Assign Taylor expansion to function

Question

When I use Maxima to calculate the Taylor series:

f(x,y) := taylor((x+y)^3, [x, y], [2, 3], 2);
f(2,3);  /* error: wrong number of arguments */

Basically I want to define a function as a expansion of (x+y)^3, which takes in x,y as parameter. How can I achieve this?

@stark I'm new to Maxima. Could you give a full example? Thanks. — gongzhitaao, Apr 25 '14 at 14:17
Never mind. I think you just need to set variable: PSEXPAND:MULTI — stark, Apr 25 '14 at 14:38
@stark Thanks. But still `taylor: wrong number of arguments. #0: f(x=2,y=3)` — gongzhitaao, Apr 25 '14 at 14:51

score 4 · Accepted Answer · answered Apr 25 '14 at 14:50

4

Try

(%i1) f(x,y) := ''(ratdisrep(taylor(('x+'y)^3, ['x, 'y], [2, 3], 2))) $

(%i2) f(2, 3);
(%o2)                                 125

or

(%i1) define(f(x, y), ratdisrep(taylor(('x+'y)^3, ['x, 'y], [2, 3], 2)))$

(%i2) f(2, 3);
(%o2)                                 125

answered Apr 25 '14 at 14:50

slitvinov

Though I don't know what's going on here, this works. I may need to dive into the Maxima manual for this. Thanks. – gongzhitaao Apr 25 '14 at 14:52
2

@gongzhitaao Ordinarily the body of a function is not evaluated when the function is defined via `:=`. The reason that `f(x, y) := ''(...))` and `define(f(x, y), ...)` work is that they evaluate the body of the function (the Taylor expansion) at the time the function is defined. – Robert Dodier Apr 25 '14 at 17:02

1 Answers1