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# Edit detail for FriCASTutorial revision 3 of 10

 1 2 3 4 5 6 7 8 9 10 Editor: hemmecke Time: 2014/03/03 12:04:17 GMT+0 Note:

changed:
-- a complete introduction to Axiom by Daniel Augot, en FranÃ§ais, is
- a complete introduction to Axiom by Daniel Augot, en Français, is


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]
 (1)
Type: List(Fraction(Integer))

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

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))
 (2)
Type: Expression(Complex(Integer))

Try this integrating this

fricas
2*x/sin(x)^2
 (3)
Type: Expression(Integer)

fricas
integrate(%,x)
 (4)
Type: Union(Expression(Integer),...)

Now differentiate it

fricas
D(%,x)
 (5)
Type: Expression(Integer)
fricas
simplify(%)
 (6)
Type: Expression(Integer)

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

fricas
simplify(%%(3) - %%(6))
 (7)
Type: Expression(Integer)

fricas
D(x^x,x)
 (8)
Type: Expression(Integer)

See, that was easy!

Here are some more things to try.

fricas
integrate(log(sin(x)),x=0..%pi)
 (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?

For more details see: FriCASProgramming? .

## Special FriCASWiki? Markup for Programming

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

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


### 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 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}