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FriCASTutorial

Edit detail for FriCASTutorial revision 10 of 10

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Editor: test1 Time: 2022/05/16 16:42:44 GMT+0
Note:

changed:
-(local copy of Texmacs files http://axiom-wiki.newsynthesis.org/public/axiom/)
(local copy of Texmacs files http://fricas-wiki.math.uni.wroc.pl/public/axiom/)

changed:
-- and a blog by
-!"Alasdair McAndrew":http://amca01.wordpress.com/category/axiom/
-containing an excellent introduction to Axiom.
- and a tutorial by 'Alasdair McAndrew' with local copy http://fricas-wiki.math.uni.wroc.pl/public/intro.pdf
based on earlier blog posts
containing an excellent introduction to FriCAS and Axiom.

Most introductory material about Axiom applies to FriCAS. The first chapters of FriCAS book http://fricas.github.io/book.pdf may serve as a tutorial.

There is a good introduction to Axiom by Martin N. Dunstan, in English, copy at: TutorialIntroductionToFriCAS
a complete introduction to Axiom by Daniel Augot, en Français, is available at http://pages.saclay.inria.fr/daniel.augot/documents/axiom_intro.pdf
an Axiom tutorial and a collection of exercises by Christophe Conil and Quentin Carpent at (local copy of Texmacs files http://fricas-wiki.math.uni.wroc.pl/public/axiom/) (released under CC-BY-SA )
and a tutorial by Alasdair McAndrew with local copy http://fricas-wiki.math.uni.wroc.pl/public/intro.pdf based on earlier blog posts containing an excellent introduction to FriCAS and 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) -> [1/7, 3/4, 5/6]

$\label{eq1}\left[{\frac{1}{7}}, \:{\frac{3}{4}}, \:{\frac{5}{6}}\right]$

(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))

$\label{eq2}\frac{-{i \ {{e}^{{i \ \Omega \ t}-{i \ \Omega \ \tau}}}}+{i \ {{e}^{-{i \ \Omega \ t}+{i \ \Omega \ \tau}}}}}{t - \tau}$

(2)

Type: Expression(Complex(Integer))

Try this integrating this

fricas

2*x/sin(x)^2

$\label{eq3}\frac{2 \ x}{{\sin \left({x}\right)}^{2}}$

(3)

Type: Expression(Integer)

fricas

integrate(%,x)

$\label{eq4}\frac{{2 \ {\sin \left({x}\right)}\ {\log \left({\frac{\sin \left({x}\right)}{2}}\right)}}-{2 \ x \ {\cos \left({x}\right)}}}{\sin \left({x}\right)}$

(4)

Type: Union(Expression(Integer),...)

Now differentiate it

fricas

D(%,x)

$\label{eq5}\frac{{2 \ x \ {{\sin \left({x}\right)}^{2}}}+{2 \ x \ {{\cos \left({x}\right)}^{2}}}}{{\sin \left({x}\right)}^{2}}$

(5)

Type: Expression(Integer)

fricas

simplify(%)

$\label{eq6}-{\frac{2 \ x}{{{\cos \left({x}\right)}^{2}}- 1}}$

(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)

$\label{eq9}\verb#"potentialPole"#$

(9)

Type: Union(pole: potentialPole,...)

fricas

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

$\label{eq10}\verb#"failed"#$

(10)

Type: Union("failed",...)

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}