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Extracting coefficients of multivariate polynomials?

asked 2013-06-05 14:46:50 -0500

Alasdair gravatar image

If I enter, say:

P.<x,y,z> = QQ[]
ex = 6*x*y^2-4*x*y*z+2*x^2*z
ex.coefficients()

then Sage returns

[6, -4, 2]

as it should. My problem is that I'm trying to obtain a list of coefficients when the coefficients are themselves expressions:

ex = (1-a^2)*x*y^2+(a-b^2+c)*x*y*z+(b^2-c^2-a)*x^2*z

What I want returned is

[1-a^2, a-b^2+c, b^2-c^2-a]

(the order doesn't matter). If I enter a, b, c as elements of the same polynomial ring as x, y, z then I have the problem of distinguishing the different variables: x, y, z, from a, b, c.

What's the best way to do this?

Thanks, Alasdair

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answered 2013-06-05 15:40:40 -0500

calc314 gravatar image

updated 2013-06-05 15:41:22 -0500

Here is a quick hack.

map(lambda w: w.subs(x=1,y=1,z=1),ex.operands())

I don't see an obvious command to extract abstract coefficients, even list doesn't work.

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Yep, that certainly works - thanks! I was hoping, though, that there might be a natural, simple command...

Alasdair gravatar imageAlasdair ( 2013-06-05 15:53:11 -0500 )edit
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answered 2016-04-14 01:45:04 -0500

nbruin gravatar image

updated 2016-04-14 01:46:57 -0500

Just define the appropriate polynomial rings so that coefficients does what you want:

sage: A.<a,b,c>=QQ[]
sage: B.<x,y,z>=A[]
sage: ex = (1-a^2)*x*y^2+(a-b^2+c)*x*y*z+(b^2-c^2-a)*x^2*z
sage: ex.coefficients()
[-a^2 + 1, b^2 - c^2 - a, -b^2 + a + c]
sage: ex.monomials()
[x*y^2, x^2*z, x*y*z]
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Asked: 2013-06-05 14:46:50 -0500

Seen: 864 times

Last updated: Apr 14 '16