#7458: [with patch, needs review] Sylvester matrix for polynomials
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Reporter: carlohamalainen | Owner: malb
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.6.1
Component: commutative algebra | Keywords: Sylvester matrix
Author: Carlo Hamalainen | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* keywords: => Sylvester matrix
* status: new => needs_work
* upstream: => N/A
* author: carlohamalainen => Carlo Hamalainen
Comment:
This is a very basic feature that has to be in Sage.
I have rebased Carlo patch to 4.6 but have not touched the code.
I have some concerns that makes me mark the patch as needs work:
- The univariate case should accept the same syntax as the multivariate
case. In the univariate case, the preferred call is f.sylvester_matrix(g),
but I do not want Sage to throw an error if I wrote f.sylvester_matrix(g,
x)
- Corner cases must be well documented.
{{{
sage: K.<x>=QQ[]
sage: K(1).sylvester_matrix(K(1))
[]
}}}
In particular, I am not sure how to deal with the sylvester matrix of 0
and constant or 0 and 0
Curretly it throws an error. My opinion is that this is not defined but
should throw a more meaningful error.
Maple for instance return the empty matrix. So in maple:
Determinant(Sylvester_Matrix) != Resultant
In this corner cases.
I will try to check what other CAS do to get a wider picture.
- An example explicitly relating Sylvester matrix and resultant should be
added.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7458#comment:1>
Sage <http://www.sagemath.org>
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