bug in gb over ZZ ? (using custom ordering)

[jakobkroeker]

if the following example is legal input, and my test ist correct, there is a bug:

R = ZZ[x_1..x_3, Weights => {-1, 2, -1}, Global=>false ]

I = ideal(1+x_1,2*x_1)

gI = ideal gens gb I;
assert( ( (gens I)%gI) == 0 );
ggI = ideal gens gb gI;
assert(numColumns (gens gI) == numColumns(gens ggI));
assert( leadingTermsEquivalent( gI, ggI ) ) ;
gI
ggI

output

      R = ZZ[x_1..x_3, Weights => {-1, 2, -1}, Global=>false ]

o64 = R

o64 : PolynomialRing

i65 : 
      I = ideal(1+x_1,2*x_1)

o65 = ideal (1 + x , 2x )
                  1    1

o65 : Ideal of R

i66 : 
      gI = ideal gens gb I;

o66 : Ideal of R

i67 : assert( ( (gens I)%gI) == 0 );

i68 : ggI = ideal gens gb gI;

o68 : Ideal of R

i69 : assert(numColumns (gens gI) == numColumns(gens ggI));
stdio:357:1:(3): error: assertion failed

i70 : assert( leadingTermsEquivalent( gI, ggI ) ) ;
stdio:358:1:(3): error: assertion failed

i71 : gI

o71 = ideal (x , 1)
              1

o71 : Ideal of R

i72 : ggI

o72 = ideal 1

o72 : Ideal of R

remark: leadingTermsEquivalent defined as

leadingTermsEquivalent := (I,J)->
(
    if (numColumns (gens I) != numColumns(gens J)) then return false;   
    for i in 0..(numColumns (gens I))-1 do
    (
        if not (leadTerm(I_i) % leadTerm(J_i) ==0 ) then
        (
            return false;
        );
        if not (leadTerm(J_i) % leadTerm(I_i) ==0 ) then
        (
            return false;
        );
    );   
    return (true);
);

[DanGrayson]

Since the monomials are not well ordered by this ordering, why should anything be true about the Groebner basis?

[mikestillman]

The algorithm uses the Mora algorithm. The bug is happening after the GB is complete, and during minimalization of the basis. I'm assigning this bug to myself.

[mikestillman]

Oops, actually, my last comment is for #292, I think. I'll still assign this to myself.

[mikestillman]

This might duplicate #291, I need to look into it.