#11431: Conversion from Singular to Sage
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Reporter: SimonKing | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: interfaces | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies: #11316
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On [http://groups.google.com/group/sage-
support/browse_thread/thread/f35e6064434dacdc sage-devel], Francisco
Botana complained about some shortcomings of the conversion from Singular
(pexpect interface) to Sage.
I think the conversions provided by this patch are quite thorough.
First of all, the patch provides a conversion of base rings, even with
minpoly, with complicated block, matrix and weighted orders (note that one
needs #11316) and even quotient rings:
{{{
sage: singular.eval('ring r1 =
(9,x),(a,b,c,d,e,f),(M((1,2,3,0)),wp(2,3),lp)')
'ring r1 = (9,x),(a,b,c,d,e,f),(M((1,2,3,0)),wp(2,3),lp);'
sage: R = singular('r1').sage_basering()
sage: R
Multivariate Polynomial Ring in a, b, c, d, e, f over Finite Field in x of
size 3^2
sage: R.term_order()
Block term order with blocks:
(Matrix term order with matrix
[1 2]
[3 0],
Weighted degree reverse lexicographic term order with weights (2, 3),
Lexicographic term order of length 2)
sage: singular.eval('ring r3 = (3,z),(a,b,c),dp')
'ring r3 = (3,z),(a,b,c),dp;'
sage: singular.eval('minpoly = 1+z+z2+z3+z4')
'minpoly = 1+z+z2+z3+z4;'
sage: singular('r3').sage_basering()
Multivariate Polynomial Ring in a, b, c over Univariate Quotient
Polynomial Ring in z over Finite Field of size 3 with modulus z^4 + z^3 +
z^2 + z + 1
sage: singular.eval('ring r5 = (9,a), (x,y,z),lp')
'ring r5 = (9,a), (x,y,z),lp;'
sage: Q = singular('std(ideal(x^2,x+y^2+z^3))', type='qring')
sage: Q.sage_basering()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a
of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
}}}
By consequence, it is now straight forward to convert polynomials or
ideals to sage:
{{{
sage: singular.eval('ring R = integer, (x,y,z),lp')
'// ** You are using coefficient rings which are not fields...'
sage: I = singular.ideal(['x^2','y*z','z+x'])
sage: I.sage() # indirect doctest
Ideal (x^2, y*z, x + z) of Multivariate Polynomial Ring in x, y, z over
Integer Ring
# Note that conversion of a Singular string to a Sage string was missing
sage: singular('ringlist(basering)').sage()
[['integer'], ['x', 'y', 'z'], [['lp', (1, 1, 1)], ['C', (0)]], Ideal (0)
of Multivariate Polynomial Ring in x, y, z over Integer Ring]
sage: singular.eval('ring r10 = (9,a), (x,y,z),lp')
'ring r10 = (9,a), (x,y,z),lp;'
sage: Q = singular('std(ideal(x^2,x+y^2+z^3))', type='qring')
sage: Q.sage()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a
of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
sage: singular('x^2+y').sage()
x^2 + y
sage: singular('x^2+y').sage().parent()
Quotient of Multivariate Polynomial Ring in x, y, z over Finite Field in a
of size 3^2 by the ideal (y^4 - y^2*z^3 + z^6, x + y^2 + z^3)
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11431>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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