#1396: Ideal.groebner_basis should accept keyword arguments for strategy
parameters
-----------------------------------+----------------------------------------
Reporter: malb | Owner: malb
Type: enhancement | Status: needs_review
Priority: minor | Milestone: sage-4.5
Component: commutative algebra | Keywords: libSingular options
Author: Simon King | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-----------------------------------+----------------------------------------
Changes (by newvalueoldvalue):
* keywords: => libSingular options
* status: needs_work => needs_review
* upstream: => N/A
* author: => Simon King
Comment:
This patch extends Martin's work on libSingular options. Now, the options
{{{degBound}}} and {{{multBound}}} can be used. A decorator, applied to
all relevant methods, ensures that standard options are used unless
explicitly requested by setting named arguments -- even if outside the
methods other options are set.
The options can be named in Python style (deg_bound) or in Singular style
({{{degBound}}}), at the user's choice.
Examples:
1. Degree bound
{{{
sage: R.<x,y> = QQ[]
sage: I = R*[x^3+y^2,x^2*y+1]
sage: from sage.libs.singular.option import opt
# Use prot and deg_bound
sage: I.groebner_basis(prot=True, deg_bound=2)
std in (0),(x,y),(dp(2),C)
[4294967295:2]3ss
(S:1)-
product criterion:0 chain criterion:0
[x^3 + y^2, x^2*y + 1]
# Set prot and degBound outside the method
sage: opt['prot'] = True
# Singular style name
sage: opt['degBound'] = 2
# ... but inside the method, standard options are used:
sage: I.groebner_basis()
[x^3 + y^2, x^2*y + 1, y^3 - x]
sage: opt['prot']
True
# Python style name
sage: opt['deg_bound']
2
# similarly in Singular, rather than libSingular
sage: I.groebner_basis(algorithm='singular',deg_bound=2)
[x^3 + y^2, x^2*y + 1]
sage: singular.eval('degBound=2')
'degBound=2;'
sage: I.groebner_basis(algorithm='singular')
[x^3 + y^2, x^2*y + 1, y^3 - x]
sage: singular.eval('degBound')
'2'
}}}
2. Multiplicity bound
{{{
sage: Rlocal.<x,y,z> = PolynomialRing(QQ, order='ds')
sage: J = [x^7+y^7+z^6,x^6+y^8+z^7,x^7+y^5+z^8,
x^2*y^3+y^2*z^3+x^3*z^2,x^3*y^2+y^3*z^2+x^2*z^3]*Rlocal
# prot:
sage: J.groebner_basis(prot=True)
std in basering
[1048575:2]5(4)s(3)s6s7s8s(4)s(5)sH(13)9(3)sH(12)8(4)s(5).s.s9....sH(11)8.10
(S:10)-----------
product criterion:9 chain criterion:30
[x^3*y^2 + y^3*z^2 + x^2*z^3, x^2*y^3 + x^3*z^2 + y^2*z^3, y^5, x^6,
x^4*z^2 - y^4*z^2 - x^2*y*z^3 + x*y^2*z^3, z^6, y^4*z^3 - y^3*z^4 -
x^2*z^5, x^3*y*z^4 - x^2*y^2*z^4 + x*y^3*z^4, x^3*z^5, x^2*y*z^5 +
y^3*z^5, x*y^3*z^5]
# bounding the multiplicity
sage: J.groebner_basis(prot=True,mult_bound=100)
std in basering
[1048575:2]5(4)s(3)s6s7s8s(4)s(5)sH(13)
(S:5)------
product criterion:7 chain criterion:7
[x^3*y^2 + y^3*z^2 + x^2*z^3, x^2*y^3 + x^3*z^2 + y^2*z^3, y^5, x^6 +
x*y^4*z^5, x^4*z^2 - y^4*z^2 - x^2*y*z^3 + x*y^2*z^3, z^6 - x*y^4*z^4 -
x^3*y*z^5]
# Set the multBound in Singular
sage: singular.eval('multBound=100')
'multBound=100;'
# ... nevertheless, the default multBound=0 is used:
sage: J.groebner_basis(algorithm='singular')
[x^3*y^2 + y^3*z^2 + x^2*z^3, x^2*y^3 + x^3*z^2 + y^2*z^3, y^5, x^6,
x^4*z^2 - y^4*z^2 - x^2*y*z^3 + x*y^2*z^3, z^6, y^4*z^3 - y^3*z^4 -
x^2*z^5, x^3*y*z^4 - x^2*y^2*z^4 + x*y^3*z^4, x^3*z^5, x^2*y*z^5 +
y^3*z^5, x*y^3*z^5]
sage: singular.eval('multBound')
'100'
# ... unless requested otherwise
sage: J.groebner_basis(algorithm='singular',mult_bound=100)
[x^3*y^2 + y^3*z^2 + x^2*z^3, x^2*y^3 + x^3*z^2 + y^2*z^3, y^5, x^6 +
x*y^4*z^5, x^4*z^2 - y^4*z^2 - x^2*y*z^3 + x*y^2*z^3, z^6 - x*y^4*z^4 -
x^3*y*z^5]
}}}
I just verified that {{{sage -testall}}} passes. So, ready for review!
One remark: It turned out to be impossible to doctest {{{libSingular's}}}
protocol output. I inserted examples with protocol in the documentation,
for illustration, but don't test these. Of course, deg_bound and
mult_bound is doctested.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1396#comment:7>
Sage <http://www.sagemath.org>
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