#5958: [with patch, needs work] MPolynomial_polydict.factor() should accept
proof
parameter
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Reporter: malb | Owner: malb
Type: defect | Status: new
Priority: major | Milestone: sage-4.1.2
Component: commutative algebra | Keywords: singular, factor
Reviewer: | Author:
Merged: |
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Comment(by john_perry):
To follow up, the problem occurs when computing the Groebner basis over
CC.
I'll use the example given:
The Groebner basis computed is [y^3 + x - y, x^2 + y^2 - 1.00000000000000,
x*y - 1.00000000000000].
The result p from elim_pol is y^4 - y^2 + 1.0. (This reflects the bugfix I
identified above; it used to return y^4-y^2.)
The first factor q of p is y - 0.866025403784439 - 0.500000000000000*I.
The reduction of B modulo q gives us
[x - 0.866025403784438 + 0.500000000000001*I,
x^2 - 0.499999999999999 + 0.866025403784439*I,
(0.866025403784439 + 0.500000000000000*I)*x - 1.00000000000000]
'''This should be a consistent system:''' the first polynomial is a factor
of the second, and the solution to the third is ''nearly'' the same as the
solution to the first: 0.866025403784438 - 0.500000000000001*I vs.
0.866025403784438 - 0.500000000000000*I. This appears to be a
roundoff/floating point error.
The system above should produce a Groebner basis with one polynomial, but
it returns [1.00000000000000] instead. This is why nothing is coming back
for x. Anyone know how to fix it?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5958#comment:10>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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