On 10/11/07, Doug Stewart <dastew at sympatico.ca> wrote:
> While trying to learn Maxima, I was going through the manual and came to
> the ratdiff function.
>
> It doesn't seem to work the same as what the manual shows.
>
> I am using Maxima at
>
> http://www.my-tool.com/mathematics/
>
> and am using the manual from
>
> http://www.ma.utexas.edu/maxima/maxima_11.html#IDX322
Doug, the manual shown above is several years out of date.
You want: http://maxima.sourceforge.net/docs/manual/en/maxima_toc.html
I'm not familiar with ratdiff so I don't know if the current version
of the manual makes sense.
RJF --- take a look at this, does this look reasonable?
-- Function: ratdiff (<expr>, <x>)
Differentiates the rational expression <expr> with respect to <x>.
<expr> must be a ratio of polynomials or a polynomial in <x>. The
argument <x> may be a variable or a subexpression of <expr>.
The result is equivalent to `diff', although perhaps in a
different form. `ratdiff' may be faster than `diff', for rational
expressions.
`ratdiff' returns a canonical rational expression (CRE) if `expr'
is a CRE. Otherwise, `ratdiff' returns a general expression.
`ratdiff' considers only the dependence of <expr> on <x>, and
ignores any dependencies established by `depends'.
Example:
(%i1) expr: (4*x^3 + 10*x - 11)/(x^5 + 5);
3
4 x + 10 x - 11
(%o1) ----------------
5
x + 5
(%i2) ratdiff (expr, x);
7 5 4 2
8 x + 40 x - 55 x - 60 x - 50
(%o2) - ---------------------------------
10 5
x + 10 x + 25
(%i3) expr: f(x)^3 - f(x)^2 + 7;
3 2
(%o3) f (x) - f (x) + 7
(%i4) ratdiff (expr, f(x));
2
(%o4) 3 f (x) - 2 f(x)
(%i5) expr: (a + b)^3 + (a + b)^2;
3 2
(%o5) (b + a) + (b + a)
(%i6) ratdiff (expr, a + b);
2 2
(%o6) 3 b + (6 a + 2) b + 3 a + 2 a
Robert Dodier