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FriCASTutorial
  
last edited 2 years ago by test1

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Most introductory material about Axiom applies to FriCAS.
The [Axiom Volume 1]: Tutorial is available in printed format at
http://publish-book.com and http://www.lulu.com/product/file-download/axiom-volume-1-tutorial/243127

- There is a good introduction to Axiom by Martin N. Dunstan,
in English, at
http://www.dcs.st-andrews.ac.uk/~mnd/documentation/axiom_tutorial (Alternate link: TutorialIntroductionToAxiom )

- a complete introduction to Axiom by Daniel Augot, en Français, is
available at http://www-rocq.inria.fr/codes/Daniel.Augot/axiom_intro.pdf

- an Axiom tutorial and a collection of exercises by Christophe Conil
and Quentin Carpent at http://la.riverotte.free.fr/axiom

- and a blog by
!"Alasdair McAndrew":http://amca01.wordpress.com/category/axiom/
containing an excellent introduction to Axiom.

A Quick Tutorial

  On this web site you can enter FriCAS commands and see the output
in proper mathematical form. These commands can also be typed
directly into FriCAS installed on your own computer.

  You must enclose each set of FriCAS commands in a '!\begin{axiom} \end{axiom}' section. For example::

    !\begin{axiom}
    [1/2, 3/4, 2/3]
    \end{axiom}

When you save the changes you make to a page, FriCAS processes the contents of each section you have marked
and the FriCAS output is displayed.

Try this command:

\begin{axiom}
[1/7, 3/4, 5/6]
\end{axiom}

Please feel free to play with this in the SandBox!

Advanced Examples

  Let's see if we can perform a finite window Fourier inversion.

\begin{axiom}
simplify(integrate(exp(%i*_\omega*t) * exp(-%i*_\omega * _\tau), _\omega=-_\Omega .. _\Omega))
\end{axiom}

Try this integrating this

\begin{axiom}
2*x/sin(x)^2
\end{axiom}

\begin{axiom}
integrate(%,x)
\end{axiom}

Now differentiate it
\begin{axiom}
D(%,x)
simplify(%)
\end{axiom}

Expressions (3) and (6) are really that same.

\begin{axiom}
simplify(%%(3) - %%(6))
\end{axiom}

\begin{axiom}
D(x^x,x)
\end{axiom}

See, that was easy!

Here are some more things to try.

\begin{axiom}
integrate(log(sin(x)),x=0..%pi)
\end{axiom}

\begin{axiom}
limit(sum(1/i^2,i=1..n),n=%plusInfinity)
\end{axiom}

Can you explain these results?

Advanced Programming

  For more details see: FriCASProgramming .

Special FriCASWiki Markup for Programming

  "Spad":AxiomCompiler

    To include Spad programs on web pages in this website click 'edit' (or when adding comments or in bug reports) use::

       !\begin{spad}
       )abbrev ...
       ...
       \end{spad}

  "Aldor":AldorForAxiom

    To include Aldor programs on pages in this website use::

       !\begin{aldor}
       ...
       \end{aldor}

    or::

       !\begin{aldor}[name]
       ...
       \end{aldor}

  LaTeX

    You can add LaTeX formatted equations to pages on this web site by::

       !$$
       ...
       $$

    and inline symbols such as $\alpha +\beta$ are written like this: !$\alpha +\beta$
 
    To include arbitrary LaTeX on pages in this website use::

       !\begin{latex}
       ...
       \end{latex}


  "Lisp":LispInAxiom

    To include Lisp programs on pages in this website use::

       !\begin{lisp}
       ...
       \end{lisp}


  "Boot":BootProgramming

    To include Boot programs on pages in this website use::

       !\begin{boot}
       ...
       \end{boot}


From Yrogirg Fri Apr 1 09:10:57 -0700 2011
From: Yrogirg
Date: Fri, 01 Apr 2011 09:10:57 -0700
Subject: Broken link
Message-ID: <20110401091057-0700@axiom-wiki.newsynthesis.org>

The link to the tutorial by Martin N. Dunstan doesn't work (http://www.dcs.st-andrews.ac.uk/~mnd/documentation/axiom_tutorial). I can't find this tutorial elsewhere.

Most introductory material about Axiom applies to FriCAS?. The [Axiom Volume 1]?: Tutorial is available in printed format at http://publish-book.com and http://www.lulu.com/product/file-download/axiom-volume-1-tutorial/243127

A Quick Tutorial

On this web site you can enter FriCAS? commands and see the output in proper mathematical form. These commands can also be typed directly into FriCAS? installed on your own computer.

You must enclose each set of FriCAS? commands in a \begin{axiom} \end{axiom} section. For example: 

    \begin{axiom}
    [1/2, 3/4, 2/3]
    \end{axiom}

When you save the changes you make to a page, FriCAS? processes the contents of each section you have marked and the FriCAS? output is displayed.

Try this command:

fricas
[1/7, 3/4, 5/6]
\label{eq1}\left[{1 \over 7}, \:{3 \over 4}, \:{5 \over 6}\right](1)
Type: List(Fraction(Integer))

Please feel free to play with this in the SandBox?!

Advanced Examples

Let's see if we can perform a finite window Fourier inversion.

fricas
simplify(integrate(exp(%i*_\omega*t) * exp(-%i*_\omega * _\tau), _\omega=-_\Omega .. _\Omega))
\label{eq2}{\left( \begin{array}{@{}l} \displaystyle -{i \ {{e}^{{i \ \Omega \ t}-{i \ \Omega \ \tau}}}}+ \ \ \displaystyle {i \ {{e}^{-{i \ \Omega \ t}+{i \ \Omega \ \tau}}}} (2)
Type: Expression(Complex(Integer))

Try this integrating this

fricas
2*x/sin(x)^2
\label{eq3}{2 \ x}\over{{\sin \left({x}\right)}^{2}}(3)
Type: Expression(Integer)

fricas
integrate(%,x)
\label{eq4}{\left( \begin{array}{@{}l} \displaystyle {2 \ {\sin \left({x}\right)}\ {\log \left({{\sin \left({x}\right)}\over{{\cos \left({x}\right)}+ 1}}\right)}}-{2 \ {\sin \left({x}\right)}\ {\log \left({2 \over{{\cos \left({x}\right)}+ 1}}\right)}}- \ \ \displaystyle {2 \ x \ {\cos \left({x}\right)}} (4)
Type: Union(Expression(Integer),...)

Now differentiate it

fricas
D(%,x)
\label{eq5}{{2 \ x \ {{\sin \left({x}\right)}^{2}}}+{2 \ x \ {{\cos \left({x}\right)}^{2}}}}\over{{\sin \left({x}\right)}^{2}}(5)
Type: Expression(Integer)
fricas
simplify(%)
\label{eq6}-{{2 \ x}\over{{{\cos \left({x}\right)}^{2}}- 1}}(6)
Type: Expression(Integer)

Expressions (3) and (6) are really that same.

fricas
simplify(%%(3) - %%(6))
\label{eq7}0(7)
Type: Expression(Integer)

fricas
D(x^x,x)
\label{eq8}{{\log \left({x}\right)}\ {{x}^{x}}}+{x \ {{x}^{x - 1}}}(8)
Type: Expression(Integer)

See, that was easy!

Here are some more things to try.

fricas
integrate(log(sin(x)),x=0..%pi)
\label{eq9}potentialPole(9)
Type: Union(pole: potentialPole,...)

fricas
limit(sum(1/i^2,i=1..n),n=%plusInfinity)

   >> Error detected within library code:
   a sum cannot be differentiated with respect to a bound

Can you explain these results?

Advanced Programming

For more details see: FriCASProgramming? .

Special FriCASWiki? Markup for Programming

Spad

To include Spad programs on web pages in this website click edit (or when adding comments or in bug reports) use: 

       \begin{spad}
       )abbrev ...
       ...
       \end{spad}

Aldor

To include Aldor programs on pages in this website use: 

       \begin{aldor}
       ...
       \end{aldor}

or: 

       \begin{aldor}[name]
       ...
       \end{aldor}

LaTeX?

You can add LaTeX? formatted equations to pages on this web site by: 

       $$
       ...
       $$

and inline symbols such as \alpha +\beta are written like this: $\alpha +\beta$

To include arbitrary LaTeX? on pages in this website use: 

       \begin{latex}
       ...
       \end{latex}

Lisp

To include Lisp programs on pages in this website use: 

       \begin{lisp}
       ...
       \end{lisp}

Boot

To include Boot programs on pages in this website use: 

       \begin{boot}
       ...
       \end{boot}

Broken link --Yrogirg, Fri, 01 Apr 2011 09:10:57 -0700 reply
The link to the tutorial by Martin N. Dunstan doesn't work (http://www.dcs.st-andrews.ac.uk/~mnd/documentation/axiom_tutorial). I can't find this tutorial elsewhere.