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diff --git a/macros/latex/contrib/calculator/README.md b/macros/latex/contrib/calculator/README.md new file mode 100644 index 0000000000..04c5147e30 --- /dev/null +++ b/macros/latex/contrib/calculator/README.md @@ -0,0 +1,143 @@ +The calculator and calculus packages: Use \LaTeX as a scientific calculator. + +Robert Fuster, 2012, 2014, 2022 + + +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 2.1 +------------------------- +- Some bugs fixed + +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, 2022/09/15 +--------------------------------------------------------------- |