Opened 11 years ago

Last modified 10 years ago

## #11431 closed defect

# Conversion from Singular to Sage — at Initial Version

Reported by: | SimonKing | Owned by: | was |
---|---|---|---|

Priority: | major | Milestone: | sage-4.7.2 |

Component: | interfaces | Keywords: | |

Cc: | malb | Merged in: | |

Authors: | Simon King | Reviewers: | |

Report Upstream: | None of the above - read trac for reasoning. | Work issues: | |

Branch: | Commit: | ||

Dependencies: | #11316 | Stopgaps: |

### Description

On 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)

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