Opened 3 years ago

Last modified 3 years ago

## #27479 closed defect

# Univariate PolynomialRing with 'negdegrevlex' order does not get 'ds' order in Singular — at Version 1

Reported by: | rburing | Owned by: | |
---|---|---|---|

Priority: | major | Milestone: | sage-8.8 |

Component: | interfaces | Keywords: | PolynomialRing, Singular, order |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

Using `_singular_init_()`

univariate polynomial rings get global monomial ordering `lp`

no matter what:

sage: R.<x> = PolynomialRing(QQ, 1, order='negdegrevlex') sage: R._singular_init_() polynomial ring, over a field, global ordering // coefficients: QQ // number of vars : 1 // block 1 : ordering lp // : names x // block 2 : ordering C

Contrast with multivariate:

sage: S.<y,z> = PolynomialRing(QQ, 2, order='negdegrevlex') sage: S._singular_init_() polynomial ring, over a field, local ordering // coefficients: QQ // number of vars : 2 // block 1 : ordering ds // : names y z // block 2 : ordering C

As long as `neg*`

orders are allowed (see #10708) this should be fixed (and it seems easy to fix).

This is also the cause of a bug in `multiplicity()`

for subschemes of the affine line:

sage: A1.<x> = AffineSpace(QQ,1) sage: X=A1.subscheme([x^1789+x]) sage: Q=X([0]) sage: X.multiplicity(Q) 1789

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