## #162 closed bug (fixed)

# std over coeff rings (with zero-divisors) for local orderings

Reported by: | seelisch | Owned by: | seelisch |
---|---|---|---|

Priority: | minor | Milestone: | 3-1-1 |

Component: | singular-kernel | Version: | 3-1-0 |

Keywords: | std, local order, zero-divisor | Cc: |

### Description

Here are two examples over Z/8 with two and three vars, resp.
Both ovecompute a wrong GB. The correct one is - in both cases - {4x, 4y+3x2, x3, 2x2}.
The first computation seems to do something with the highest corner (as the ideal is 0-dim) which is not correct over this ground ring.
The second has an additional variable z, so that the ideal is no longer 0-dim. Still here, the computed basis is not complete, as 2x^{2 is still missing.
}

$ ./Singular

SINGULAR / Development

A Computer Algebra System for Polynomial Computations / version 3-1-0

0<

by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Mar 2009

FB Mathematik der Universitaet, D-67653 Kaiserslautern \
* executing /home/seelisch/sandbox/Singular/LIB/.singularrc
*

ring r = (integer, 2, 3), (x, y), ds;

* You are using coefficient rings which are not fields.
*

**Please note that only limited functionality is available**

**for these coefficients.**

**The following commands are meant to work:****- basic polynomial arithmetic**

**- std****- lift**

**- reduce**poly f = 4y + 3x2; poly g = 4x; ideal i = f, g; i = std(i); i;

$ ./Singular

SINGULAR / Development

A Computer Algebra System for Polynomial Computations / version 3-1-0

0<

by: G.-M. Greuel, G. Pfister, H. Schoenemann \ Mar 2009

FB Mathematik der Universitaet, D-67653 Kaiserslautern \
* executing /home/seelisch/sandbox/Singular/LIB/.singularrc
*

ring r = (integer, 2, 3), (x, y, z), ds;

* You are using coefficient rings which are not fields.
*

**Please note that only limited functionality is available**

**for these coefficients.**

**The following commands are meant to work:****- basic polynomial arithmetic**

**- std****- lift**

**- reduce**poly f = 4y + 3x2; poly g = 4x; ideal i = f, g; i = std(i); i;

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Caused by wrong selection of completion function (mora was used). Only the bba function is prepared to handle coefficient rings. Fixed in [12415].