The Axiom Volume 1: Tutorial is available in printed format at http://lulu.com
A Quick TutorialOn this web site you can enter Axiom commands and see the output in proper mathematical form. These commands can also be typed directly into Axiom installed on your own computer. You must enclose each set of Axiom commands in a
\begin{axiom}
[1/2, 3/4, 2/3]
\end{axiom}
When you save the changes you make to a page, Axiom processes the contents of each section you have marked and the Axiom output is displayed. Try this command: axiom [1/7, 3/4, 5/6]
Type: List(Fraction(Integer)) Please feel free to play with this in the SandBox! Advanced ExamplesLet's see if we can perform a finite window Fourier inversion. axiom simplify(integrate(exp(%i*_\omega*t) * exp(-%i*_\omega * _\tau), _\omega=-_\Omega .. _\Omega))
Type: Expression(Complex(Integer)) Try this integrating this axiom 2*x/sin(x)^2
Type: Expression(Integer) axiom integrate(%,x)
Type: Union(Expression(Integer),...) Now differentiate it axiom D(%,x)
Type: Expression(Integer) axiom simplify(%)
Type: Expression(Integer) Expressions (3) and (6) are really that same. axiom simplify(%%(3) - %%(6))
Type: Expression(Integer) axiom D(x^x,x)
Type: Expression(Integer) See, that was easy! Here are some more things to try. axiom integrate(log(sin(x)),x=0..%pi)
Type: Union(pole: potentialPole,...) axiom limit(sum(1/i^2,i=1..n),n=%plusInfinity)
Type: Union("failed",...)Can you explain these results? Advanced ProgrammingFor more details see: AxiomProgramming . Spad To include Spad programs on web pages in this website click
\begin{spad}
)abbrev ...
...
\end{spad}
AldorTo include Aldor programs on pages in this website use:
\begin{aldor}
...
\end{aldor}
or:
\begin{aldor}[name]
...
\end{aldor}
LaTeXYou can add LaTeX formatted equations to pages on this web site by:
$$
...
$$
and inline symbols are written like this: $\alpha +\beta$ To include arbitrary LaTeX on pages in this website use:
\begin{latex}
...
\end{latex}
LispTo include Lisp programs on pages in this website use:
\begin{lisp}
...
\end{lisp}
BootTo include Boot programs on pages in this website use:
\begin{boot}
...
\end{boot}
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