The calculator and calculus packages: Use \LaTeX as a scientific calculator.

Robert Fuster, 2012, 2014


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. Changes in version 2.0
-------------------------
- Inverse trigonometric and inverse hyperbolic functions are added
  (this completes the typical elementary functions)

- Also vector (cross) product and angle between vectors can be evaluated

- New length operations

- ... and some other minor additions and changes

3. 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 calculations I need in 
my package "xpicture" 
(http://ctan.org/pkg/xpicture, http://www.upv.es/~rfuster/xpicture), 
but the numeric abilities of "calculator" and "calculus" may be useful 
in other contexts.

3.1 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, trigonometric, exponential, 
  logarithmic, hyperbolic, inverse trigonometric 
  and inverse 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}{\tempc}{\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.


3.2. 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. 


4. Installation and documentation
---------------------------------
1. Compile the installation file "calculator.ins",

     >> latex calculator.ins

   to generate the two essential files,

      "calculator.sty" and "calculus.sty".
     
       Move these two files where LaTeX  search for 
       (typically, in a local texmf tree, at tex/latex/calculator) 
       and refresh the file database.

2. To have the documentation and user's manual, "calculator.pdf",
   compile 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
     >> pdflatex calculator.dtx

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, 2014/02/23
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