs{cctr@solAB}, \dots, \cs{cctr@solCC}
+% to a $3\times3$ matrix.
+% This macro is used to store the results of a matrix operation.
+%    \begin{macrocode}  
+\def\@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \COPY{\cctr@solAA}{#1}
+       \COPY{\cctr@solAB}{#2}
+       \COPY{\cctr@solAC}{#3}
+       \COPY{\cctr@solBA}{#4}
+       \COPY{\cctr@solBB}{#5}
+       \COPY{\cctr@solBC}{#6}
+       \COPY{\cctr@solCA}{#7}
+       \COPY{\cctr@solCB}{#8}
+       \COPY{\cctr@solCC}{#9}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@TDMATRIXGLOBALSOL}
+% 
+%    \begin{macrocode}  
+\def\@TDMATRIXGLOBALSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \GLOBALCOPY{\cctr@solAA}{#1}
+       \GLOBALCOPY{\cctr@solAB}{#2}
+       \GLOBALCOPY{\cctr@solAC}{#3}
+       \GLOBALCOPY{\cctr@solBA}{#4}
+       \GLOBALCOPY{\cctr@solBB}{#5}
+       \GLOBALCOPY{\cctr@solBC}{#6}
+       \GLOBALCOPY{\cctr@solCA}{#7}
+       \GLOBALCOPY{\cctr@solCB}{#8}
+       \GLOBALCOPY{\cctr@solCC}{#9}}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\@TDMATRIXNOSOL}
+% This command undefines a $3\times3$ matrix
+% when a matrix problem has no solution.
+%    \begin{macrocode}         
+\def\@TDMATRIXNOSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%       
+          \let#1\undefined
+          \let#2\undefined
+          \let#3\undefined
+          \let#4\undefined
+          \let#5\undefined
+          \let#6\undefined
+          \let#7\undefined
+          \let#8\undefined
+          \let#9\undefined
+          }
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\@@TDMATRIXSOL}
+% This command stores or undefines the solution.
+%    \begin{macrocode}  
+\def\@@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){% 
+       \ifx\cctr@solAA\undefined
+          \@TDMATRIXNOSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9)%
+       \else 
+          \@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9)\fi}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\@NUMBERSOL}
+% This command stores the scalar solution of a matrix operation.
+%    \begin{macrocode}   
+\def\@NUMBERSOL#1{\COPY{\cctr@sol}{#1}} 
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\MATRIXSIZE}
+% Size ($2$ or $3$) of a matrix.
+%    \begin{macrocode} 
+\def\MATRIXSIZE(#1)#2{\expandafter\@MATRIXSIZE(#1;;){#2}}
+\def\@MATRIXSIZE(#1;#2;#3;#4)#5{\ifx$#3$\COPY{2}{#5}
+                                \else\COPY{3}{#5}\fi\ignorespaces}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\MATRIXCOPY}
+% Store a matrix in 4 or 9 commands.
+%    \begin{macrocode} 
+\def\@@MATRIXCOPY(#1,#2;#3,#4)(#5,#6;#7,#8){%
+    \COPY{#1}{#5}\COPY{#2}{#6}\COPY{#3}{#7}\COPY{#4}{#8}}
+
+\def\@@@MATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+     \@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+     \@TDMATRIXSOL}
+
+\def\MATRIXCOPY(#1)(#2){%
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXCOPY(#1)(#2)
+        \else \@@@MATRIXCOPY(#1)(#2)\fi} 
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\MATRIXGLOBALCOPY}
+% Global version of \cs{MATRIXCOPY}.
+%    \begin{macrocode} 
+\def\@@MATRIXGLOBALCOPY(#1,#2;#3,#4)(#5,#6;#7,#8){%
+    \GLOBALCOPY{#1}{#5}\GLOBALCOPY{#2}{#6}\GLOBALCOPY{#3}{#7}\GLOBALCOPY{#4}{#8}}
+
+\def\@@@MATRIXGLOBALCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+     \@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+     \@TDMATRIXGLOBALSOL}
+
+\def\MATRIXGLOBALCOPY(#1)(#2){%
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXGLOBALCOPY(#1)(#2)
+        \else \@@@MATRIXGLOBALCOPY(#1)(#2)\fi} 
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@OUTPUTMATRIX}
+%    \begin{macrocode}
+\def\@@OUTPUTMATRIX(#1,#2;#3,#4){%
+    \MATRIXGLOBALCOPY(#1,#2;#3,#4)(\cctr@outa,\cctr@outb;\cctr@outc,\cctr@outd)
+    \endgroup\MATRIXCOPY(\cctr@outa,\cctr@outb;\cctr@outc,\cctr@outd)(#1,#2;#3,#4)}
+    
+\def\@@@OUTPUTMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+    \MATRIXGLOBALCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)(%
+        \cctr@outa,\cctr@outb,\cctr@outc;
+        \cctr@outd,\cctr@oute,\cctr@outf;
+        \cctr@outg,\cctr@outh,\cctr@outi)
+    \endgroup\MATRIXCOPY(%
+        \cctr@outa,\cctr@outb,\cctr@outc;
+        \cctr@outd,\cctr@oute,\cctr@outf;
+        \cctr@outg,\cctr@outh,\cctr@outi)(#1,#2,#3;#4,#5,#6;#7,#8,#9)}   
+
+\def\@OUTPUTMATRIX(#1){\MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@OUTPUTMATRIX(#1)
+        \else \@@@OUTPUTMATRIX(#1)\fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TRANSPOSEMATRIX}
+% Matrix transposition.
+%    \begin{macrocode}         
+\def\@@TRANSPOSEMATRIX(#1,#2;#3,#4)(#5,#6;#7,#8){%
+       \COPY{#1}{#5}\COPY{#3}{#6}\COPY{#2}{#7}\COPY{#4}{#8}}
+
+\def\@@@TRANSPOSEMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \@TDMATRIXCOPY(#1,#4,#7;#2,#5,#8;#3,#6,#9)      
+       \@TDMATRIXSOL}
+
+\def\TRANSPOSEMATRIX(#1)(#2){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@TRANSPOSEMATRIX(#1)(#2)
+        \else \@@@TRANSPOSEMATRIX(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+%    \end{macrocode}
+% \end{macro}         
+% \begin{macro}{\MATRIXADD}
+% Sum of two matrices.
+%    \begin{macrocode} 
+\def\@@MATRIXADD(#1;#2)(#3;#4)(#5,#6;#7,#8){%
+       \VECTORADD(#1)(#3)(#5,#6)
+       \VECTORADD(#2)(#4)(#7,#8)}
+       
+\def\@@@MATRIXADD(#1;#2;#3)(#4;#5;#6){%
+       \VECTORADD(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORADD(#2)(#5)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORADD(#3)(#6)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+       
+\def\MATRIXADD(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXADD(#1)(#2)(#3)
+        \else \@@@MATRIXADD(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+%    \end{macrocode}
+% \end{macro}                       
+% \begin{macro}{\MATRIXSUB}
+% Difference of two matrices.
+%    \begin{macrocode}                 
+\def\@@MATRIXSUB(#1;#2)(#3;#4)(#5,#6;#7,#8){%
+       \VECTORSUB(#1)(#3)(#5,#6)
+       \VECTORSUB(#2)(#4)(#7,#8)}
+       
+\def\@@@MATRIXSUB(#1;#2;#3)(#4;#5;#6){%
+       \VECTORSUB(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORSUB(#2)(#5)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORSUB(#3)(#6)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL} 
+       
+\def\MATRIXSUB(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXSUB(#1)(#2)(#3)
+        \else \@@@MATRIXSUB(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)} 
+%    \end{macrocode}
+% \end{macro}                     
+% \begin{macro}{\MATRIXABSVALUE}
+% Absolute value (of each entry) of a matrix.
+%    \begin{macrocode}  
+\def\@@MATRIXABSVALUE(#1;#2)(#3;#4){%
+       \VECTORABSVALUE(#1)(#3)\VECTORABSVALUE(#2)(#4)}
+
+\def\@@@MATRIXABSVALUE(#1;#2;#3)(#4;#5;#6){%
+       \VECTORABSVALUE(#1)(#4)\VECTORABSVALUE(#2)(#5)\VECTORABSVALUE(#3)(#6)}
+       
+\def\MATRIXABSVALUE(#1)(#2){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXABSVALUE(#1)(#2)
+        \else \@@@MATRIXABSVALUE(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+%    \end{macrocode}
+% \end{macro} 
+
+% \begin{macro}{\MATRIXVECTORPRODUCT}
+% Matrix-vector product.
+%    \begin{macrocode} 
+\def\@@MATRIXVECTORPRODUCT(#1;#2)(#3)(#4,#5){%
+       \SCALARPRODUCT(#1)(#3){#4}
+       \SCALARPRODUCT(#2)(#3){#5}}
+              
+\def\@@@MATRIXVECTORPRODUCT(#1;#2;#3)(#4)(#5,#6,#7){%
+       \SCALARPRODUCT(#1)(#4){#5}
+       \SCALARPRODUCT(#2)(#4){#6}
+       \SCALARPRODUCT(#3)(#4){#7}}
+       
+\def\MATRIXVECTORPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXVECTORPRODUCT(#1)(#2)(#3)
+        \else \@@@MATRIXVECTORPRODUCT(#1)(#2)(#3)\fi\@OUTPUTVECTOR(#3)}             
+%    \end{macrocode}
+% \end{macro}
+
+
+% \begin{macro}{\VECTORMATRIXPRODUCT}
+% Vector-matrix product.
+%    \begin{macrocode} 
+\def\@@VECTORMATRIXPRODUCT(#1)(#2,#3;#4,#5)(#6,#7){%
+       \SCALARPRODUCT(#1)(#2,#4){#6}
+       \SCALARPRODUCT(#1)(#3,#5){#7}}
+      
+\def\@@@VECTORMATRIXPRODUCT(#1,#2,#3)(#4;#5;#6)(#7){%
+       \SCALARVECTORPRODUCT{#1}(#4)(#7)
+       \SCALARVECTORPRODUCT{#2}(#5)(\cctr@tempa,\cctr@tempb,\cctr@tempc)
+       \VECTORADD(#7)(\cctr@tempa,\cctr@tempb,\cctr@tempc)(#7)
+       \SCALARVECTORPRODUCT{#3}(#6)(\cctr@tempa,\cctr@tempb,\cctr@tempc)
+       \VECTORADD(#7)(\cctr@tempa,\cctr@tempb,\cctr@tempc)(#7)}
+       
+\def\VECTORMATRIXPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORMATRIXPRODUCT(#1)(#2)(#3)
+        \else \@@@VECTORMATRIXPRODUCT(#1)(#2)(#3)\fi\@OUTPUTVECTOR(#3)}            
+%    \end{macrocode}
+% \end{macro} 
+
+
+% \begin{macro}{\SCALARMATRIXPRODUCT}
+% Scalar-matrix product.
+%    \begin{macrocode} 
+\def\@@SCALARMATRIXPRODUCT#1(#2;#3)(#4,#5;#6,#7){%
+       \SCALARVECTORPRODUCT{#1}(#2)(#4,#5)
+       \SCALARVECTORPRODUCT{#1}(#3)(#6,#7)}  
+       
+\def\@@@SCALARMATRIXPRODUCT#1(#2;#3;#4){%
+       \SCALARVECTORPRODUCT{#1}(#2)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \SCALARVECTORPRODUCT{#1}(#3)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \SCALARVECTORPRODUCT{#1}(#4)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}  
+       
+\def\SCALARMATRIXPRODUCT#1(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#2){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARMATRIXPRODUCT{#1}(#2)(#3)
+        \else \@@@SCALARMATRIXPRODUCT{#1}(#2)(#3)\fi\@OUTPUTMATRIX(#3)}                 
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\MATRIXPRODUCT}
+% Product of two matrices.
+%    \begin{macrocode} 
+\def\@@MATRIXPRODUCT(#1)(#2,#3;#4,#5)(#6,#7;#8,#9){%
+       \MATRIXVECTORPRODUCT(#1)(#2,#4)(#6,#8)
+       \MATRIXVECTORPRODUCT(#1)(#3,#5)(#7,#9)}
+       
+\def\@@@MATRIXPRODUCT(#1;#2;#3)(#4){%
+       \VECTORMATRIXPRODUCT(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORMATRIXPRODUCT(#2)(#4)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORMATRIXPRODUCT(#3)(#4)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+
+\def\MATRIXPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXPRODUCT(#1)(#2)(#3)
+        \else \@@@MATRIXPRODUCT(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\DETERMINANT}
+% Determinant of a  matrix.
+%    \begin{macrocode} 
+\def\@@DETERMINANT(#1,#2;#3,#4)#5{%
+       \MULTIPLY{#1}{#4}{#5}
+       \MULTIPLY{#2}{#3}{\cctr@tempa}
+       \SUBTRACT{#5}{\cctr@tempa}{#5}}
+       
+\def\@@@DETERMINANT(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \DETERMINANT(#5,#6;#8,#9){\cctr@det}\MULTIPLY{#1}{\cctr@det}{\cctr@sol}
+       \DETERMINANT(#6,#4;#9,#7){\cctr@det}\MULTIPLY{#2}{\cctr@det}{\cctr@det}
+                                        \ADD{\cctr@sol}{\cctr@det}{\cctr@sol}
+       \DETERMINANT(#4,#5;#7,#8){\cctr@det}\MULTIPLY{#3}{\cctr@det}{\cctr@det}
+                                        \ADD{\cctr@sol}{\cctr@det}{\cctr@sol}
+       \@NUMBERSOL}       
+
+\def\DETERMINANT(#1)#2{%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@DETERMINANT(#1){#2}
+        \else \@@@DETERMINANT(#1){#2}\fi\@OUTPUTSOL{#2}}
+%    \end{macrocode}
+% \end{macro} 
+% \begin{macro}{\INVERSEMATRIX}
+% Inverse of a matrix.
+%    \begin{macrocode} 
+\def\@@INVERSEMATRIX(#1,#2;#3,#4)(#5,#6;#7,#8){%
+       \ifdim \cctr@@det\p@ <\cctr@epsilon  % Matrix is singular 
+          \let#5\undefined
+          \let#6\undefined
+          \let#7\undefined
+          \let#8\undefined
+          \cctr@Warnsingmatrix{#1}{#2}{#3}{#4}%            
+       \else \COPY{#1}{#8} 
+          \COPY{#4}{#5}
+          \MULTIPLY{-1}{#3}{#7}
+          \MULTIPLY{-1}{#2}{#6}
+          \DIVIDE{1}{\cctr@det}{\cctr@det}
+          \SCALARMATRIXPRODUCT{\cctr@det}(#5,#6;#7,#8)(#5,#6;#7,#8)
+       \fi}
+
+\def\@@@INVERSEMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+              \ifdim \cctr@@det\p@ <\cctr@epsilon  % Matrix is singular 
+          \@TDMATRIXNOSOL(\cctr@solAA,\cctr@solAB,\cctr@solAC;
+                          \cctr@solBA,\cctr@solBB,\cctr@solBC;
+                          \cctr@solCA,\cctr@solCB,\cctr@solCC)
+          \cctr@WarnsingTDmatrix{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}{#9}%        
+       \else 
+          \@ADJMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solAA,\cctr@solAB,\cctr@solAC)(%
+                                   \cctr@solAA,\cctr@solAB,\cctr@solAC)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solBA,\cctr@solBB,\cctr@solBC)(%
+                                   \cctr@solBA,\cctr@solBB,\cctr@solBC)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solCA,\cctr@solCB,\cctr@solCC)(%
+                                   \cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \fi
+       \@@TDMATRIXSOL}
+
+\def\@SCLRDIVVECT#1(#2,#3,#4)(#5,#6,#7){%
+             \DIVIDE{#2}{#1}{#5}\DIVIDE{#3}{#1}{#6}\DIVIDE{#4}{#1}{#7}}
+
+\def\@ADJMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+          \DETERMINANT(#5,#6;#8,#9){\cctr@solAA}
+          \DETERMINANT(#6,#4;#9,#7){\cctr@solBA}
+          \DETERMINANT(#4,#5;#7,#8){\cctr@solCA}
+          \DETERMINANT(#8,#9;#2,#3){\cctr@solAB}
+          \DETERMINANT(#1,#3;#7,#9){\cctr@solBB}
+          \DETERMINANT(#2,#1;#8,#7){\cctr@solCB}
+          \DETERMINANT(#2,#3;#5,#6){\cctr@solAC}
+          \DETERMINANT(#3,#1;#6,#4){\cctr@solBC}
+          \DETERMINANT(#1,#2;#4,#5){\cctr@solCC}}
+                    
+\def\INVERSEMATRIX(#1)(#2){%
+        \begingroup
+        \DETERMINANT(#1){\cctr@det}
+        \ABSVALUE{\cctr@det}{\cctr@@det}
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@INVERSEMATRIX(#1)(#2)
+        \else 
+           \@@@INVERSEMATRIX(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\SOLVELINEARSYSTEM}
+% Solving a linear system (two equations and two unknowns
+% or three equations and three unknowns).
+%    \begin{macrocode} 
+\def\@INCSYS#1#2{\cctr@WarnIncLinSys
+       \let#1\undefined\let#2\undefined}
+       
+\def\@SOLPART#1#2#3#4{\cctr@WarnIndLinSys
+                      \DIVIDE{#1}{#2}{#3}
+                      \COPY{0}{#4}}
+
+\def\@TDINCSYS(#1,#2,#3){\cctr@WarnIncTDLinSys
+                         \let#1\undefined
+                         \let#2\undefined
+                         \let#3\undefined}
+
+\def\@@SOLVELINEARSYSTEM(#1,#2;#3,#4)(#5,#6)(#7,#8){%
+        \DETERMINANT(#1,#2;#3,#4)\cctr@deta
+        \DETERMINANT(#5,#2;#6,#4)\cctr@detb
+        \DETERMINANT(#1,#5;#3,#6)\cctr@detc
+        \ABSVALUE{\cctr@deta}{\cctr@@deta}
+        \ABSVALUE{\cctr@detb}{\cctr@@detb}
+        \ABSVALUE{\cctr@detc}{\cctr@@detc}
+        \ifdim \cctr@@deta\p@>\cctr@epsilon% Regular matrix. Determinate system
+           \DIVIDE{\cctr@detb}{\cctr@deta}{#7}
+           \DIVIDE{\cctr@detc}{\cctr@deta}{#8}
+        \else  % Singular matrix    \cctr@deta=0 
+           \ifdim \cctr@@detb\p@>\cctr@epsilon% Incompatible system
+              \@INCSYS#7#8
+           \else   
+              \ifdim \cctr@@detc\p@>\cctr@epsilon% Incompatible system
+                 \@INCSYS#7#8
+              \else
+                 \MATRIXABSVALUE(#1,#2;#3,#4)(\cctr@tempa,\cctr@tempb;
+                                              \cctr@tempc,\cctr@tempd)
+                 \ifdim \cctr@tempa\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                    \@SOLPART{#5}{#1}{#7}{#8}
+                 \else
+                    \ifdim \cctr@tempb\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                       \@SOLPART{#5}{#2}{#8}{#7}
+                    \else
+                       \ifdim \cctr@tempc\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                          \@SOLPART{#6}{#3}{#7}{#8}
+                       \else
+                          \ifdim \cctr@tempd\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                             \@SOLPART{#6}{#4}{#8}{#7}
+                          \else
+                             \VECTORNORM(#5,#6){\cctr@tempa}
+                             \ifdim \cctr@tempa\p@ > \cctr@epsilon
+                                               % Incompatible system
+                                \@INCSYS#7#8
+                             \else 
+                                   \cctr@WarnZeroLinSys
+                                   \COPY{0}{#7}\COPY{0}{#8}
+                                               % 0x=0 Indeterminate system
+        \fi\fi\fi\fi\fi\fi\fi\fi}
+
+\def\@@@SOLVELINEARSYSTEM(#1)(#2)(#3){%
+       \DETERMINANT(#1){\cctr@det}
+       \ABSVALUE{\cctr@det}{\cctr@@det}
+       \ifdim\cctr@@det\p@<\cctr@epsilon
+          \@TDINCSYS(#3)
+          \else
+             \@ADJMATRIX(#1)
+             \MATRIXVECTORPRODUCT(\cctr@solAA,\cctr@solAB,\cctr@solAC;
+                                  \cctr@solBA,\cctr@solBB,\cctr@solBC;
+                                  \cctr@solCA,\cctr@solCB,\cctr@solCC)(#2)(#3)
+             \@SCLRDIVVECT{\cctr@det}(#3)(#3)
+          \fi}
+       
+\def\SOLVELINEARSYSTEM(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SOLVELINEARSYSTEM(#1)(#2)(#3)
+        \else 
+           \@@@SOLVELINEARSYSTEM(#1)(#2)(#3)
+        \fi\@OUTPUTVECTOR(#3)}
+%    \end{macrocode}
+% \end{macro}                 
+% \subsection*{Predefined numbers}
+% \begin{macro}{\numberPI} 
+% The number $\pi$
+%    \begin{macrocode}
+\def\numberPI{3.14159}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberTWOPI}
+% $2\pi$
+%    \begin{macrocode}
+\MULTIPLY{\numberPI}{2}{\numberTWOPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberHALFPI}
+% $\pi/2$
+%    \begin{macrocode}
+\DIVIDE{\numberPI}{2}{\numberHALFPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberTHREEHALFPI}
+% $3\pi/2$
+%    \begin{macrocode}
+\MULTIPLY{\numberPI}{1.5}{\numberTHREEHALFPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberTHIRDPI}
+% $\pi/3$
+%    \begin{macrocode}
+\DIVIDE{\numberPI}{3}{\numberTHIRDPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberQUARTERPI}
+% $\pi/4$
+%    \begin{macrocode}
+\DIVIDE{\numberPI}{4}{\numberQUARTERPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberFIFTHPI}
+% $\pi/5$
+%    \begin{macrocode}
+\DIVIDE{\numberPI}{5}{\numberFIFTHPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberSIXTHPI}
+% $\pi/6$
+%    \begin{macrocode}
+\DIVIDE{\numberPI}{6}{\numberSIXTHPI}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberE}
+% The number $\mathrm e$ 
+%    \begin{macrocode}
+\def\numberE{2.71828}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberINVE}
+% $1/{\mathrm e}$ 
+%    \begin{macrocode}
+\DIVIDE{1}{\numberE}{\numberINVE}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberETWO}
+% $\mathrm e^2$
+%    \begin{macrocode}
+\SQUARE{\numberE}{\numberETWO}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberINVETWO}
+% $1/{\mathrm e^2}$
+%    \begin{macrocode}
+\SQUARE{\numberINVE}{\numberINVETWO}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberLOGTEN}
+% $\log 10$
+%    \begin{macrocode}
+\def\numberLOGTEN{2.30258}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberGOLD}
+% The golden ratio $\phi$
+%    \begin{macrocode}
+\def\numberGOLD{1.61803}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberINVGOLD}
+% $1/\phi$
+%    \begin{macrocode}
+\def\numberINVGOLD{0.61803}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberSQRTTWO}
+% $\sqrt 2$
+%    \begin{macrocode}
+\def\numberSQRTTWO{1.41421}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberSQRTTHREE}
+% $\sqrt 3$
+%    \begin{macrocode}
+\def\numberSQRTTHREE{1.73205}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberSQRTFIVE}
+% $\sqrt 5$
+%    \begin{macrocode}
+\def\numberSQRTFIVE{2.23607}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberCOSXLV}
+% $\cos 45^{\mathrm o}$ (or $\cos \pi/4$)
+%    \begin{macrocode}
+\def\numberCOSXLV{0.70711}
+%    \end{macrocode}
+% \end{macro}                 
+% \begin{macro}{\numberCOSXXX}
+% $\cos 30^{\mathrm o}$ (or $\cos \pi/6$)
+%    \begin{macrocode}
+\def\numberCOSXXX{0.86603}
+%    \end{macrocode}
+% \end{macro}
+%    \begin{macrocode}
+%</calculator>
+%    \end{macrocode}             
+%
+% \section{Implementation (\textsf{calculator})}
+%    \begin{macrocode}
+%<*calculus>
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{calculus}
+   [2012/06/10 v.1.0a]
+%    \end{macrocode}   
+% This package requires the calculator package. 
+%    \begin{macrocode}  
+\RequirePackage{calculator}
+%    \end{macrocode}
+% \subsection{Error and info messages}
+% \subsubsection*{For scalar functions}
+%
+% Error message to be issued when you attempt to define, with \cs{newfunction},
+% an already defined command:
+%    \begin{macrocode}
+\def\ccls@ErrorFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1 command as a 
+         function\MessageBreak
+         please, use the \noexpand\renewfunction command}}
+%    \end{macrocode}
+% Error message to be issued when you attempt to redefine, 
+% with \cs{renewfunction}, an undefined command:
+%    \begin{macrocode}
+\def\ccls@ErrorFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence is not currently defined\MessageBreak
+         If you want to define the \noexpand#1 command as a function\MessageBreak
+         please, use the \noexpand\newfunction command}}
+%    \end{macrocode}
+% Info message to be issued when \cs{ensurefunction} does not changes
+% an already defined command:
+%    \begin{macrocode}
+\def\ccls@InfoFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurefunction command will not redefine it}}
+%    \end{macrocode}
+% \subsubsection*{For polar functions}
+%    \begin{macrocode}
+\def\ccls@ErrorPFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1
+         command as a polar function\MessageBreak
+         please, use the \noexpand\renewpolarfunction command}}
+
+\def\ccls@ErrorPFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence 
+         is not currently defined.\MessageBreak
+         If you want to define the \noexpand#1 command as a polar
+         function\MessageBreak
+         please, use the \noexpand\newpolarfunction command}}
+
+\def\ccls@InfoPFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurepolarfunction command does not redefine it}}
+%    \end{macrocode}      
+% \subsubsection*{For vector functions}
+%    \begin{macrocode}
+\def\ccls@ErrorVFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1 command as a vector
+         function\MessageBreak
+         please, use the \noexpand\renewvectorfunction command}}
+
+\def\ccls@ErrorVFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence is not currently
+         defined.\MessageBreak
+         If you want to define the \noexpand#1 command as a vector
+         function\MessageBreak
+         please, use the \noexpand\newvectorfunction command}}
+
+\def\ccls@InfoVFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurevectorfunction command does not redefine it}}
+%    \end{macrocode}
+% \subsection{New functions}
+% \subsubsection*{New scalar functions}
+%
+% \begin{macro}{\newfunction}
+% The \cs{newfunction\{\#1\}\{\#2\}} instruction defines
+% a new function called \#1.
+% \#2 is the list of instructions to calculate the function
+% \cs{y} and his derivative \cs{Dy} from the \cs{t} variable.
+%    \begin{macrocode}
+\def\newfunction#1#2{%  
+       \ifx #1\undefined
+         \ccls@deffunction{#1}{#2}
+       \else
+          \ccls@ErrorFuncDef{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewfunction}
+% \cs{renewfunction} redefines \#1, as a new function,
+% if this command is already defined.
+%    \begin{macrocode}
+\def\renewfunction#1#2{% 
+       \ifx #1\undefined
+          \ccls@ErrorFuncUnDef{#1}
+       \else
+          \ccls@deffunction{#1}{#2}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensurefunction}
+% \cs{ensurefunction} defines the new function \#1
+% (only if this macro is undefined).
+%    \begin{macrocode}
+\def\ensurefunction#1#2{%
+       \ifx #1\undefined\ccls@deffunction{#1}{#2}
+       \else
+          \ccls@InfoFuncEns{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forcefunction}
+% \cs{forcefunction} defines (if undefined) or redefines (if defined)
+% the new function \#1.
+%    \begin{macrocode}
+\def\forcefunction#1#2{%
+       \ccls@deffunction{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@deffunction}
+% The private \cs{ccls@deffunction} command makes the real work.
+% The new functions will have three arguments:
+% \#\#1, a number, \#\#2, the value of the new function in that number,
+% and \#\#3, the derivative.
+%    \begin{macrocode} 
+\def\ccls@deffunction#1#2{%
+    \def#1##1##2##3{%    
+             \begingroup
+             \def\t{##1}%
+                  #2
+                 \xdef##2{\y}%
+                 \xdef##3{\Dy}%
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{New polar functions}
+%
+% \begin{macro}{\newpolarfunction} 
+% The \cs{newpolarfunction\{\#1\}\{\#2\}} instruction defines
+% a new polar function called \#1.
+% \#2 is the list of instructions to calculate the radius \cs{r}
+% and his derivative \cs{Dr} from the \cs{t} arc variable.
+%    \begin{macrocode}
+\def\newpolarfunction#1#2{%
+       \ifx #1\undefined
+         \ccls@defpolarfunction{#1}{#2}
+       \else
+          \ccls@ErrorPFuncDef{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewpolarfunction} 
+% \cs{renewpolarfunction} redefines \#1 if already defined.
+%    \begin{macrocode}
+\def\renewpolarfunction#1#2{% 
+       \ifx #1\undefined
+          \ccls@ErrorPFuncUnDef{#1}
+       \else
+          \ccls@defpolarfunction{#1}{#2}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensurepolarfunction} 
+% \cs{ensurepolarfunction} defines (only if undefined) \#1.
+%    \begin{macrocode}
+\def\ensurepolarfunction#1#2{%
+       \ifx #1\undefined\ccls@defpolarfunction{#1}{#2}
+       \else
+          \ccls@InfoPFuncEns{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forcepolarfunction} 
+% \cs{forcepolarfunction} defines (if undefined) or redefines (if defined) \#1.
+%    \begin{macrocode}
+\def\forcepolarfunction#1#2{%
+       \ccls@defpolarfunction{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@defpolarfunction}
+% The private \cs{ccls@defpolarfunction} command makes the real work.
+% The new functions will have three arguments:
+% \#\#1, a number (the polar radius), 
+% \#\#2, \#\#3, \#\#4, and \#\#5, the x and y component functions and
+% its derivatives at \#\#1.
+%    \begin{macrocode} 
+\def\ccls@defpolarfunction#1#2{%
+       \def#1##1##2##3##4##5{%  
+       \begingroup
+         \def\t{##1}
+       #2
+       \COS{\t}\ccls@cost
+       \MULTIPLY\r\ccls@cost{\x}
+       \SIN{\t}\ccls@sint
+       \MULTIPLY\r\ccls@sint{\y}
+       \MULTIPLY\ccls@cost\Dr\Dx
+       \SUBTRACT{\Dx}{\y}{\Dx}
+       \MULTIPLY\ccls@sint\Dr\Dy
+       \ADD{\Dy}{\x}{\Dy}
+       \xdef##2{\x}
+       \xdef##3{\Dx}
+       \xdef##4{\y}
+       \xdef##5{\Dy}       
+       \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{New vector functions}
+%
+% \begin{macro}{\newvectorfunction} 
+% The \cs{newvectorfunction\{\#1\}\{\#2\}} instruction defines 
+% a new vector (parametric) function called \#1.
+% \#2 is the list of instructions to calculate 
+% \cs{x}, \cs{y}, \cs{Dx} and \cs{Dy} from the \cs{t} arc variable.
+%    \begin{macrocode}
+\def\newvectorfunction#1#2{%
+       \ifx #1\undefined
+         \ccls@defvectorfunction{#1}{#2}
+       \else
+          \ccls@ErrorVFuncDef{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewvectorfunction} 
+% \cs{renewvectorfunction} redefines \#1 if already defined.
+%    \begin{macrocode}
+\def\renewvectorfunction#1#2{% 
+       \ifx #1\undefined
+          \ccls@ErrorVFuncUnDef{#1}
+       \else
+          \ccls@defvectorfunction{#1}{#2}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensurevectorfunction} 
+% \cs{ensurevectorfunction} defines (only if undefined) \#1.
+%    \begin{macrocode}
+\def\ensurevectorfunction#1#2{%
+       \ifx #1\undefined\ccls@defvectorfunction{#1}{#2}
+       \else
+          \ccls@InfoVFuncEns{#1}
+       \fi}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forcevectorfunction} 
+% \cs{forcevectorfunction} defines (if undefined)
+% or redefines (if defined) \#1.
+%    \begin{macrocode}
+\def\forcevectorfunction#1#2{%
+       \ccls@defvectorfunction{#1}{#2}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@defvectorfunction}
+% The private \cs{ccls@defvectorfunction} command makes the real work.
+% The new functions will have three arguments:
+% \#\#1, a number, 
+% \#\#2, \#\#3, \#\#4, and \#\#5, the x and y component functions
+% and its derivatives at \#\#1.
+%    \begin{macrocode} 
+\def\ccls@defvectorfunction#1#2{%
+       \def#1##1##2##3##4##5{%
+       \begingroup
+         \def\t{##1}
+       #2       
+       \xdef##2{\x}
+       \xdef##3{\Dx}
+       \xdef##4{\y}
+       \xdef##5{\Dy}
+       \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Polynomials}
+% \subsubsection*{Linear (first degreee) polynomials}
+%
+% \begin{macro}{\newlpoly}
+% The \cs{newlpoly\{\#1\}\{\#2\}\{\#3\}} instruction defines
+% the linear polynomial
+% 
+% $\#1=\#2+\#3t$.
+%    \begin{macrocode}
+\def\newlpoly#1#2#3{%    
+    \newfunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewlpoly}
+% We define also the \cs{renewlpoly}, \cs{ensurelpoly}
+% and \cs{forcelpoly} variants.
+%    \begin{macrocode}
+\def\renewlpoly#1#2#3{%    
+    \renewfunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensurelpoly}
+%    \begin{macrocode}
+\def\ensurelpoly#1#2#3{%    
+    \ensurefunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forcelpoly}
+%    \begin{macrocode}      
+\def\forcelpoly#1#2#3{%    
+    \forcefunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}  
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@lpoly}
+% The \cs{ccls@lpoly\{\#1\}\{\#2\}} macro defines the new polynomial function.
+%    \begin{macrocode}   
+\def\ccls@lpoly#1#2{%
+        \MULTIPLY{#2}{\t}{\y}
+        \ADD{\y}{#1}{\y}
+        \COPY{#2}{\Dy}}   
+%    \end{macrocode}           
+% \end{macro}     
+% \subsubsection*{Quadratic polynomials}
+%
+% \begin{macro}{\newqpoly}
+% The \cs{newqpoly\{\#1\}\{\#2\}\{\#3\}\{\#4\}} 
+% instruction defines the quadratic polynomial 
+%
+% $\#1=\#2+\#3t+\#4t^2$.
+%    \begin{macrocode}
+\def\newqpoly#1#2#3#4{%  
+    \newfunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewqpoly}
+%    \begin{macrocode} 
+\def\renewqpoly#1#2#3#4{%   
+    \renewfunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensureqpoly}
+%    \begin{macrocode} 
+\def\ensureqpoly#1#2#3#4{%    
+    \ensurefunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forceqpoly}
+%    \begin{macrocode}        
+\def\forceqpoly#1#2#3#4{%    
+    \forcefunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}        
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@qpoly}
+% The \cs{ccls@qpoly\{\#1\}\{\#2\}} macro defines the new polynomial function.
+%    \begin{macrocode}
+\def\ccls@qpoly#1#2#3{%
+        \MULTIPLY{\t}{#3}{\y}
+           \MULTIPLY{2}{\y}{\Dy}
+           \ADD{#2}{\Dy}{\Dy}
+        \ADD{#2}{\y}{\y}
+        \MULTIPLY{\t}{\y}{\y}
+        \ADD{#1}{\y}{\y}}         
+%    \end{macrocode}
+% \end{macro}
+% \subsubsection*{Cubic polynomials}
+%
+% \begin{macro}{\newcpoly}
+% The \cs{newcpoly\{\#1\}\{\#2\}\{\#3\}\{\#4\}\{\#5\}} 
+% instruction defines the cubic polynomial 
+%
+% $\#1=\#2+\#3t+\#4t^2+\#5t^3$.
+%    \begin{macrocode}
+\def\newcpoly#1#2#3#4#5{%    
+    \newfunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\renewcpoly}
+%    \begin{macrocode} 
+\def\renewcpoly#1#2#3#4#5{%   
+    \renewfunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ensurecpoly}
+%    \begin{macrocode} 
+\def\ensurecpoly#1#2#3#4#5{%   
+    \ensurefunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\forcecpoly}
+%    \begin{macrocode} 
+\def\forcecpoly#1#2#3#4#5{%   
+    \forcefunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ccls@cpoly}
+% The \cs{ccls@cpoly\{\#1\}\{\#2\}} macro defines the new polynomial function.
+%    \begin{macrocode}       
+\def\ccls@cpoly#1#2#3#4{%
+        \MULTIPLY{\t}{#4}{\y}
+           \MULTIPLY{3}{\y}{\Dy}
+        \ADD{#3}{\y}{\y}
+           \MULTIPLY{2}{#3}{\ccls@temp}    
+           \ADD{\ccls@temp}{\Dy}{\Dy}
+        \MULTIPLY{\t}{\y}{\y}   
+           \MULTIPLY{\t}{\Dy}{\Dy} 
+        \ADD{#2}{\y}{\y}   
+           \ADD{#2}{\Dy}{\Dy}
+        \MULTIPLY{\t}{\y}{\y}   
+        \ADD{#1}{\y}{\y}     
+        }  
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Elementary functions}
+% \begin{macro}{\ONEfunction}
+% The \cs{ONEfunction}: $y(t)=1$, $y'(t)=0$
+%    \begin{macrocode}               
+\newfunction{\ONEfunction}{%
+      \COPY{1}{\y}
+      \COPY{0}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\ZEROfunction}
+% The \cs{ZEROfunction}: $y(t)=0$, $y'(t)=0$
+%    \begin{macrocode}
+\newfunction{\ZEROfunction}{%
+      \COPY{0}{\y}
+      \COPY{0}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\IDENTITYfunction}
+% The \cs{IDENTITYfunction}: $y(t)=t$, $y'(t)=1$
+%    \begin{macrocode}
+\newfunction{\IDENTITYfunction}{%
+      \COPY{\t}{\y}
+      \COPY{1}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\RECIPROCALfunction}
+% The \cs{RECIPROCALfunction}: $y(t)=1/t$, $y'(t)=-1/t^2$
+%    \begin{macrocode}
+\newfunction{\RECIPROCALfunction}{%
+      \DIVIDE{1}{\t}{\y}
+      \SQUARE{\y}{\Dy}
+      \MULTIPLY{-1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SQUAREfunction}
+% The \cs{SQUAREfunction}: $y(t)=t^2$, $y'(t)=2t$
+%    \begin{macrocode}
+\newfunction{\SQUAREfunction}{%
+      \SQUARE{\t}{\y}
+      \MULTIPLY{2}{\t}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\CUBEfunction}
+% The \cs{CUBEfunction}: $y(t)=t^3$, $y'(t)=3t^2$
+%    \begin{macrocode}
+\newfunction{\CUBEfunction}{%
+      \SQUARE{\t}{\Dy}
+      \MULTIPLY{\t}{\Dy}{\y}
+      \MULTIPLY{3}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SQRTfunction}
+% The \cs{SQRTfunction}: $y(t)=\sqrt t$, $y'(t)=1/(2\sqrt t)$
+%    \begin{macrocode}
+\newfunction{\SQRTfunction}{%
+      \SQRT{\t}{\y}
+      \DIVIDE{0.5}{\y}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\EXPfunction}
+% The \cs{EXPfunction}: $y(t)=\exp t$, $y'(t)=\exp t$
+%    \begin{macrocode}
+\newfunction{\EXPfunction}{%
+     \EXP{\t}{\y}
+     \COPY{\y}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COSfunction}
+% The \cs{COSfunction}: $y(t)=\cos t$, $y'(t)=-\sin t$
+%    \begin{macrocode}
+\newfunction{\COSfunction}{%
+     \COS{\t}{\y}
+     \SIN{\t}{\Dy}
+     \MULTIPLY{-1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SINfunction}
+% The \cs{SINfunction}: $y(t)=\sin t$, $y'(t)=\cos t$
+%    \begin{macrocode}
+\newfunction{\SINfunction}{%
+     \SIN{\t}{\y}
+     \COS{\t}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TANfunction}
+% The \cs{TANfunction}: $y(t)=\tan t$, $y'(t)=1/(\cos t)^2$
+%    \begin{macrocode}
+\newfunction{\TANfunction}{%
+     \TAN{\t}{\y}
+     \COS{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COTfunction}
+% The \cs{COTfunction}: $y(t)=\cot t$, $y'(t)=-1/(\sin t)^2$
+%    \begin{macrocode}
+\newfunction{\COTfunction}{%
+     \COTAN{\t}{\y}
+     \SIN{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{-1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COSHfunction}
+% The \cs{COSHfunction}: $y(t)=\cosh t$, $y'(t)=\sinh t$
+%    \begin{macrocode}
+\newfunction{\COSHfunction}{%
+     \COSH{\t}{\y}
+     \SINH{\t}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SINHfunction}
+% The \cs{SINHfunction}: $y(t)=\sinh t$, $y'(t)=\cosh t$
+%    \begin{macrocode}
+\newfunction{\SINHfunction}{%
+     \SINH{\t}{\y}
+     \COSH{\t}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\TANHfunction}
+% The \cs{TANHfunction}: $y(t)=\tanh t$, $y'(t)=1/(\cosh t)^2$
+%    \begin{macrocode}
+\newfunction{\TANHfunction}{%
+     \TANH{\t}{\y}
+     \COSH{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COTHfunction}
+% The \cs{COTHfunction}: $y(t)=\coth t$, $y'(t)=-1/(\sinh t)^2$
+%    \begin{macrocode}
+\newfunction{\COTHfunction}{%
+     \COTANH{\t}{\y}
+     \SINH{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{-1}{\Dy}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\LOGfunction}
+% The \cs{LOGfunction}: $y(t)=\log t$, $y'(t)=1/t$
+%    \begin{macrocode}
+\newfunction{\LOGfunction}{%
+     \LOG{\t}{\y}
+     \DIVIDE{1}{\t}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\HEAVISIDEfunction}
+% The \cs{HEAVISIDEfunction}: 
+% $y(t)=\begin{cases} 
+% 0 & \text{if } t<0 \\
+% 1 & \text{if } t\geq 0
+% \end{cases}$, 
+% $y'(t)=0$
+%    \begin{macrocode}
+\newfunction{\HEAVISIDEfunction}{%
+     \ifdim \t\p@<\z@ \COPY{0}{\y}\else\COPY{1}{\y}\fi
+      \COPY{0}{\Dy}}
+%    \end{macrocode}
+% \end{macro}
+% \subsection{Operations with functions}
+% \begin{macro}{\CONSTANTfunction}
+% \cs{CONSTANTfunction} defines \#2 as the constant function $f(t)=\#1$.
+%    \begin{macrocode}
+\def\CONSTANTfunction#1#2{%
+              \def#2##1##2##3{%
+                          \xdef##2{#1}%
+                          \xdef##3{0}}}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SUMfunction}
+% \cs{SUMfunction} defines \#3 as the sum of functions \#1 and \#2.
+%    \begin{macrocode}
+\def\SUMfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@SUMf}{\ccls@SUMDf}%         
+                    #2{##1}{\ccls@SUMg}{\ccls@SUMDg}%
+                    \ADD{\ccls@SUMf}{\ccls@SUMg}{\ccls@SUMfg}
+                    \ADD{\ccls@SUMDf}{\ccls@SUMDg}{\ccls@SUMDfg}
+                         \xdef##2{\ccls@SUMfg}%
+                         \xdef##3{\ccls@SUMDfg}%         
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SUBTRACTfunction}
+% \cs{SUBTRACTfunction} defines \#3 as the difference of functions \#1 and \#2.
+%    \begin{macrocode}
+\def\SUBTRACTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@SUBf}{\ccls@SUBDf}%       
+                    #2{##1}{\ccls@SUBg}{\ccls@SUBDg}%
+                    \SUBTRACT{\ccls@SUBf}{\ccls@SUBg}{\ccls@SUBfg}
+                    \SUBTRACT{\ccls@SUBDf}{\ccls@SUBDg}{\ccls@SUBDfg}
+                         \xdef##2{\ccls@SUBfg}%
+                         \xdef##3{\ccls@SUBDfg}%         
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\PRODUCTfunction}
+% \cs{PRODUCTfunction} defines \#3 as the product of functions \#1 and \#2.
+%    \begin{macrocode}
+\def\PRODUCTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@PROf}{\ccls@PRODf}%         
+                    #2{##1}{\ccls@PROg}{\ccls@PRODg}%
+                    \MULTIPLY{\ccls@PROf}{\ccls@PROg}{\ccls@PROfg}
+                    \MULTIPLY{\ccls@PROf}{\ccls@PRODg}{\ccls@PROfDg}
+                    \MULTIPLY{\ccls@PRODf}{\ccls@PROg}{\ccls@PRODfg}
+                    \ADD{\ccls@PROfDg}{\ccls@PRODfg}{\ccls@PRODfg}
+                         \xdef##2{\ccls@PROfg}%
+                         \xdef##3{\ccls@PRODfg}%         
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\QUOTIENTfunction}
+% \cs{QUOTIENTfunction} defines \#3 as the quotient of functions \#1 and \#2.
+%    \begin{macrocode}
+\def\QUOTIENTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@QUOf}{\ccls@QUODf}% 
+                    #2{##1}{\ccls@QUOg}{\ccls@QUODg}%
+                    \DIVIDE{\ccls@QUOf}{\ccls@QUOg}{\ccls@QUOfg}
+                    \MULTIPLY{\ccls@QUOf}{\ccls@QUODg}{\ccls@QUOfDg}
+                    \MULTIPLY{\ccls@QUODf}{\ccls@QUOg}{\ccls@QUODfg}
+                    \SUBTRACT{\ccls@QUODfg}{\ccls@QUOfDg}{\ccls@QUOnum}
+                    \SQUARE{\ccls@QUOg}{\ccls@qsquaretempg}
+                    \DIVIDE{\ccls@QUOnum}{\ccls@qsquaretempg}{\ccls@QUODfg}
+                         \xdef##2{\ccls@QUOfg}%
+                         \xdef##3{\ccls@QUODfg}%          
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\COMPOSITIONfunction}
+% \cs{COMPOSITIONfunction} defines \#3 as the composition
+% of functions \#1 and \#2.
+%    \begin{macrocode}
+\def\COMPOSITIONfunction#1#2#3{%  #3=#1(#2)
+            \def#3##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@COMg}{\ccls@COMDg}%  
+                    #1{\ccls@COMg}{\ccls@COMf}{\ccls@COMDf}%  
+                    \MULTIPLY{\ccls@COMDg}{\ccls@COMDf}{\ccls@COMDf}
+                         \xdef##2{\ccls@COMf}%
+                         \xdef##3{\ccls@COMDf}%          
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SCALEfunction}
+% \cs{SCALEfunction} defines \#3 as the product of number \#1 and function \#2.
+%    \begin{macrocode}
+\def\SCALEfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@SCFf}{\ccls@SCFDf}%       
+                    \MULTIPLY{#1}{\ccls@SCFf}{\ccls@SCFaf}
+                    \MULTIPLY{#1}{\ccls@SCFDf}{\ccls@SCFDaf}
+                         \xdef##2{\ccls@SCFaf}%
+                         \xdef##3{\ccls@SCFDaf}%         
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\SCALEVARIABLEfunction}
+% \cs{SCALEVARIABLEfunction} scales the variable by number \#1
+% and aplies function \#2.
+%    \begin{macrocode}
+\def\SCALEVARIABLEfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup%
+                    \MULTIPLY{#1}{##1}{\ccls@SCVat}
+                    #2{\ccls@SCVat}{\ccls@SCVf}{\ccls@SCVDf}%         
+                    \MULTIPLY{#1}{\ccls@SCVDf}{\ccls@SCVDf}
+                         \xdef##2{\ccls@SCVf}%
+                         \xdef##3{\ccls@SCVDf}%   
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\POWERfunction}
+% \cs{POWERfunction} defines \#3 as the power of function \#1 to exponent \#2.
+%    \begin{macrocode}
+\def\POWERfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@POWf}{\ccls@POWDf}%         
+                    \POWER{\ccls@POWf}{#2}{\ccls@POWfn}
+                   \SUBTRACT{#2}{1}{\ccls@nminusone}
+                   \POWER{\ccls@POWf}{\ccls@nminusone}{\ccls@POWDfn}
+                  \MULTIPLY{#2}{\ccls@POWDfn}{\ccls@POWDfn}
+                  \MULTIPLY{\ccls@POWDfn}{\ccls@POWDf}{\ccls@POWDfn}
+                         \xdef##2{\ccls@POWfn}%
+                         \xdef##3{\ccls@POWDfn}%          
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\LINEARCOMBINATIONfunction}
+% \cs{LINEARCOMBINATIONfunction} defines the new function \#5
+% as the linear combination \#1\#2+\#3\#4.
+% \#1 and \#3 are two numbers. \#1 and \#3 are two functions.
+
+%    \begin{macrocode}
+\def\LINEARCOMBINATIONfunction#1#2#3#4#5{%
+            \def#5##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@LINf}{\ccls@LINDf}%        
+                    #4{##1}{\ccls@LINg}{\ccls@LINDg}%
+                    \MULTIPLY{#1}{\ccls@LINf}{\ccls@LINf}
+                    \MULTIPLY{#3}{\ccls@LINg}{\ccls@LINg}
+                    \MULTIPLY{#1}{\ccls@LINDf}{\ccls@LINDf}
+                    \MULTIPLY{#3}{\ccls@LINDg}{\ccls@LINDg}
+                    \ADD{\ccls@LINf}{\ccls@LINg}{\ccls@LINafbg}
+                    \ADD{\ccls@LINDf}{\ccls@LINDg}{\ccls@LINDafbg}
+                         \xdef##2{\ccls@LINafbg}%
+                         \xdef##3{\ccls@LINDafbg}%      
+             \endgroup}\ignorespaces}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\POLARfunction}
+% \cs{POLARfunction} defines the polar curve \#2.
+% \#1 is a previously defined function.
+%    \begin{macrocode}
+\def\POLARfunction#1#2{%
+       \PRODUCTfunction{#1}{\COSfunction}{\ccls@polarx}
+       \PRODUCTfunction{#1}{\SINfunction}{\ccls@polary}
+       \PARAMETRICfunction{\ccls@polarx}{\ccls@polary}{#2}}
+%    \end{macrocode}
+% \end{macro}           
+% \begin{macro}{\PARAMETRICfunction}
+% \cs{PARAMETRICfunction} defines the parametric curve \#3.
+% \#1 and \#2 are the components functions (two previuosly defined functions).
+%    \begin{macrocode}
+\def\PARAMETRICfunction#1#2#3{%
+       \def#3##1##2##3##4##5{%
+                #1{##1}{##2}{##3}
+                #2{##1}{##4}{##5}}}
+%    \end{macrocode}
+% \end{macro}                
+% \begin{macro}{\VECTORfunction}
+% \cs{VECTORfunction}: an alias of \cs{PARAMETRICfunction}.
+%    \begin{macrocode}                
+\let\VECTORfunction\PARAMETRICfunction              
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%    \begin{macrocode}                     
+% </calculus>          
+%    \end{macrocode}
+% \Finale
+%
\ No newline at end of file
diff --git a/Master/texmf-dist/tex/latex/calculator/calculator.sty b/Master/texmf-dist/tex/latex/calculator/calculator.sty
new file mode 100644
index 00000000000..eb17a0715c0
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/calculator/calculator.sty
@@ -0,0 +1,1212 @@
+%%
+%% This is file `calculator.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% calculator.dtx  (with options: `calculator')
+%% ------------------------------------------------------------------
+%% The calculator and calculus packages
+%% Copyright (C) 2012 by Robert Fuster <rfuster@mat.upv.es>
+%% All rights reserved
+%% 
+%% This file may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in:
+%% 
+%%     http://www.latex-project.org/lppl.txt
+%% 
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% ------------------------------------------------------------------
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+
+
+
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{calculator}[2012/06/10 v.1.0a]
+\newdimen\cctr@lengtha
+\newdimen\cctr@lengthb
+\newdimen\cctr@epsilon
+\cctr@epsilon=1sp
+\def\cctr@logmaxnum{9.704}
+\def\cctr@Warndivzero#1#2{%
+      \PackageWarning{calculator}%
+        {Division by 0.\MessageBreak
+         I can't define #1/#2}}
+
+\def\cctr@Warnnogcd{%
+      \PackageWarning{calculator}%
+        {gcd(0,0) is not well defined}}
+
+\def\cctr@Warnnoposrad#1{%
+      \PackageWarning{calculator}%
+                    {The argument in square root\MessageBreak
+                     must be non negative\MessageBreak
+                     I can't define sqrt(#1)}}
+
+\def\cctr@Warnnointexp#1#2{%
+      \PackageWarning{calculator}%
+                    {The exponent in power function\MessageBreak
+                     must be an integer\MessageBreak
+                     I can't define #1^#2}}
+
+\def\cctr@Warnsingmatrix#1#2#3#4{%
+      \PackageWarning{calculator}%
+        {Matrix (#1 #2 ; #3 #4) is singular\MessageBreak
+         Its inverse is not defined}}
+
+\def\cctr@WarnsingTDmatrix#1#2#3#4#5#6#7#8#9{%
+      \PackageWarning{calculator}%
+        {Matrix (#1 #2 #3; #4 #5 #6; #7 #8 #9) is singular\MessageBreak
+         Its inverse is not defined}}
+
+\def\cctr@WarnIncLinSys{\PackageWarning{xpicture}{%
+      Incompatible linear system}}
+
+\def\cctr@WarnIncTDLinSys{\PackageWarning{xpicture}{%
+      Incompatible or indeterminate linear system\MessageBreak
+      For 3x3 systems I can solve only determinate systems}}
+
+\def\cctr@WarnIndLinSys{\PackageWarning{xpicture}{%
+      Indeterminate linear system.\MessageBreak
+      I will choose one of the infinite solutions}}
+
+\def\cctr@WarnZeroLinSys{\PackageWarning{xpicture}{%
+      0x=0 linear system. Every vector is a solution!\MessageBreak
+      I will choose the (0,0) solution}}
+
+\def\cctr@Warninftan#1{%
+             \PackageWarning{calculator}{%
+                    Undefined tangent.\MessageBreak
+                           The cosine of #1 is zero and, then,\MessageBreak
+                           the tangent of #1 is not defined}}
+
+\def\cctr@Warninfcotan#1{%
+             \PackageWarning{calculator}{%
+                    Undefined cotangent.\MessageBreak
+                           The sine of #1 is zero and, then,\MessageBreak
+                           the cotangent of #1 is not defined}}
+
+\def\cctr@Warninfexp#1{%
+             \PackageWarning{calculator}{%
+                    The absolute value of the variable\MessageBreak
+                    in the exponential function must be less than
+                    \cctr@logmaxnum\MessageBreak
+                   (the logarithm of the max number I know)\MessageBreak
+                    I can't define exp(#1)}}
+
+\def\cctr@Warninfexpb#1#2{%
+             \PackageWarning{calculator}{%
+                    The base\MessageBreak
+                    in the exponential function must be positive.
+                    \MessageBreak
+                    I can't define #1^(#2)}}
+
+\def\cctr@Warninflog#1{%
+             \PackageWarning{calculator}{%
+                    The value of the variable\MessageBreak
+                    in the logarithm function must be positive\MessageBreak
+                    I can't define log(#1)}}
+\def\COPY#1#2{\edef#2{#1}\ignorespaces}
+\def\GLOBALCOPY#1#2{\xdef#2{#1}\ignorespaces}
+\def\@OUTPUTSOL#1{\GLOBALCOPY{#1}{\cctr@outa}\endgroup\COPY{\cctr@outa}{#1}}
+\def\@OUTPUTSOLS#1#2{\GLOBALCOPY{#1}{\cctr@outa}
+                     \GLOBALCOPY{#2}{\cctr@outb}\endgroup
+                     \COPY{\cctr@outa}{#1}\COPY{\cctr@outb}{#2}}
+\def\MAX#1#2#3{%
+   \ifdim #1\p@ < #2\p@
+      \COPY{#2}{#3}\else\COPY{#1}{#3}\fi\ignorespaces}
+\def\MIN#1#2#3{%
+   \ifdim #1\p@ > #2\p@
+      \COPY{#2}{#3}\else\COPY{#1}{#3}\fi\ignorespaces}
+\def\ABSVALUE#1#2{%
+    \ifdim #1\p@<\z@
+          \MULTIPLY{-1}{#1}{#2}\else\COPY{#1}{#2}\fi}
+\def\MULTIPLY#1#2#3{\cctr@lengtha=#1\p@
+       \cctr@lengtha=#2\cctr@lengtha
+       \edef#3{\expandafter\strip@pt\cctr@lengtha}\ignorespaces}
+\def\ADD#1#2#3{\cctr@lengtha=#1\p@
+       \cctr@lengthb=#2\p@
+       \advance\cctr@lengtha by \cctr@lengthb
+       \edef#3{\expandafter\strip@pt\cctr@lengtha}\ignorespaces}
+\def\SUBTRACT#1#2#3{\ADD{#1}{-#2}{#3}}
+\def\DIVIDE#1#2#3{%
+     \begingroup
+       \ABSVALUE{#1}{\cctr@tempD}
+       \ABSVALUE{#2}{\cctr@tempd}
+       \ifdim#1\p@<\z@\ifdim#2\p@>\z@\COPY{-1}{\cctr@sign}
+          \else\COPY{1}{\cctr@sign}\fi
+       \else\ifdim#2\p@>\z@\COPY{1}{\cctr@sign}
+               \else\COPY{-1}{\cctr@sign}\fi
+            \fi
+       \@DIVIDE{\cctr@tempD}{\cctr@tempd}{\cctr@tempq}{\cctr@tempr}
+       \COPY{\cctr@tempq.}{\cctr@Q}
+       \COPY{0}{\cctr@ndec}
+       \@whilenum \cctr@ndec<5 \do{%
+           \ifdim\cctr@tempr\p@<1638\p@
+              \MULTIPLY{\cctr@tempr}{10}{\cctr@tempD}
+           \else
+              \COPY{\cctr@tempr}{\cctr@tempD}
+              \MULTIPLY{\cctr@tempd}{0.1}{\cctr@tempd}
+           \fi
+           \@DIVIDE{\cctr@tempD}{\cctr@tempd}{\cctr@tempq}{\cctr@tempr}
+           \COPY{\cctr@Q\cctr@tempq}{\cctr@Q}
+           \ADD{1}{\cctr@ndec}{\cctr@ndec}}%
+       \MULTIPLY{\cctr@sign}{\cctr@Q}{#3}
+       \@OUTPUTSOL{#3}}
+  \def\@DIVIDE#1#2#3#4{%
+       \@INTEGERDIVIDE{#1}{#2}{#3}
+       \MULTIPLY{#2}{#3}{#4}
+       \SUBTRACT{#1}{#4}{#4}}
+\def\@INTEGERDIVIDE#1#2#3{%
+       \cctr@lengtha=#1\p@
+       \cctr@lengthb=#2\p@
+       \ifdim\cctr@lengthb=\z@
+          \let#3\undefined
+          \cctr@Warndivzero#1#2%
+       \else
+          \divide\cctr@lengtha\cctr@lengthb
+          \COPY{\number\cctr@lengtha}{#3}
+       \fi\ignorespaces}
+\def\LENGTHDIVIDE#1#2#3{%
+       \begingroup
+       \cctr@lengtha=#1
+       \cctr@lengthb=#2
+       \edef\cctr@tempa{\expandafter\strip@pt\cctr@lengtha}%
+       \edef\cctr@tempb{\expandafter\strip@pt\cctr@lengthb}%
+       \DIVIDE{\cctr@tempa}{\cctr@tempb}{#3}
+       \@OUTPUTSOL{#3}}
+\def\SQUARE#1#2{\MULTIPLY{#1}{#1}{#2}}
+\def\CUBE#1#2{\MULTIPLY{#1}{#1}{#2}\MULTIPLY{#2}{#1}{#2}}
+\def\POWER#1#2#3{%
+       \begingroup
+       \INTEGERPART{#2}{\cctr@tempexp}
+       \ifdim \cctr@tempexp\p@<#2\p@
+         \cctr@Warnnointexp{#1}{#2}
+         \let#3\undefined
+       \else
+          \@POWER{#1}{#2}{#3}\fi\@OUTPUTSOL{#3}}
+\def\@POWER#1#2#3{%
+      \begingroup
+      \ifdim #2\p@<\z@
+             \DIVIDE{1}{#1}{\cctr@tempb}
+             \MULTIPLY{-1}{#2}{\cctr@tempc}
+             \@POWER{\cctr@tempb}{\cctr@tempc}{#3}
+          \else
+             \COPY{0}{\cctr@tempa}
+             \COPY{1}{#3}
+             \@whilenum \cctr@tempa<#2 \do {%
+                \MULTIPLY{#1}{#3}{#3}
+                \ADD{1}{\cctr@tempa}{\cctr@tempa}}%
+       \fi\@OUTPUTSOL{#3}}
+
+\def\INTEGERDIVISION#1#2#3#4{%
+       \begingroup
+       \ABSVALUE{#2}{\cctr@tempd}
+       \@DIVIDE{#1}{#2}{#3}{#4}
+       \ifdim #4\p@<\z@
+          \ifdim #1\p@<\z@
+             \ifdim #2\p@<\z@
+                \ADD{#3}{1}{#3}
+             \else
+                \SUBTRACT{#3}{1}{#3}
+             \fi
+             \ADD{#4}{\cctr@tempd}{#4}
+       \fi\fi\@OUTPUTSOLS{#3}{#4}}
+\def\MODULO#1#2#3{%
+       \begingroup
+       \INTEGERDIVISION{#1}{#2}{\cctr@temp}{#3}\@OUTPUTSOL{#3}}
+\def\INTEGERQUOTIENT#1#2#3{%
+       \begingroup
+       \INTEGERDIVISION{#1}{#2}{#3}{\cctr@temp}\@OUTPUTSOL{#3}}
+\def\@@INTEGERPART#1.#2.#3)#4{\ifnum #11=1 \COPY{0}{#4}
+                              \else \COPY{#1}{#4}\fi}
+\def\@INTEGERPART#1#2{\expandafter\@@INTEGERPART#1..){#2}}
+\def\INTEGERPART#1#2{\begingroup
+                     \ifdim #1\p@<\z@
+                        \MULTIPLY{-1}{#1}{\cctr@temp}
+                        \INTEGERPART{\cctr@temp}{#2}
+                        \ifdim #2\p@<\cctr@temp\p@
+                           \SUBTRACT{-#2}{1}{#2}
+                        \else \COPY{-#2}{#2}
+                        \fi
+                     \else
+                        \@INTEGERPART{#1}{#2}
+                     \fi\@OUTPUTSOL{#2}}
+\let\FLOOR\INTEGERPART
+\def\@@FRACTIONALPART#1.#2.#3)#4{\ifnum #2=11  \COPY{0}{#4}
+                                \else \COPY{0.#2}{#4}\fi}
+\def\@FRACTIONALPART#1#2{\expandafter\@@FRACTIONALPART#1..){#2}}
+\def\FRACTIONALPART#1#2{\begingroup
+                     \ifdim #1\p@<\z@
+                        \INTEGERPART{#1}{\cctr@tempA}
+                        \SUBTRACT{#1}{\cctr@tempA}{#2}
+                     \else
+                        \@FRACTIONALPART{#1}{#2}
+                     \fi\@OUTPUTSOL{#2}}
+\def\TRUNCATE{\@ifnextchar[\@@TRUNCATE\@TRUNCATE}
+\def\@TRUNCATE#1#2{\@@TRUNCATE[2]{#1}{#2}}
+\def\@@TRUNCATE[#1]#2#3{%
+    \begingroup
+    \INTEGERPART{#2}{\cctr@tempa}
+    \ifdim \cctr@tempa\p@ = #2\p@
+       \expandafter\@@@TRUNCATE#2.00000)[#1]{#3}
+    \else
+       \expandafter\@@@TRUNCATE#200000.)[#1]{#3}
+    \fi
+    \@OUTPUTSOL{#3}}
+\def\@@@TRUNCATE#1.#2#3#4#5#6.#7)[#8]#9{%
+    \ifcase #8
+       \COPY{#1}{#9}
+    \or\COPY{#1.#2}{#9}
+    \or\COPY{#1.#2#3}{#9}
+    \or\COPY{#1.#2#3#4}{#9}
+    \or\COPY{#1.#2#3#4#5}{#9}
+    \fi}
+\def\ROUND{\@ifnextchar[\@@ROUND\@ROUND}
+\def\@ROUND#1#2{\@@ROUND[2]{#1}{#2}}
+\def\@@ROUND[#1]#2#3{%
+       \begingroup
+       \ifdim#2\p@<\z@
+           \MULTIPLY{-1}{#2}{\cctr@temp}
+           \@@ROUND[#1]{\cctr@temp}{#3}\COPY{-#3}{#3}
+       \else
+          \@@TRUNCATE[#1]{#2}{\cctr@tempe}
+          \SUBTRACT{#2}{\cctr@tempe}{\cctr@tempc}
+          \POWER{10}{#1}{\cctr@tempb}
+          \MULTIPLY{\cctr@tempb}{\cctr@tempc}{\cctr@tempc}
+          \ifdim\cctr@tempc\p@<0.5\p@
+          \else
+             \DIVIDE{1}{\cctr@tempb}{\cctr@tempb}
+             \ADD{\cctr@tempe}{\cctr@tempb}{\cctr@tempe}
+          \fi
+          \@@TRUNCATE[#1]{\cctr@tempe}{#3}
+       \fi
+       \@OUTPUTSOL{#3}}
+\def\GCD#1#2#3{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa}
+       \ABSVALUE{#2}{\cctr@tempb}
+       \MAX{\cctr@tempa}{\cctr@tempb}{\cctr@tempc}
+       \MIN{\cctr@tempa}{\cctr@tempb}{\cctr@tempa}
+       \COPY{\cctr@tempc}{\cctr@tempb}
+       \ifnum \cctr@tempa = 0
+          \ifnum \cctr@tempb = 0
+             \cctr@Warnnogcd
+             \let#3\undefined
+          \else
+          \COPY{\cctr@tempb}{#3}
+          \fi
+       \else
+          \@whilenum \cctr@tempa > \z@ \do {%
+             \COPY{\cctr@tempa}{#3}%
+             \MODULO{\cctr@tempb}{\cctr@tempa}{\cctr@tempc}%
+             \COPY\cctr@tempa\cctr@tempb%
+             \COPY\cctr@tempc\cctr@tempa}
+       \fi\ignorespaces\@OUTPUTSOL{#3}}
+\def\LCM#1#2#3{%
+       \GCD{#1}{#2}{#3}%
+       \ifx #3\undefined \COPY{0}{#3}
+       \else
+          \DIVIDE{#1}{#3}{#3}
+          \MULTIPLY{#2}{#3}{#3}
+          \ABSVALUE{#3}{#3}
+       \fi}
+\def\FRACTIONSIMPLIFY#1#2#3#4{%
+       \ifnum #1=\z@
+          \COPY{0}{#3}\COPY{1}{#4}
+       \else
+          \GCD{#1}{#2}{#3}%
+          \DIVIDE{#2}{#3}{#4}
+          \DIVIDE{#1}{#3}{#3}
+          \ifnum #4<0 \MULTIPLY{-1}{#4}{#4}\MULTIPLY{-1}{#3}{#3}\fi
+       \fi\ignorespaces}
+\def\SQUAREROOT#1#2{%
+       \begingroup
+       \ifdim #1\p@ = \z@
+         \COPY{0}{#2}
+       \else
+         \ifdim #1\p@ < \z@
+             \let#2\undefined
+             \cctr@Warnnoposrad{#1}%
+          \else
+             \COPY{#1}{#2}
+             \cctr@lengthb=5\p@
+             \@whilenum \cctr@lengthb>\cctr@epsilon \do {%
+                \COPY{#2}{\cctr@tempw}
+                \DIVIDE{#1}{\cctr@tempw}{\cctr@tempz}
+                \ADD{\cctr@tempw}{\cctr@tempz}{\cctr@tempz}
+                \DIVIDE{\cctr@tempz}{2}{\cctr@tempz}
+                \COPY{\cctr@tempz}{#2}
+                \SUBTRACT{#2}{\cctr@tempw}{\cctr@tempw}
+                \cctr@lengthb=\cctr@tempw\p@%
+                \ifnum
+                   \cctr@lengthb<\z@ \cctr@lengthb=-\cctr@lengthb
+                \fi}
+       \fi\fi\@OUTPUTSOL{#2}}
+\let\SQRT\SQUAREROOT
+\def\SIN#1#2{%
+    \begingroup
+    \ifdim #1\p@=-\numberHALFPI\p@ \COPY{-1}{#2}
+    \else
+         \ifdim #1\p@=\numberHALFPI\p@ \COPY{1}{#2}
+         \else
+              \ifdim #1\p@=\numberTHREEHALFPI\p@ \COPY{-1}{#2}
+               \else
+                   \ifdim#1\p@<-\numberHALFPI\p@
+                      \ADD{#1}{\numberTWOPI}{\cctr@tempb}
+                      \SIN{\cctr@tempb}{#2}
+                   \else
+                      \ifdim #1\p@<\numberHALFPI\p@
+                         \@BASICSINE{#1}{#2}
+                      \else
+                         \ifdim #1\p@<\numberTHREEHALFPI\p@
+                           \SUBTRACT{\numberPI}{#1}{\cctr@tempb}
+                           \SIN{\cctr@tempb}{#2}
+                        \else
+                          \SUBTRACT{#1}{\numberTWOPI}{\cctr@tempb}
+                          \SIN{\cctr@tempb}{#2}
+  \fi\fi\fi\fi\fi\fi\@OUTPUTSOL{#2}}
+\def\@BASICSINE#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa}
+          \ifdim\cctr@tempa\p@=\z@ \COPY{0}{#2}
+          \else
+             \ifdim \cctr@tempa\p@<0.009\p@\COPY{#1}{#2}
+             \else
+                \SQUARE{#1}{\cctr@tempa}
+                \DIVIDE{\cctr@tempa}{42}{#2}
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{\cctr@tempa}{#2}
+                \DIVIDE{#2}{20}{#2}
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{\cctr@tempa}{#2}
+                \DIVIDE{#2}{6}{#2}
+                \SUBTRACT{1}{#2}{#2}
+                \MULTIPLY{#2}{#1}{#2}
+          \fi\fi\@OUTPUTSOL{#2}}
+\def\COS#1#2{%
+        \begingroup
+        \ADD{\numberHALFPI}{#1}{\cctr@tempc}
+        \SIN{\cctr@tempc}{#2}\@OUTPUTSOL{#2}}
+\def\TAN#1#2{%
+          \begingroup
+          \ifdim #1\p@=-\numberHALFPI\p@
+             \cctr@Warninftan{#1}
+             \let#2\undefined
+          \else
+             \ifdim #1\p@=\numberHALFPI\p@
+                 \cctr@Warninftan{#1}
+                 \let#2\undefined
+             \else
+                \ifdim #1\p@<-\numberHALFPI\p@
+                   \ADD{#1}{\numberPI}{\cctr@tempb}
+                   \TAN{\cctr@tempb}{#2}
+                \else
+                   \ifdim #1\p@<\numberHALFPI\p@
+                      \@BASICTAN{#1}{#2}
+                   \else
+                      \SUBTRACT{#1}{\numberPI}{\cctr@tempb}
+                      \TAN{\cctr@tempb}{#2}
+          \fi\fi\fi\fi\@OUTPUTSOL{#2}}
+\def\@BASICTAN#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@tempa}
+          \ifdim\cctr@tempa\p@=\z@ \COPY{0}{#2}
+          \else
+             \ifdim\cctr@tempa\p@<0.04\p@
+                \COPY{#1}{#2}
+             \else
+                \DIVIDE{#1}{11}{#2}
+                \DIVIDE{9}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{7}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{5}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{3}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+                \DIVIDE{1}{#1}{\cctr@tempa}
+                \SUBTRACT{\cctr@tempa}{#2}{#2}
+                \DIVIDE{1}{#2}{#2}
+          \fi\fi\@OUTPUTSOL{#2}}
+\def\COT#1#2{%
+        \begingroup
+        \COS{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \COPY{0}{#2}
+        \else
+        \TAN{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \cctr@Warninfcotan{#1}
+        \let#2\undefined
+        \else
+        \DIVIDE{1}{#2}{#2}
+        \fi\fi\@OUTPUTSOL{#2}}
+\def\DEGtoRAD#1#2{\DIVIDE{#1}{57.29578}{#2}}
+\def\RADtoDEG#1#2{\MULTIPLY{#1}{57.29578}{#2}}
+\def\REDUCERADIANSANGLE#1#2{%
+         \COPY{#1}{#2}
+         \ifdim #1\p@ < -\numberPI\p@
+                 \ADD{#1}{\numberTWOPI}{#2}
+                 \REDUCERADIANSANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ >  \numberPI\p@
+                 \SUBTRACT{#1}{\numberTWOPI}{#2}
+                 \REDUCERADIANSANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ = -180\p@ \COPY{\numberPI}{#2} \fi}
+\def\REDUCEDEGREESANGLE#1#2{%
+         \COPY{#1}{#2}
+         \ifdim #1\p@ < -180\p@
+                 \ADD{#1}{360}{#2}
+                 \REDUCEDEGREESANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ >  180\p@
+                 \SUBTRACT{#1}{360}{#2}
+                 \REDUCEDEGREESANGLE{#2}{#2}
+         \fi
+         \ifdim #1\p@ = -180\p@ \COPY{180}{#2} \fi}
+\def\DEGREESSIN{\@ifnextchar[\@@DEGREESSIN\@DEGREESSIN}
+\def\DEGREESCOS{\@ifnextchar[\@@DEGREESCOS\@DEGREESCOS}
+\def\DEGREESTAN{\@ifnextchar[\@@DEGREESTAN\@DEGREESTAN}
+\def\DEGREESCOT{\@ifnextchar[\@@DEGREESCOT\@DEGREESCOT}
+\def\@DEGREESSIN#1#2{%
+    \begingroup
+    \ifdim #1\p@=-90\p@ \COPY{-1}{#2}
+    \else
+         \ifdim #1\p@=90\p@ \COPY{1}{#2}
+         \else
+                  \ifdim #1\p@=270\p@ \COPY{-1}{#2}
+         \else
+           \ifdim#1\p@<-90\p@
+                \ADD{#1}{360}{\cctr@tempb}
+                \DEGREESSIN{\cctr@tempb}{#2}
+           \else
+              \ifdim #1\p@<90\p@
+                    \DEGtoRAD{#1}{\cctr@tempb}
+                    \@BASICSINE{\cctr@tempb}{#2}
+                  \else
+                       \ifdim #1\p@<270\p@
+                         \SUBTRACT{180}{#1}{\cctr@tempb}
+                          \DEGREESSIN{\cctr@tempb}{#2}
+                         \else
+                              \SUBTRACT{#1}{360}{\cctr@tempb}
+                              \DEGREESSIN{\cctr@tempb}{#2}
+  \fi\fi\fi\fi\fi\fi\@OUTPUTSOL{#2}}
+\def\@DEGREESCOS#1#2{%
+        \begingroup
+        \ADD{90}{#1}{\cctr@tempc}
+        \DEGREESSIN{\cctr@tempc}{#2}\@OUTPUTSOL{#2}}
+\def\@DEGREESTAN#1#2{%
+          \begingroup
+          \ifdim #1\p@=-90\p@
+          \cctr@Warninftan{#1}
+          \let#2\undefined
+          \else
+            \ifdim #1\p@=90\p@
+            \cctr@Warninftan{#1}
+            \let#2\undefined
+          \else
+          \ifdim #1\p@<-90\p@
+            \ADD{#1}{180}{\cctr@tempb} \DEGREESTAN{\cctr@tempb}{#2}
+          \else
+              \ifdim #1\p@<90\p@
+                   \DEGtoRAD{#1}{\cctr@tempb}
+                   \@BASICTAN{\cctr@tempb}{#2}
+                 \else
+                     \SUBTRACT{#1}{180}{\cctr@tempb}
+                     \DEGREESTAN{\cctr@tempb}{#2}
+   \fi\fi\fi\fi\@OUTPUTSOL{#2}}
+\def\@DEGREESCOT#1#2{%
+        \begingroup
+        \DEGREESCOS{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \COPY{0}{#2}
+        \else
+        \DEGREESTAN{#1}{#2}
+        \ifdim #2\p@ = \z@
+        \cctr@Warninfcotan{#1}
+        \let#2\undefined
+        \else
+        \DIVIDE{1}{#2}{#2}
+        \fi\fi\@OUTPUTSOL{#2}}
+\def\@@DEGREESSIN[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \@DEGREESSIN{\@DEGREES}{#3}}
+\def\@@DEGREESCOS[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESCOS{\@DEGREES}{#3}}
+\def\@@DEGREESTAN[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESTAN{\@DEGREES}{#3}}
+\def\@@DEGREESCOT[#1]#2#3{\@CONVERTDEG{#1}{#2}
+        \DEGREESCOT{\@DEGREES}{#3}}
+\def\@CONVERTDEG#1#2{\DIVIDE{#2}{#1}{\@DEGREES}
+        \MULTIPLY{\@DEGREES}{360}{\@DEGREES}}
+\def\EXP{\@ifnextchar[\@@EXP\@EXP}
+\def\@@EXP[#1]#2#3{%
+      \begingroup
+      \ifdim #1\p@<\cctr@epsilon
+          \cctr@Warninfexpb{#1}{#2}
+          \let#3\undefined
+      \else
+          \LOG{#1}{\cctr@log}
+          \MULTIPLY{#2}{\cctr@log}{\cctr@log}
+          \@EXP{\cctr@log}{#3}
+      \fi\@OUTPUTSOL{#3}}
+\def\@EXP#1#2{%
+      \begingroup
+      \ABSVALUE{#1}{\cctr@absval}
+      \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+              \cctr@Warninfexp{#1}
+             \let#2\undefined
+      \else
+          \ifdim #1\p@ < \z@
+            \ifdim #1\p@ > -6.00002\p@
+               \@BASICEXP{#1}{#2}
+            \else
+               \DIVIDE{#1}{2}{\cctr@expt}
+               \@EXP{\cctr@expt}{\cctr@expy}
+               \SQUARE{\cctr@expy}{#2}
+            \fi
+          \else
+               \ifdim #1\p@ < 3.00002\p@
+                  \@BASICEXP{#1}{#2}
+               \else
+                  \DIVIDE{#1}{2}{\cctr@expt}
+                  \@EXP{\cctr@expt}{\cctr@expy}
+                  \SQUARE{\cctr@expy}{#2}
+               \fi
+\fi\fi\@OUTPUTSOL{#2}}
+\def\@BASICEXP#1#2{%
+       \begingroup
+       \SQUARE{#1}\cctr@tempa
+       \DIVIDE{\cctr@tempa}{396}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{256}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{140}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{60}{#2}
+       \ADD{1}{#2}{#2}
+       \DIVIDE\cctr@tempa{#2}{#2}
+       \DIVIDE{#2}{6}{#2}
+       \ADD{2}{#2}{#2}
+       \SUBTRACT{#2}{#1}{#2}
+       \DIVIDE{#1}{#2}{#2}
+       \MULTIPLY{2}{#2}{#2}
+       \ADD{1}{#2}{#2}\@OUTPUTSOL{#2}}
+\def\COSH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \EXP{#1}{\cctr@expx}
+          \MULTIPLY{-1}{#1}{\cctr@minust}
+          \EXP{\cctr@minust}{\cctr@expminusx}
+          \ADD{\cctr@expx}{\cctr@expminusx}{#2}
+          \DIVIDE{#2}{2}{#2}
+       \fi\@OUTPUTSOL{#2}}
+\def\SINH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \EXP{#1}{\cctr@expx}
+          \MULTIPLY{-1}{#1}{\cctr@minust}
+          \EXP{\cctr@minust}{\cctr@expminusx}
+          \SUBTRACT{\cctr@expx}{\cctr@expminusx}{#2}
+          \DIVIDE{#2}{2}{#2}
+       \fi\@OUTPUTSOL{#2}}
+\def\TANH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \SINH{#1}{\cctr@tanhnum}
+          \COSH{#1}{\cctr@tanhden}
+          \DIVIDE{\cctr@tanhnum}{\cctr@tanhden}{#2}
+       \fi\@OUTPUTSOL{#2}}
+\def\COTH#1#2{%
+       \begingroup
+       \ABSVALUE{#1}{\cctr@absval}
+       \ifdim \cctr@absval\p@>\cctr@logmaxnum\p@
+          \cctr@Warninfexp{#1}
+          \let#2\undefined
+       \else
+          \SINH{#1}{\cctr@tanhden}
+          \COSH{#1}{\cctr@tanhnum}
+          \DIVIDE\cctr@tanhnum\cctr@tanhden{#2}
+       \fi\@OUTPUTSOL{#2}}
+\def\LOG{\@ifnextchar[\@@LOG\@LOG}
+\def\@LOG#1#2{%
+       \begingroup
+       \ifdim #1\p@<\cctr@epsilon
+          \cctr@Warninflog{#1}
+          \let#2\undefined
+       \else
+       \ifdim #1\p@ > \numberETWO\p@
+          \DIVIDE{#1}{\numberE}{\cctr@ae}
+          \@LOG{\cctr@ae}{#2}
+          \ADD{1}{#2}{#2}
+       \else
+          \ifdim #1\p@ < 1\p@
+             \MULTIPLY{\numberE}{#1}{\cctr@ae}
+             \LOG{\cctr@ae}{#2}
+             \SUBTRACT{#2}{1}{#2}
+          \else
+             \@BASICLOG{#1}{#2}
+\fi\fi\fi\@OUTPUTSOL{#2}}
+\def\@@LOG[#1]#2#3{\begingroup
+       \@LOG{#1}{\cctr@loga}
+       \@LOG{#2}{\cctr@logx}
+       \DIVIDE{\cctr@logx}{\cctr@loga}{#3}\@OUTPUTSOL{#3}}
+\def\@BASICLOG#1#2{\begingroup
+             \SUBTRACT{#1}{1}{\cctr@tempw}
+             \cctr@lengthb=5\p@%
+             \cctr@lengtha=\cctr@epsilon%
+       \@whilenum \cctr@lengthb>\cctr@lengtha \do {%
+           \COPY{\cctr@tempw}{\cctr@tempoldw}
+           \EXP{\cctr@tempw}{\cctr@tempxw}
+           \DIVIDE{#1}{\cctr@tempxw}{\cctr@tempxw}
+           \ADD{\cctr@tempw}{\cctr@tempxw}{\cctr@tempw}
+           \SUBTRACT{\cctr@tempw}{1}{\cctr@tempw}
+           \SUBTRACT{\cctr@tempw}{\cctr@tempoldw}{\cctr@tempdif}
+           \cctr@lengthb=\cctr@tempdif\p@%
+           \ifnum
+              \cctr@lengthb<\z@ \cctr@lengthb=-\cctr@lengthb
+           \fi}%
+       \COPY{\cctr@tempw}{#2}\@OUTPUTSOL{#2}}
+\def\VECTORSIZE(#1)#2{\expandafter\@VECTORSIZE(#1,,){#2}}
+\def\@VECTORSIZE(#1,#2,#3,#4)#5{\ifx$#3$\COPY{2}{#5}
+                                \else\COPY{3}{#5}\fi\ignorespaces}
+\def\@@VECTORCOPY(#1,#2)(#3,#4){%
+    \COPY{#1}{#3}\COPY{#2}{#4}}
+
+\def\@@@VECTORCOPY(#1,#2,#3)(#4,#5,#6){%
+    \COPY{#1}{#4}\COPY{#2}{#5}\COPY{#3}{#6}}
+
+\def\VECTORCOPY(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORCOPY(#1)(#2)
+        \else \@@@VECTORCOPY(#1)(#2)\fi}
+\def\@@VECTORGLOBALCOPY(#1,#2)(#3,#4){%
+    \GLOBALCOPY{#1}{#3}\GLOBALCOPY{#2}{#4}}
+
+\def\@@@VECTORGLOBALCOPY(#1,#2,#3)(#4,#5,#6){%
+    \GLOBALCOPY{#1}{#4}\GLOBALCOPY{#2}{#5}\GLOBALCOPY{#3}{#6}}
+
+\def\VECTORGLOBALCOPY(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORGLOBALCOPY(#1)(#2)
+        \else \@@@VECTORGLOBALCOPY(#1)(#2)\fi}
+\def\@@OUTPUTVECTOR(#1,#2){%
+    \VECTORGLOBALCOPY(#1,#2)(\cctr@outa,\cctr@outb)
+    \endgroup\VECTORCOPY(\cctr@outa,\cctr@outb)(#1,#2)}
+
+\def\@@@OUTPUTVECTOR(#1,#2,#3){%
+    \VECTORGLOBALCOPY(#1,#2,#3)(\cctr@outa,\cctr@outb,\cctr@outc)
+    \endgroup\VECTORCOPY(\cctr@outa,\cctr@outb,\cctr@outc)(#1,#2,#3)}
+
+\def\@OUTPUTVECTOR(#1){\VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@OUTPUTVECTOR(#1)
+        \else \@@@OUTPUTVECTOR(#1)\fi}
+\def\@@SCALARPRODUCT(#1,#2)(#3,#4)#5{%
+       \MULTIPLY{#1}{#3}{#5}
+       \MULTIPLY{#2}{#4}\cctr@tempa
+       \ADD{#5}{\cctr@tempa}{#5}}
+
+\def\@@@SCALARPRODUCT(#1,#2,#3)(#4,#5,#6)#7{%
+       \MULTIPLY{#1}{#4}{#7}
+       \MULTIPLY{#2}{#5}\cctr@tempa
+       \ADD{#7}{\cctr@tempa}{#7}
+       \MULTIPLY{#3}{#6}\cctr@tempa
+       \ADD{#7}{\cctr@tempa}{#7}}
+
+\def\SCALARPRODUCT(#1)(#2)#3{%
+        \begingroup
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARPRODUCT(#1)(#2){#3}
+        \else \@@@SCALARPRODUCT(#1)(#2){#3}\fi\@OUTPUTSOL{#3}}
+\def\@@VECTORADD(#1,#2)(#3,#4)(#5,#6){%
+       \ADD{#1}{#3}{#5}
+       \ADD{#2}{#4}{#6}}
+
+\def\@@@VECTORADD(#1,#2,#3)(#4,#5,#6)(#7,#8,#9){%
+       \ADD{#1}{#4}{#7}
+       \ADD{#2}{#5}{#8}
+       \ADD{#3}{#6}{#9}}
+
+\def\VECTORADD(#1)(#2)(#3){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORADD(#1)(#2)(#3)
+        \else \@@@VECTORADD(#1)(#2)(#3)\fi}
+\def\@@VECTORSUB(#1,#2)(#3,#4)(#5,#6){%
+       \VECTORADD(#1,#2)(-#3,-#4)(#5,#6)}
+
+\def\@@@VECTORSUB(#1,#2,#3)(#4,#5,#6)(#7,#8,#9){%
+       \VECTORADD(#1,#2,#3)(-#4,-#5,-#6)(#7,#8,#9)}
+
+\def\VECTORSUB(#1)(#2)(#3){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORSUB(#1)(#2)(#3)
+        \else \@@@VECTORSUB(#1)(#2)(#3)\fi}
+\def\@@VECTORABSVALUE(#1,#2)(#3,#4){%
+       \ABSVALUE{#1}{#3}\ABSVALUE{#2}{#4}}
+
+\def\@@@VECTORABSVALUE(#1,#2,#3)(#4,#5,#6){%
+       \ABSVALUE{#1}{#4}\ABSVALUE{#2}{#5}\ABSVALUE{#3}{#6}}
+
+\def\VECTORABSVALUE(#1)(#2){%
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORABSVALUE(#1)(#2)
+        \else \@@@VECTORABSVALUE(#1)(#2)\fi}
+\def\@@SCALARVECTORPRODUCT#1(#2,#3)(#4,#5){%
+       \MULTIPLY{#1}{#2}{#4}
+       \MULTIPLY{#1}{#3}{#5}}
+
+\def\@@@SCALARVECTORPRODUCT#1(#2,#3,#4)(#5,#6,#7){%
+       \MULTIPLY{#1}{#2}{#5}
+       \MULTIPLY{#1}{#3}{#6}
+       \MULTIPLY{#1}{#4}{#7}}
+
+\def\SCALARVECTORPRODUCT#1(#2)(#3){%
+        \VECTORSIZE(#2){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARVECTORPRODUCT{#1}(#2)(#3)
+        \else \@@@SCALARVECTORPRODUCT{#1}(#2)(#3)\fi}
+\def\VECTORNORM(#1)#2{%
+       \begingroup
+       \SCALARPRODUCT(#1)(#1){\cctr@temp}
+       \SQUAREROOT{\cctr@temp}{#2}\@OUTPUTSOL{#2}}
+\def\UNITVECTOR(#1)(#2){%
+       \begingroup
+       \VECTORNORM(#1){\cctr@tempa}
+       \DIVIDE{1}{\cctr@tempa}{\cctr@tempa}
+       \SCALARVECTORPRODUCT{\cctr@tempa}(#1)(#2)\@OUTPUTVECTOR(#2)}
+\def\@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \COPY{#1}{\cctr@solAA}
+       \COPY{#2}{\cctr@solAB}
+       \COPY{#3}{\cctr@solAC}
+       \COPY{#4}{\cctr@solBA}
+       \COPY{#5}{\cctr@solBB}
+       \COPY{#6}{\cctr@solBC}
+       \COPY{#7}{\cctr@solCA}
+       \COPY{#8}{\cctr@solCB}
+       \COPY{#9}{\cctr@solCC}}
+\def\@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \COPY{\cctr@solAA}{#1}
+       \COPY{\cctr@solAB}{#2}
+       \COPY{\cctr@solAC}{#3}
+       \COPY{\cctr@solBA}{#4}
+       \COPY{\cctr@solBB}{#5}
+       \COPY{\cctr@solBC}{#6}
+       \COPY{\cctr@solCA}{#7}
+       \COPY{\cctr@solCB}{#8}
+       \COPY{\cctr@solCC}{#9}}
+\def\@TDMATRIXGLOBALSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \GLOBALCOPY{\cctr@solAA}{#1}
+       \GLOBALCOPY{\cctr@solAB}{#2}
+       \GLOBALCOPY{\cctr@solAC}{#3}
+       \GLOBALCOPY{\cctr@solBA}{#4}
+       \GLOBALCOPY{\cctr@solBB}{#5}
+       \GLOBALCOPY{\cctr@solBC}{#6}
+       \GLOBALCOPY{\cctr@solCA}{#7}
+       \GLOBALCOPY{\cctr@solCB}{#8}
+       \GLOBALCOPY{\cctr@solCC}{#9}}
+\def\@TDMATRIXNOSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+          \let#1\undefined
+          \let#2\undefined
+          \let#3\undefined
+          \let#4\undefined
+          \let#5\undefined
+          \let#6\undefined
+          \let#7\undefined
+          \let#8\undefined
+          \let#9\undefined
+          }
+\def\@@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \ifx\cctr@solAA\undefined
+          \@TDMATRIXNOSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9)%
+       \else
+          \@TDMATRIXSOL(#1,#2,#3;#4,#5,#6;#7,#8,#9)\fi}
+\def\@NUMBERSOL#1{\COPY{\cctr@sol}{#1}}
+\def\MATRIXSIZE(#1)#2{\expandafter\@MATRIXSIZE(#1;;){#2}}
+\def\@MATRIXSIZE(#1;#2;#3;#4)#5{\ifx$#3$\COPY{2}{#5}
+                                \else\COPY{3}{#5}\fi\ignorespaces}
+\def\@@MATRIXCOPY(#1,#2;#3,#4)(#5,#6;#7,#8){%
+    \COPY{#1}{#5}\COPY{#2}{#6}\COPY{#3}{#7}\COPY{#4}{#8}}
+
+\def\@@@MATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+     \@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+     \@TDMATRIXSOL}
+
+\def\MATRIXCOPY(#1)(#2){%
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXCOPY(#1)(#2)
+        \else \@@@MATRIXCOPY(#1)(#2)\fi}
+\def\@@MATRIXGLOBALCOPY(#1,#2;#3,#4)(#5,#6;#7,#8){%
+    \GLOBALCOPY{#1}{#5}\GLOBALCOPY{#2}{#6}\GLOBALCOPY{#3}{#7}\GLOBALCOPY{#4}{#8}}
+
+\def\@@@MATRIXGLOBALCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+     \@TDMATRIXCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+     \@TDMATRIXGLOBALSOL}
+
+\def\MATRIXGLOBALCOPY(#1)(#2){%
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXGLOBALCOPY(#1)(#2)
+        \else \@@@MATRIXGLOBALCOPY(#1)(#2)\fi}
+\def\@@OUTPUTMATRIX(#1,#2;#3,#4){%
+    \MATRIXGLOBALCOPY(#1,#2;#3,#4)(\cctr@outa,\cctr@outb;\cctr@outc,\cctr@outd)
+    \endgroup\MATRIXCOPY(\cctr@outa,\cctr@outb;\cctr@outc,\cctr@outd)(#1,#2;#3,#4)}
+
+\def\@@@OUTPUTMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+    \MATRIXGLOBALCOPY(#1,#2,#3;#4,#5,#6;#7,#8,#9)(%
+        \cctr@outa,\cctr@outb,\cctr@outc;
+        \cctr@outd,\cctr@oute,\cctr@outf;
+        \cctr@outg,\cctr@outh,\cctr@outi)
+    \endgroup\MATRIXCOPY(%
+        \cctr@outa,\cctr@outb,\cctr@outc;
+        \cctr@outd,\cctr@oute,\cctr@outf;
+        \cctr@outg,\cctr@outh,\cctr@outi)(#1,#2,#3;#4,#5,#6;#7,#8,#9)}
+
+\def\@OUTPUTMATRIX(#1){\MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@OUTPUTMATRIX(#1)
+        \else \@@@OUTPUTMATRIX(#1)\fi}
+\def\@@TRANSPOSEMATRIX(#1,#2;#3,#4)(#5,#6;#7,#8){%
+       \COPY{#1}{#5}\COPY{#3}{#6}\COPY{#2}{#7}\COPY{#4}{#8}}
+
+\def\@@@TRANSPOSEMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \@TDMATRIXCOPY(#1,#4,#7;#2,#5,#8;#3,#6,#9)
+       \@TDMATRIXSOL}
+
+\def\TRANSPOSEMATRIX(#1)(#2){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@TRANSPOSEMATRIX(#1)(#2)
+        \else \@@@TRANSPOSEMATRIX(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+\def\@@MATRIXADD(#1;#2)(#3;#4)(#5,#6;#7,#8){%
+       \VECTORADD(#1)(#3)(#5,#6)
+       \VECTORADD(#2)(#4)(#7,#8)}
+
+\def\@@@MATRIXADD(#1;#2;#3)(#4;#5;#6){%
+       \VECTORADD(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORADD(#2)(#5)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORADD(#3)(#6)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+
+\def\MATRIXADD(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXADD(#1)(#2)(#3)
+        \else \@@@MATRIXADD(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+\def\@@MATRIXSUB(#1;#2)(#3;#4)(#5,#6;#7,#8){%
+       \VECTORSUB(#1)(#3)(#5,#6)
+       \VECTORSUB(#2)(#4)(#7,#8)}
+
+\def\@@@MATRIXSUB(#1;#2;#3)(#4;#5;#6){%
+       \VECTORSUB(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORSUB(#2)(#5)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORSUB(#3)(#6)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+
+\def\MATRIXSUB(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXSUB(#1)(#2)(#3)
+        \else \@@@MATRIXSUB(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+\def\@@MATRIXABSVALUE(#1;#2)(#3;#4){%
+       \VECTORABSVALUE(#1)(#3)\VECTORABSVALUE(#2)(#4)}
+
+\def\@@@MATRIXABSVALUE(#1;#2;#3)(#4;#5;#6){%
+       \VECTORABSVALUE(#1)(#4)\VECTORABSVALUE(#2)(#5)\VECTORABSVALUE(#3)(#6)}
+
+\def\MATRIXABSVALUE(#1)(#2){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXABSVALUE(#1)(#2)
+        \else \@@@MATRIXABSVALUE(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+
+\def\@@MATRIXVECTORPRODUCT(#1;#2)(#3)(#4,#5){%
+       \SCALARPRODUCT(#1)(#3){#4}
+       \SCALARPRODUCT(#2)(#3){#5}}
+
+\def\@@@MATRIXVECTORPRODUCT(#1;#2;#3)(#4)(#5,#6,#7){%
+       \SCALARPRODUCT(#1)(#4){#5}
+       \SCALARPRODUCT(#2)(#4){#6}
+       \SCALARPRODUCT(#3)(#4){#7}}
+
+\def\MATRIXVECTORPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXVECTORPRODUCT(#1)(#2)(#3)
+        \else \@@@MATRIXVECTORPRODUCT(#1)(#2)(#3)\fi\@OUTPUTVECTOR(#3)}
+
+\def\@@VECTORMATRIXPRODUCT(#1)(#2,#3;#4,#5)(#6,#7){%
+       \SCALARPRODUCT(#1)(#2,#4){#6}
+       \SCALARPRODUCT(#1)(#3,#5){#7}}
+
+\def\@@@VECTORMATRIXPRODUCT(#1,#2,#3)(#4;#5;#6)(#7){%
+       \SCALARVECTORPRODUCT{#1}(#4)(#7)
+       \SCALARVECTORPRODUCT{#2}(#5)(\cctr@tempa,\cctr@tempb,\cctr@tempc)
+       \VECTORADD(#7)(\cctr@tempa,\cctr@tempb,\cctr@tempc)(#7)
+       \SCALARVECTORPRODUCT{#3}(#6)(\cctr@tempa,\cctr@tempb,\cctr@tempc)
+       \VECTORADD(#7)(\cctr@tempa,\cctr@tempb,\cctr@tempc)(#7)}
+
+\def\VECTORMATRIXPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \VECTORSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@VECTORMATRIXPRODUCT(#1)(#2)(#3)
+        \else \@@@VECTORMATRIXPRODUCT(#1)(#2)(#3)\fi\@OUTPUTVECTOR(#3)}
+
+\def\@@SCALARMATRIXPRODUCT#1(#2;#3)(#4,#5;#6,#7){%
+       \SCALARVECTORPRODUCT{#1}(#2)(#4,#5)
+       \SCALARVECTORPRODUCT{#1}(#3)(#6,#7)}
+
+\def\@@@SCALARMATRIXPRODUCT#1(#2;#3;#4){%
+       \SCALARVECTORPRODUCT{#1}(#2)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \SCALARVECTORPRODUCT{#1}(#3)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \SCALARVECTORPRODUCT{#1}(#4)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+
+\def\SCALARMATRIXPRODUCT#1(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#2){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SCALARMATRIXPRODUCT{#1}(#2)(#3)
+        \else \@@@SCALARMATRIXPRODUCT{#1}(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+\def\@@MATRIXPRODUCT(#1)(#2,#3;#4,#5)(#6,#7;#8,#9){%
+       \MATRIXVECTORPRODUCT(#1)(#2,#4)(#6,#8)
+       \MATRIXVECTORPRODUCT(#1)(#3,#5)(#7,#9)}
+
+\def\@@@MATRIXPRODUCT(#1;#2;#3)(#4){%
+       \VECTORMATRIXPRODUCT(#1)(#4)(\cctr@solAA,\cctr@solAB,\cctr@solAC)
+       \VECTORMATRIXPRODUCT(#2)(#4)(\cctr@solBA,\cctr@solBB,\cctr@solBC)
+       \VECTORMATRIXPRODUCT(#3)(#4)(\cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \@TDMATRIXSOL}
+
+\def\MATRIXPRODUCT(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@MATRIXPRODUCT(#1)(#2)(#3)
+        \else \@@@MATRIXPRODUCT(#1)(#2)(#3)\fi\@OUTPUTMATRIX(#3)}
+\def\@@DETERMINANT(#1,#2;#3,#4)#5{%
+       \MULTIPLY{#1}{#4}{#5}
+       \MULTIPLY{#2}{#3}{\cctr@tempa}
+       \SUBTRACT{#5}{\cctr@tempa}{#5}}
+
+\def\@@@DETERMINANT(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+       \DETERMINANT(#5,#6;#8,#9){\cctr@det}\MULTIPLY{#1}{\cctr@det}{\cctr@sol}
+       \DETERMINANT(#6,#4;#9,#7){\cctr@det}\MULTIPLY{#2}{\cctr@det}{\cctr@det}
+                                        \ADD{\cctr@sol}{\cctr@det}{\cctr@sol}
+       \DETERMINANT(#4,#5;#7,#8){\cctr@det}\MULTIPLY{#3}{\cctr@det}{\cctr@det}
+                                        \ADD{\cctr@sol}{\cctr@det}{\cctr@sol}
+       \@NUMBERSOL}
+
+\def\DETERMINANT(#1)#2{%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@DETERMINANT(#1){#2}
+        \else \@@@DETERMINANT(#1){#2}\fi\@OUTPUTSOL{#2}}
+\def\@@INVERSEMATRIX(#1,#2;#3,#4)(#5,#6;#7,#8){%
+       \ifdim \cctr@@det\p@ <\cctr@epsilon  % Matrix is singular
+          \let#5\undefined
+          \let#6\undefined
+          \let#7\undefined
+          \let#8\undefined
+          \cctr@Warnsingmatrix{#1}{#2}{#3}{#4}%
+       \else \COPY{#1}{#8}
+          \COPY{#4}{#5}
+          \MULTIPLY{-1}{#3}{#7}
+          \MULTIPLY{-1}{#2}{#6}
+          \DIVIDE{1}{\cctr@det}{\cctr@det}
+          \SCALARMATRIXPRODUCT{\cctr@det}(#5,#6;#7,#8)(#5,#6;#7,#8)
+       \fi}
+
+\def\@@@INVERSEMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+              \ifdim \cctr@@det\p@ <\cctr@epsilon  % Matrix is singular
+          \@TDMATRIXNOSOL(\cctr@solAA,\cctr@solAB,\cctr@solAC;
+                          \cctr@solBA,\cctr@solBB,\cctr@solBC;
+                          \cctr@solCA,\cctr@solCB,\cctr@solCC)
+          \cctr@WarnsingTDmatrix{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}{#9}%
+       \else
+          \@ADJMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solAA,\cctr@solAB,\cctr@solAC)(%
+                                   \cctr@solAA,\cctr@solAB,\cctr@solAC)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solBA,\cctr@solBB,\cctr@solBC)(%
+                                   \cctr@solBA,\cctr@solBB,\cctr@solBC)
+          \@SCLRDIVVECT{\cctr@det}(\cctr@solCA,\cctr@solCB,\cctr@solCC)(%
+                                   \cctr@solCA,\cctr@solCB,\cctr@solCC)
+       \fi
+       \@@TDMATRIXSOL}
+
+\def\@SCLRDIVVECT#1(#2,#3,#4)(#5,#6,#7){%
+             \DIVIDE{#2}{#1}{#5}\DIVIDE{#3}{#1}{#6}\DIVIDE{#4}{#1}{#7}}
+
+\def\@ADJMATRIX(#1,#2,#3;#4,#5,#6;#7,#8,#9){%
+          \DETERMINANT(#5,#6;#8,#9){\cctr@solAA}
+          \DETERMINANT(#6,#4;#9,#7){\cctr@solBA}
+          \DETERMINANT(#4,#5;#7,#8){\cctr@solCA}
+          \DETERMINANT(#8,#9;#2,#3){\cctr@solAB}
+          \DETERMINANT(#1,#3;#7,#9){\cctr@solBB}
+          \DETERMINANT(#2,#1;#8,#7){\cctr@solCB}
+          \DETERMINANT(#2,#3;#5,#6){\cctr@solAC}
+          \DETERMINANT(#3,#1;#6,#4){\cctr@solBC}
+          \DETERMINANT(#1,#2;#4,#5){\cctr@solCC}}
+
+\def\INVERSEMATRIX(#1)(#2){%
+        \begingroup
+        \DETERMINANT(#1){\cctr@det}
+        \ABSVALUE{\cctr@det}{\cctr@@det}
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@INVERSEMATRIX(#1)(#2)
+        \else
+           \@@@INVERSEMATRIX(#1)(#2)\fi\@OUTPUTMATRIX(#2)}
+\def\@INCSYS#1#2{\cctr@WarnIncLinSys
+       \let#1\undefined\let#2\undefined}
+
+\def\@SOLPART#1#2#3#4{\cctr@WarnIndLinSys
+                      \DIVIDE{#1}{#2}{#3}
+                      \COPY{0}{#4}}
+
+\def\@TDINCSYS(#1,#2,#3){\cctr@WarnIncTDLinSys
+                         \let#1\undefined
+                         \let#2\undefined
+                         \let#3\undefined}
+
+\def\@@SOLVELINEARSYSTEM(#1,#2;#3,#4)(#5,#6)(#7,#8){%
+        \DETERMINANT(#1,#2;#3,#4)\cctr@deta
+        \DETERMINANT(#5,#2;#6,#4)\cctr@detb
+        \DETERMINANT(#1,#5;#3,#6)\cctr@detc
+        \ABSVALUE{\cctr@deta}{\cctr@@deta}
+        \ABSVALUE{\cctr@detb}{\cctr@@detb}
+        \ABSVALUE{\cctr@detc}{\cctr@@detc}
+        \ifdim \cctr@@deta\p@>\cctr@epsilon% Regular matrix. Determinate system
+           \DIVIDE{\cctr@detb}{\cctr@deta}{#7}
+           \DIVIDE{\cctr@detc}{\cctr@deta}{#8}
+        \else  % Singular matrix    \cctr@deta=0
+           \ifdim \cctr@@detb\p@>\cctr@epsilon% Incompatible system
+              \@INCSYS#7#8
+           \else
+              \ifdim \cctr@@detc\p@>\cctr@epsilon% Incompatible system
+                 \@INCSYS#7#8
+              \else
+                 \MATRIXABSVALUE(#1,#2;#3,#4)(\cctr@tempa,\cctr@tempb;
+                                              \cctr@tempc,\cctr@tempd)
+                 \ifdim \cctr@tempa\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                    \@SOLPART{#5}{#1}{#7}{#8}
+                 \else
+                    \ifdim \cctr@tempb\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                       \@SOLPART{#5}{#2}{#8}{#7}
+                    \else
+                       \ifdim \cctr@tempc\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                          \@SOLPART{#6}{#3}{#7}{#8}
+                       \else
+                          \ifdim \cctr@tempd\p@ > \cctr@epsilon
+                                               % Indeterminate system
+                             \@SOLPART{#6}{#4}{#8}{#7}
+                          \else
+                             \VECTORNORM(#5,#6){\cctr@tempa}
+                             \ifdim \cctr@tempa\p@ > \cctr@epsilon
+                                               % Incompatible system
+                                \@INCSYS#7#8
+                             \else
+                                   \cctr@WarnZeroLinSys
+                                   \COPY{0}{#7}\COPY{0}{#8}
+                                               % 0x=0 Indeterminate system
+        \fi\fi\fi\fi\fi\fi\fi\fi}
+
+\def\@@@SOLVELINEARSYSTEM(#1)(#2)(#3){%
+       \DETERMINANT(#1){\cctr@det}
+       \ABSVALUE{\cctr@det}{\cctr@@det}
+       \ifdim\cctr@@det\p@<\cctr@epsilon
+          \@TDINCSYS(#3)
+          \else
+             \@ADJMATRIX(#1)
+             \MATRIXVECTORPRODUCT(\cctr@solAA,\cctr@solAB,\cctr@solAC;
+                                  \cctr@solBA,\cctr@solBB,\cctr@solBC;
+                                  \cctr@solCA,\cctr@solCB,\cctr@solCC)(#2)(#3)
+             \@SCLRDIVVECT{\cctr@det}(#3)(#3)
+          \fi}
+
+\def\SOLVELINEARSYSTEM(#1)(#2)(#3){%
+        \begingroup
+        \MATRIXSIZE(#1){\cctr@size}
+        \ifnum\cctr@size=2
+           \@@SOLVELINEARSYSTEM(#1)(#2)(#3)
+        \else
+           \@@@SOLVELINEARSYSTEM(#1)(#2)(#3)
+        \fi\@OUTPUTVECTOR(#3)}
+\def\numberPI{3.14159}
+\MULTIPLY{\numberPI}{2}{\numberTWOPI}
+\DIVIDE{\numberPI}{2}{\numberHALFPI}
+\MULTIPLY{\numberPI}{1.5}{\numberTHREEHALFPI}
+\DIVIDE{\numberPI}{3}{\numberTHIRDPI}
+\DIVIDE{\numberPI}{4}{\numberQUARTERPI}
+\DIVIDE{\numberPI}{5}{\numberFIFTHPI}
+\DIVIDE{\numberPI}{6}{\numberSIXTHPI}
+\def\numberE{2.71828}
+\DIVIDE{1}{\numberE}{\numberINVE}
+\SQUARE{\numberE}{\numberETWO}
+\SQUARE{\numberINVE}{\numberINVETWO}
+\def\numberLOGTEN{2.30258}
+\def\numberGOLD{1.61803}
+\def\numberINVGOLD{0.61803}
+\def\numberSQRTTWO{1.41421}
+\def\numberSQRTTHREE{1.73205}
+\def\numberSQRTFIVE{2.23607}
+\def\numberCOSXLV{0.70711}
+\def\numberCOSXXX{0.86603}
+%% 
+%%
+%% End of file `calculator.sty'.
diff --git a/Master/texmf-dist/tex/latex/calculator/calculus.sty b/Master/texmf-dist/tex/latex/calculator/calculus.sty
new file mode 100644
index 00000000000..c90dabece8a
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/calculator/calculus.sty
@@ -0,0 +1,438 @@
+%%
+%% This is file `calculus.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% calculator.dtx  (with options: `calculus')
+%% ------------------------------------------------------------------
+%% The calculator and calculus packages
+%% Copyright (C) 2012 by Robert Fuster <rfuster@mat.upv.es>
+%% All rights reserved
+%% 
+%% This file may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%% The latest version of this license is in:
+%% 
+%%     http://www.latex-project.org/lppl.txt
+%% 
+%% and version 1.3 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% ------------------------------------------------------------------
+%% \CharacterTable
+%%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%%   Digits        \0\1\2\3\4\5\6\7\8\9
+%%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%%   Dollar        \$     Percent       \%     Ampersand     \&
+%%   Acute accent  \'     Left paren    \(     Right paren   \)
+%%   Asterisk      \*     Plus          \+     Comma         \,
+%%   Minus         \-     Point         \.     Solidus       \/
+%%   Colon         \:     Semicolon     \;     Less than     \<
+%%   Equals        \=     Greater than  \>     Question mark \?
+%%   Commercial at \@     Left bracket  \[     Backslash     \\
+%%   Right bracket \]     Circumflex    \^     Underscore    \_
+%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%%   Right brace   \}     Tilde         \~}
+
+
+
+
+\NeedsTeXFormat{LaTeX2e}
+\ProvidesPackage{calculus}
+   [2012/06/10 v.1.0a]
+\RequirePackage{calculator}
+\def\ccls@ErrorFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1 command as a
+         function\MessageBreak
+         please, use the \noexpand\renewfunction command}}
+\def\ccls@ErrorFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence is not currently defined\MessageBreak
+         If you want to define the \noexpand#1 command as a function\MessageBreak
+         please, use the \noexpand\newfunction command}}
+\def\ccls@InfoFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurefunction command will not redefine it}}
+\def\ccls@ErrorPFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1
+         command as a polar function\MessageBreak
+         please, use the \noexpand\renewpolarfunction command}}
+
+\def\ccls@ErrorPFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence
+         is not currently defined.\MessageBreak
+         If you want to define the \noexpand#1 command as a polar
+         function\MessageBreak
+         please, use the \noexpand\newpolarfunction command}}
+
+\def\ccls@InfoPFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurepolarfunction command does not redefine it}}
+\def\ccls@ErrorVFuncDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command already defined}
+        {The \noexpand#1 control sequence is already defined\MessageBreak
+         If you want to redefine the \noexpand#1 command as a vector
+         function\MessageBreak
+         please, use the \noexpand\renewvectorfunction command}}
+
+\def\ccls@ErrorVFuncUnDef#1{%
+      \PackageError{calculus}%
+        {\noexpand#1 command undefined}
+        {The \noexpand#1 control sequence is not currently
+         defined.\MessageBreak
+         If you want to define the \noexpand#1 command as a vector
+         function\MessageBreak
+         please, use the \noexpand\newvectorfunction command}}
+
+\def\ccls@InfoVFuncEns#1{%
+      \PackageInfo{calculus}%
+      {\noexpand#1 command already defined\MessageBreak
+       the \noexpand\ensurevectorfunction command does not redefine it}}
+\def\newfunction#1#2{%
+       \ifx #1\undefined
+         \ccls@deffunction{#1}{#2}
+       \else
+          \ccls@ErrorFuncDef{#1}
+       \fi}
+\def\renewfunction#1#2{%
+       \ifx #1\undefined
+          \ccls@ErrorFuncUnDef{#1}
+       \else
+          \ccls@deffunction{#1}{#2}
+       \fi}
+\def\ensurefunction#1#2{%
+       \ifx #1\undefined\ccls@deffunction{#1}{#2}
+       \else
+          \ccls@InfoFuncEns{#1}
+       \fi}
+\def\forcefunction#1#2{%
+       \ccls@deffunction{#1}{#2}}
+\def\ccls@deffunction#1#2{%
+    \def#1##1##2##3{%
+             \begingroup
+             \def\t{##1}%
+                  #2
+                 \xdef##2{\y}%
+                 \xdef##3{\Dy}%
+             \endgroup}\ignorespaces}
+\def\newpolarfunction#1#2{%
+       \ifx #1\undefined
+         \ccls@defpolarfunction{#1}{#2}
+       \else
+          \ccls@ErrorPFuncDef{#1}
+       \fi}
+\def\renewpolarfunction#1#2{%
+       \ifx #1\undefined
+          \ccls@ErrorPFuncUnDef{#1}
+       \else
+          \ccls@defpolarfunction{#1}{#2}
+       \fi}
+\def\ensurepolarfunction#1#2{%
+       \ifx #1\undefined\ccls@defpolarfunction{#1}{#2}
+       \else
+          \ccls@InfoPFuncEns{#1}
+       \fi}
+\def\forcepolarfunction#1#2{%
+       \ccls@defpolarfunction{#1}{#2}}
+\def\ccls@defpolarfunction#1#2{%
+       \def#1##1##2##3##4##5{%
+       \begingroup
+         \def\t{##1}
+       #2
+       \COS{\t}\ccls@cost
+       \MULTIPLY\r\ccls@cost{\x}
+       \SIN{\t}\ccls@sint
+       \MULTIPLY\r\ccls@sint{\y}
+       \MULTIPLY\ccls@cost\Dr\Dx
+       \SUBTRACT{\Dx}{\y}{\Dx}
+       \MULTIPLY\ccls@sint\Dr\Dy
+       \ADD{\Dy}{\x}{\Dy}
+       \xdef##2{\x}
+       \xdef##3{\Dx}
+       \xdef##4{\y}
+       \xdef##5{\Dy}
+       \endgroup}\ignorespaces}
+\def\newvectorfunction#1#2{%
+       \ifx #1\undefined
+         \ccls@defvectorfunction{#1}{#2}
+       \else
+          \ccls@ErrorVFuncDef{#1}
+       \fi}
+\def\renewvectorfunction#1#2{%
+       \ifx #1\undefined
+          \ccls@ErrorVFuncUnDef{#1}
+       \else
+          \ccls@defvectorfunction{#1}{#2}
+       \fi}
+\def\ensurevectorfunction#1#2{%
+       \ifx #1\undefined\ccls@defvectorfunction{#1}{#2}
+       \else
+          \ccls@InfoVFuncEns{#1}
+       \fi}
+\def\forcevectorfunction#1#2{%
+       \ccls@defvectorfunction{#1}{#2}}
+\def\ccls@defvectorfunction#1#2{%
+       \def#1##1##2##3##4##5{%
+       \begingroup
+         \def\t{##1}
+       #2
+       \xdef##2{\x}
+       \xdef##3{\Dx}
+       \xdef##4{\y}
+       \xdef##5{\Dy}
+       \endgroup}\ignorespaces}
+\def\newlpoly#1#2#3{%
+    \newfunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+\def\renewlpoly#1#2#3{%
+    \renewfunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+\def\ensurelpoly#1#2#3{%
+    \ensurefunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+\def\forcelpoly#1#2#3{%
+    \forcefunction{#1}{%
+        \ccls@lpoly{#2}{#3}}}
+\def\ccls@lpoly#1#2{%
+        \MULTIPLY{#2}{\t}{\y}
+        \ADD{\y}{#1}{\y}
+        \COPY{#2}{\Dy}}
+\def\newqpoly#1#2#3#4{%
+    \newfunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+\def\renewqpoly#1#2#3#4{%
+    \renewfunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+\def\ensureqpoly#1#2#3#4{%
+    \ensurefunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+\def\forceqpoly#1#2#3#4{%
+    \forcefunction{#1}{%
+        \ccls@qpoly{#2}{#3}{#4}}}
+\def\ccls@qpoly#1#2#3{%
+        \MULTIPLY{\t}{#3}{\y}
+           \MULTIPLY{2}{\y}{\Dy}
+           \ADD{#2}{\Dy}{\Dy}
+        \ADD{#2}{\y}{\y}
+        \MULTIPLY{\t}{\y}{\y}
+        \ADD{#1}{\y}{\y}}
+\def\newcpoly#1#2#3#4#5{%
+    \newfunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+\def\renewcpoly#1#2#3#4#5{%
+    \renewfunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+\def\ensurecpoly#1#2#3#4#5{%
+    \ensurefunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+\def\forcecpoly#1#2#3#4#5{%
+    \forcefunction{#1}{%
+        \ccls@cpoly{#2}{#3}{#4}{#5}}}
+\def\ccls@cpoly#1#2#3#4{%
+        \MULTIPLY{\t}{#4}{\y}
+           \MULTIPLY{3}{\y}{\Dy}
+        \ADD{#3}{\y}{\y}
+           \MULTIPLY{2}{#3}{\ccls@temp}
+           \ADD{\ccls@temp}{\Dy}{\Dy}
+        \MULTIPLY{\t}{\y}{\y}
+           \MULTIPLY{\t}{\Dy}{\Dy}
+        \ADD{#2}{\y}{\y}
+           \ADD{#2}{\Dy}{\Dy}
+        \MULTIPLY{\t}{\y}{\y}
+        \ADD{#1}{\y}{\y}
+        }
+\newfunction{\ONEfunction}{%
+      \COPY{1}{\y}
+      \COPY{0}{\Dy}}
+\newfunction{\ZEROfunction}{%
+      \COPY{0}{\y}
+      \COPY{0}{\Dy}}
+\newfunction{\IDENTITYfunction}{%
+      \COPY{\t}{\y}
+      \COPY{1}{\Dy}}
+\newfunction{\RECIPROCALfunction}{%
+      \DIVIDE{1}{\t}{\y}
+      \SQUARE{\y}{\Dy}
+      \MULTIPLY{-1}{\Dy}{\Dy}}
+\newfunction{\SQUAREfunction}{%
+      \SQUARE{\t}{\y}
+      \MULTIPLY{2}{\t}{\Dy}}
+\newfunction{\CUBEfunction}{%
+      \SQUARE{\t}{\Dy}
+      \MULTIPLY{\t}{\Dy}{\y}
+      \MULTIPLY{3}{\Dy}{\Dy}}
+\newfunction{\SQRTfunction}{%
+      \SQRT{\t}{\y}
+      \DIVIDE{0.5}{\y}{\Dy}}
+\newfunction{\EXPfunction}{%
+     \EXP{\t}{\y}
+     \COPY{\y}{\Dy}}
+\newfunction{\COSfunction}{%
+     \COS{\t}{\y}
+     \SIN{\t}{\Dy}
+     \MULTIPLY{-1}{\Dy}{\Dy}}
+\newfunction{\SINfunction}{%
+     \SIN{\t}{\y}
+     \COS{\t}{\Dy}}
+\newfunction{\TANfunction}{%
+     \TAN{\t}{\y}
+     \COS{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{1}{\Dy}{\Dy}}
+\newfunction{\COTfunction}{%
+     \COTAN{\t}{\y}
+     \SIN{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{-1}{\Dy}{\Dy}}
+\newfunction{\COSHfunction}{%
+     \COSH{\t}{\y}
+     \SINH{\t}{\Dy}}
+\newfunction{\SINHfunction}{%
+     \SINH{\t}{\y}
+     \COSH{\t}{\Dy}}
+\newfunction{\TANHfunction}{%
+     \TANH{\t}{\y}
+     \COSH{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{1}{\Dy}{\Dy}}
+\newfunction{\COTHfunction}{%
+     \COTANH{\t}{\y}
+     \SINH{\t}{\Dy}
+     \SQUARE{\Dy}{\Dy}
+     \DIVIDE{-1}{\Dy}{\Dy}}
+\newfunction{\LOGfunction}{%
+     \LOG{\t}{\y}
+     \DIVIDE{1}{\t}{\Dy}}
+\newfunction{\HEAVISIDEfunction}{%
+     \ifdim \t\p@<\z@ \COPY{0}{\y}\else\COPY{1}{\y}\fi
+      \COPY{0}{\Dy}}
+\def\CONSTANTfunction#1#2{%
+              \def#2##1##2##3{%
+                          \xdef##2{#1}%
+                          \xdef##3{0}}}
+\def\SUMfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@SUMf}{\ccls@SUMDf}%
+                    #2{##1}{\ccls@SUMg}{\ccls@SUMDg}%
+                    \ADD{\ccls@SUMf}{\ccls@SUMg}{\ccls@SUMfg}
+                    \ADD{\ccls@SUMDf}{\ccls@SUMDg}{\ccls@SUMDfg}
+                         \xdef##2{\ccls@SUMfg}%
+                         \xdef##3{\ccls@SUMDfg}%
+             \endgroup}\ignorespaces}
+\def\SUBTRACTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@SUBf}{\ccls@SUBDf}%
+                    #2{##1}{\ccls@SUBg}{\ccls@SUBDg}%
+                    \SUBTRACT{\ccls@SUBf}{\ccls@SUBg}{\ccls@SUBfg}
+                    \SUBTRACT{\ccls@SUBDf}{\ccls@SUBDg}{\ccls@SUBDfg}
+                         \xdef##2{\ccls@SUBfg}%
+                         \xdef##3{\ccls@SUBDfg}%
+             \endgroup}\ignorespaces}
+\def\PRODUCTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@PROf}{\ccls@PRODf}%
+                    #2{##1}{\ccls@PROg}{\ccls@PRODg}%
+                    \MULTIPLY{\ccls@PROf}{\ccls@PROg}{\ccls@PROfg}
+                    \MULTIPLY{\ccls@PROf}{\ccls@PRODg}{\ccls@PROfDg}
+                    \MULTIPLY{\ccls@PRODf}{\ccls@PROg}{\ccls@PRODfg}
+                    \ADD{\ccls@PROfDg}{\ccls@PRODfg}{\ccls@PRODfg}
+                         \xdef##2{\ccls@PROfg}%
+                         \xdef##3{\ccls@PRODfg}%
+             \endgroup}\ignorespaces}
+\def\QUOTIENTfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@QUOf}{\ccls@QUODf}%
+                    #2{##1}{\ccls@QUOg}{\ccls@QUODg}%
+                    \DIVIDE{\ccls@QUOf}{\ccls@QUOg}{\ccls@QUOfg}
+                    \MULTIPLY{\ccls@QUOf}{\ccls@QUODg}{\ccls@QUOfDg}
+                    \MULTIPLY{\ccls@QUODf}{\ccls@QUOg}{\ccls@QUODfg}
+                    \SUBTRACT{\ccls@QUODfg}{\ccls@QUOfDg}{\ccls@QUOnum}
+                    \SQUARE{\ccls@QUOg}{\ccls@qsquaretempg}
+                    \DIVIDE{\ccls@QUOnum}{\ccls@qsquaretempg}{\ccls@QUODfg}
+                         \xdef##2{\ccls@QUOfg}%
+                         \xdef##3{\ccls@QUODfg}%
+             \endgroup}\ignorespaces}
+\def\COMPOSITIONfunction#1#2#3{%  #3=#1(#2)
+            \def#3##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@COMg}{\ccls@COMDg}%
+                    #1{\ccls@COMg}{\ccls@COMf}{\ccls@COMDf}%
+                    \MULTIPLY{\ccls@COMDg}{\ccls@COMDf}{\ccls@COMDf}
+                         \xdef##2{\ccls@COMf}%
+                         \xdef##3{\ccls@COMDf}%
+             \endgroup}\ignorespaces}
+\def\SCALEfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@SCFf}{\ccls@SCFDf}%
+                    \MULTIPLY{#1}{\ccls@SCFf}{\ccls@SCFaf}
+                    \MULTIPLY{#1}{\ccls@SCFDf}{\ccls@SCFDaf}
+                         \xdef##2{\ccls@SCFaf}%
+                         \xdef##3{\ccls@SCFDaf}%
+             \endgroup}\ignorespaces}
+\def\SCALEVARIABLEfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup%
+                    \MULTIPLY{#1}{##1}{\ccls@SCVat}
+                    #2{\ccls@SCVat}{\ccls@SCVf}{\ccls@SCVDf}%
+                    \MULTIPLY{#1}{\ccls@SCVDf}{\ccls@SCVDf}
+                         \xdef##2{\ccls@SCVf}%
+                         \xdef##3{\ccls@SCVDf}%
+             \endgroup}\ignorespaces}
+\def\POWERfunction#1#2#3{%
+            \def#3##1##2##3{%
+             \begingroup
+                    #1{##1}{\ccls@POWf}{\ccls@POWDf}%
+                    \POWER{\ccls@POWf}{#2}{\ccls@POWfn}
+                   \SUBTRACT{#2}{1}{\ccls@nminusone}
+                   \POWER{\ccls@POWf}{\ccls@nminusone}{\ccls@POWDfn}
+                  \MULTIPLY{#2}{\ccls@POWDfn}{\ccls@POWDfn}
+                  \MULTIPLY{\ccls@POWDfn}{\ccls@POWDf}{\ccls@POWDfn}
+                         \xdef##2{\ccls@POWfn}%
+                         \xdef##3{\ccls@POWDfn}%
+             \endgroup}\ignorespaces}
+
+\def\LINEARCOMBINATIONfunction#1#2#3#4#5{%
+            \def#5##1##2##3{%
+             \begingroup
+                    #2{##1}{\ccls@LINf}{\ccls@LINDf}%
+                    #4{##1}{\ccls@LINg}{\ccls@LINDg}%
+                    \MULTIPLY{#1}{\ccls@LINf}{\ccls@LINf}
+                    \MULTIPLY{#3}{\ccls@LINg}{\ccls@LINg}
+                    \MULTIPLY{#1}{\ccls@LINDf}{\ccls@LINDf}
+                    \MULTIPLY{#3}{\ccls@LINDg}{\ccls@LINDg}
+                    \ADD{\ccls@LINf}{\ccls@LINg}{\ccls@LINafbg}
+                    \ADD{\ccls@LINDf}{\ccls@LINDg}{\ccls@LINDafbg}
+                         \xdef##2{\ccls@LINafbg}%
+                         \xdef##3{\ccls@LINDafbg}%
+             \endgroup}\ignorespaces}
+\def\POLARfunction#1#2{%
+       \PRODUCTfunction{#1}{\COSfunction}{\ccls@polarx}
+       \PRODUCTfunction{#1}{\SINfunction}{\ccls@polary}
+       \PARAMETRICfunction{\ccls@polarx}{\ccls@polary}{#2}}
+\def\PARAMETRICfunction#1#2#3{%
+       \def#3##1##2##3##4##5{%
+                #1{##1}{##2}{##3}
+                #2{##1}{##4}{##5}}}
+\let\VECTORfunction\PARAMETRICfunction
+%% 
+%%
+%% End of file `calculus.sty'.
diff --git a/Master/tlpkg/bin/tlpkg-ctan-check b/Master/tlpkg/bin/tlpkg-ctan-check
index 68f4a64aa52..82cb980bb17 100755
--- a/Master/tlpkg/bin/tlpkg-ctan-check
+++ b/Master/tlpkg/bin/tlpkg-ctan-check
@@ -75,7 +75,7 @@ my @TLP_working = qw(
     boxedminipage boxhandler bpchem bpolynomial
     bracketkey braids braille braket breakcites breakurl
     bullcntr bundledoc burmese bussproofs bytefield 
-  c-pascal cachepic calctab
+  c-pascal cachepic calctab calculator
     calligra calligra-type1 calrsfs cals calxxxx-yyyy cancel
     canoniclayout cantarell
     capt-of captcont captdef caption carlisle carolmin-ps
diff --git a/Master/tlpkg/libexec/ctan2tds b/Master/tlpkg/libexec/ctan2tds
index f432084d745..a1b71240ef0 100755
--- a/Master/tlpkg/libexec/ctan2tds
+++ b/Master/tlpkg/libexec/ctan2tds
@@ -1824,6 +1824,7 @@ $standardsource='\.(bat|c|drv|dtx|fea|fdd|ins|sfd)$|configure.*|install-sh';
  'booktabs-de',	'NULL',			# doc, no need to build
  'blacklettert1','NULL',  # don't try to do fontinst
  'bosisio',	'.*\.dtx',
+ 'calculator',	"$package.dtx",
  'canoniclayout','.*\.dtx',
  'carlisle',	'\.ins|ltxtable.tex',
  'ccfonts',	'ccfonts.ins',
diff --git a/Master/tlpkg/tlpsrc/calculator.tlpsrc b/Master/tlpkg/tlpsrc/calculator.tlpsrc
new file mode 100644
index 00000000000..e69de29bb2d
--- /dev/null
+++ b/Master/tlpkg/tlpsrc/calculator.tlpsrc
diff --git a/Master/tlpkg/tlpsrc/collection-latexextra.tlpsrc b/Master/tlpkg/tlpsrc/collection-latexextra.tlpsrc
index f3536864966..3a8692db3e5 100644
--- a/Master/tlpkg/tlpsrc/collection-latexextra.tlpsrc
+++ b/Master/tlpkg/tlpsrc/collection-latexextra.tlpsrc
@@ -72,6 +72,7 @@ depend breakurl
 depend bullcntr
 depend bussproofs
 depend calctab
+depend calculator
 depend calrsfs
 depend cals
 depend calxxxx-yyyy