#4539: plural wrapper
---------------------------+------------------------------------------------
Reporter: burcin | Owner: OleksandrMotsak, AlexanderDreyer
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.2
Component: algebra | Keywords: libsingular plural wrapper sd10
sd23.5 sd24 sd34
Work_issues: doc tests | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies: #11068 #11316 #11856
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Comment(by SimonKing):
Sorry, I couldn't resist to add one more feature: Ideal containment, which
is a direct application of normal form computation.
With the new version of the third patch, we have:
{{{
sage: A.<x,y,z> = FreeAlgebra(QQ, 3)
sage: H.<x,y,z> = A.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y})
sage: JL = H.ideal([x^3, y^3, z^3 - 4*z])
sage: JL.std()
Left Ideal (z^3 - 4*z, y*z^2 - 2*y*z, x*z^2 + 2*x*z, 2*x*y*z - z^2 - 2*z,
y^3, x^3) of Noncommutative Multivariate Polynomial Ring in x, y, z over
Rational Field, nc-relations: {y*x: x*y - z, z*y: y*z - 2*y, z*x: x*z +
2*x}
sage: JT = H.ideal([x^3, y^3, z^3 - 4*z], side='twosided')
sage: JT.std()
Twosided Ideal (z^3 - 4*z, y*z^2 - 2*y*z, x*z^2 + 2*x*z, y^2*z - 2*y^2,
2*x*y*z - z^2 - 2*z, x^2*z + 2*x^2, y^3, x*y^2 - y*z, x^2*y - x*z - 2*x,
x^3) of Noncommutative Multivariate Polynomial Ring in x, y, z over
Rational Field, nc-relations: {y*x: x*y - z, z*y: y*z - 2*y, z*x: x*z +
2*x}
}}}
Apparently, ``x*y^2-y*z`` should be in the two-sided, but not in the left
ideal. And that is indeed what we get:
{{{
sage: x*y^2-y*z in JL
False
sage: x*y^2-y*z in JT
True
}}}
Docs are still to fix. And I promise to focus on it - no new features...
Apply trac4539_libplural.patch trac4539_pickling.patch
trac4539_normal_forms.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4539#comment:80>
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