primdecSY over characteristic 2: unequal primary vs. prime ideals

[seelisch]

reported by Franziska Hinkelman, March 26, 2009:

Singular team,

I'm working on an algorithm and I was wondering if I could get some help from you. I almost think there's a bug in primdecSY.

I'm working over a ring with 8 variables, characteristic 2, and the quotient ring from the ideal x2+x for all 8 variables (polynomials in R = F_2[x1, ... x8]). So every primary ideal should be a prime ideal, because b^{n = b for any b in R and any n.}

But when I run primdecSY I sometimes get a primary ideal that differs from its associated prime ideal.

I'm attaching a little script to reproduce the error (execute with "sh singular.sh")

I greatly appreciate your help with this. Thank you,

Franziska

---

name=Franziska B Hinkelmann email=fhinkel@… type=bug version=Singular for ix86Mac-darwin version 3-0-4 (3041-2008082012) Aug 20 2008 12:46:36 platform=Mac OS 10.5

---

characteristic : 2 number of vars : 8 block 1 : ordering lp : names c123 c23 c13 c12 c3 c2 c1 c0 block 2 : ordering C quotient ring from ideal _[1]=c02+c0 _[2]=c12+c1 _[3]=c22+c2 _[4]=c32+c3 _[5]=c122+c12 _[6]=c132+c13 _[7]=c232+c23 _[8]=c1232+c123 First entry of primdecSY first_primary_ideal[1]=c0 first_primary_ideal[2]=c1+1 first_primary_ideal[3]=c2 first_primary_ideal[4]=c3 first_primary_ideal[5]=c12 first_primary_ideal[6]=c13 first_primary_ideal[7]=c23+1 first_primary_ideal[8]=c123+1

first_prime_ideal[1]=c0 first_prime_ideal[2]=c2 first_prime_ideal[3]=c3 first_prime_ideal[4]=c12 first_prime_ideal[5]=c13+c1+1 first_prime_ideal[6]=c23+1 first_prime_ideal[7]=c123+1

#!/usr/bin/bash

#Shell script to run Singuarl

echo "This script runs Singular to reduce typing effort"; echo "LIB \"primdec.lib\";

ring C_ring = 2, (c123, c23,c13,c12, c3,c2,c1, c0), lp; option(redSB); ideal I = c02 + c0,

c12+c1, c22+c2, c32+c3, c122+c12, c132+c13, c232+c23, c1232+c123;

qring qR = std(I); ideal C = c0,

c2, c12*c1+c3*c1, c12*c3+c12, c13+c3+c1+1, c23+c3+1, c123+1;

C = std(C); C = reduce (C, std(0) ); list pr = primdecSY(C); pr; ideal first_primary_ideal = pr[1][1]; ideal first_prime_ideal = pr[1][2]; basering; print (\"First entry of primdecSY\"); first_primary_ideal; print (\" \"); first_prime_ideal; quit;" | Singular

[seelisch]

Frank Seelisch, April 2:

I close this ticket, and

1. make sure that the manual points out that up to now, algorithms apply for poly rings with global ordering only but not for quotient rings,
2. open new enhancement ticket for implementing the proposed quotient ring workaround