#11431: Conversion from Singular to Sage
-------------------------------------------------------------+--------------
Reporter: SimonKing | Owner:
was
Type: defect | Status:
positive_review
Priority: major | Milestone:
sage-4.7.2
Component: interfaces | Resolution:
Keywords: | Work_issues:
Upstream: None of the above - read trac for reasoning. | Reviewer:
Martin Albrecht
Author: Simon King | Merged:
Dependencies: #11316, #11645 |
-------------------------------------------------------------+--------------
Old description:
> 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)
> }}}
>
> Apply all patches
New description:
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)
}}}
----
Apply
1. [attachment:trac11431_singular_sage_conversion.patch]
1. [attachment:trac11431_singular_sage_documentation.patch]
to the Sage library.
--
Comment(by leif):
Simon, are you ok with dropping the (IMHO obsolete) Solaris patch?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11431#comment:27>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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