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changed: - 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
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:
[1/7,3/4, 5/6]
![]() | (1) |
Please feel free to play with this in the SandBox?!
Let's see if we can perform a finite window Fourier inversion.
simplify(integrate(exp(%i*_\omega*t) * exp(-%i*_\omega * _\tau),_\omega=-_\Omega .. _\Omega))
![]() | (2) |
Try this integrating this
2*x/sin(x)^2
![]() | (3) |
integrate(%,x)
![]() | (4) |
Now differentiate it
D(%,x)
![]() | (5) |
simplify(%)
![]() | (6) |
Expressions (3) and (6) are really that same.
simplify(%%(3) - %%(6))
![]() | (7) |
D(x^x,x)
![]() | (8) |
See, that was easy!
Here are some more things to try.
integrate(log(sin(x)),x=0..%pi)
![]() | (9) |
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?
For more details see: FriCASProgramming? .
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}
To include Aldor programs on pages in this website use:
\begin{aldor} ... \end{aldor}
or:
\begin{aldor}[name] ... \end{aldor}
You can add LaTeX? formatted equations to pages on this web site by:
$$ ... $$
and inline symbols such as are written like this: $\alpha +\beta$
To include arbitrary LaTeX? on pages in this website use:
\begin{latex} ... \end{latex}
To include Lisp programs on pages in this website use:
\begin{lisp} ... \end{lisp}
To include Boot programs on pages in this website use:
\begin{boot} ... \end{boot}