Edit detail for FriCASTutorial revision 6 of 10

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://pages.saclay.inria.fr/daniel.augot/documents/axiom_intro.pdf
 
(local copy http://axiom-wiki.newsynthesis.org/public/axiom/)
(released under CC-BY-SA )
and a blog by
Alasdair McAndrew
containing an excellent introduction to Axiom.
Extending the FriCAS library is done in the programming language SPAD.
Find introductory material on the page ProgrammingSPAD.


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]
\begin{equation*}
\label{eq1}\left[{1 \over 7}, \:{3 \over 4}, \:{5 \over 6}\right]?\end{equation*}
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))
\begin{equation}
\label{eq2}{\left(
\begin{array}{@{}l}
\displaystyle
-{i \ {{e}^{{i \  \Omega \  t}-{i \  \Omega \  \tau}}}}+ 
\
\
\displaystyle
{i \ {{e}^{-{i \  \Omega \  t}+{i \  \Omega \  \tau}}}}
\end{array}
\right)}\over{t - \tau}\end{equation}
Type: Expression(Complex(Integer))

Try this integrating this
fricas
2*x/sin(x)^2
\begin{equation}
\label{eq3}{2 \  x}\over{{\sin \left({x}\right)}^{2}}\end{equation}
Type: Expression(Integer)

fricas
integrate(%,x)
\begin{equation}
\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)}}
\end{array}
\right)}\over{\sin \left({x}\right)}\end{equation}
Type: Union(Expression(Integer),...)

Now differentiate it
fricas
D(%,x)
\begin{equation}
\label{eq5}{{2 \  x \ {{\sin \left({x}\right)}^{2}}}+{2 \  x \ {{\cos \left({x}\right)}^{2}}}}\over{{\sin \left({x}\right)}^{2}}\end{equation}
Type: Expression(Integer)
fricas
simplify(%)
\begin{equation}
\label{eq6}-{{2 \  x}\over{{{\cos \left({x}\right)}^{2}}- 1}}\end{equation}
Type: Expression(Integer)

Expressions (3) and (6) are really that same.
fricas
simplify(%%(3) - %%(6))
\begin{equation}
\label{eq7}0\end{equation}
Type: Expression(Integer)

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

See, that was easy!
Here are some more things to try.
fricas
integrate(log(sin(x)),x=0..%pi)
\begin{equation}
\label{eq9}\mbox{\tt "potentialPole"}\end{equation}
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.

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