#7472: Taylor polynomial in two variables does not work
----------------------------+-----------------------------------------------
Reporter: robert.marik | Owner: burcin
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: calculus | Keywords: taylor polynomial, derivative
Work_issues: | Author: Robert Marik
Upstream: N/A | Reviewer: Karl-Dieter Crisman
Merged: |
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Comment(by robert.marik):
Replying to [comment:10 kcrisman]:
> I assume the idea of different degrees for different variables was lost?
That really doesn't matter to me, though.
Yes, different degrees for different variables seem odd to me (from the
point of view of pure caculcus) and I do not know, if there is a demand to
keep this functionality.
>
> What about this one, from the documentation?
> {{{
> sage: x,y=var('x y'); taylor(x*y^3,(x,1),(y,-1),4)
> (y + 1)^3*(x - 1) + (y + 1)^3 - 3*(y + 1)^2*(x - 1) - 3*(y + 1)^2 + 3*(y
+ 1)*(x - 1) - x + 3*y + 3
> }}}
> Why doesn't it end this way?
> {{{
> -(x-1)+3*(y+1) -1
> }}}
> Maybe this is documented in Maxima? It does seem odd, though, if I'm
understanding what a multivariable Taylor polynomial is supposed to look
like.
Very good question :). Maxima in fact returns
{{{
-(x-1)+3*(y+1) -1
}}}
and Sage changes it somehow into
{{{
-x+3y+....
}}}
I do not know why, perhaps I should ask on sage-devel. The same problem is
also in current Sage. The linear Taylor polynomial hal always slope
intercept form f'(a)*x+q, but should be (and Maxima returns) point slope
form f'(a)*(x-a)+f(a)
{{{
----------------------------------------------------------------------
| Sage Version 4.3, Release Date: 2009-12-24 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: maxima("taylor(x^3,x,2,1)")
8+12*(x-2)
sage: maxima("taylor(x^3,x,2,1)").sage()
12*x - 16
sage: taylor(x^3,x,2,1)
12*x - 16
sage:
}}}
>
> But overall this looks fine, assuming the Maxima computations are
correct. I am waiting for 4.3.alpha2 to build to see if there needs to be
a rebase, but surely it would be trivial if so.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7472#comment:11>
Sage <http://www.sagemath.org>
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