Bug #1371
French students' example with GFan
Description
I have just tried the French students' example as argument to GroebnerFanIdeals, and it computed all 167 GBases quite quickly.
I had supposed it would get stuck on the "lex" basis.
Why didn't it? What am I not understanding?
Related issues
History
#1
Updated by John Abbott over 4 years ago
Updated by Just for completeness here is the input:
I := ideal(x^2*y*z + x*y^3*z - 1, x^4*y*z - 1 , x*y^4 + x*y*z-1 ); GF := GroebnerFanIdeals(I); --> takes less than 5 sec.
#2
Updated by John Abbott over 4 years ago
- Status changed from New to In Progress
- % Done changed from 0 to 10
The time taken depends on the current ring ordering!
If I create the ideal in the ring QQ[x,y,z] with DegRevLex, then the GFan computation takes about 2.2s.
If I create the ideal in the ring QQ[x,y,z] with Lex, then the GFan computation takes ages...
This cannot be right!?!
#3
Updated by Anna Maria Bigatti over 4 years ago
Updated by Just for curiosity, this lex GBasis can be computed instantly using GBasisByHomog(I).
Then, together with Robbiano, we also checked which ordering in GFan gives the same LT as lex (which is [y, x, z^18]).
This is the ordering, and indeed using it the GBasis is very fast:
/**/ P := NewPolyRing(QQ, "x,y,z", mat([[16,18,1], [257,288,0], [0,0,-1]]), 0); /**/ use P; /**/ I_P := ideal(x^2*y*z + x*y^3*z - 1, x^4*y*z - 1, x*y^4 + x*y*z-1); /**/ GBasis(I_P);
#4
Updated by John Abbott over 4 years ago
I find it quite strange that the term ordering used to obtain the same LT actually looks to be far away from lex:
Lex is
mat([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
The ordering found is roughly:
mat([[1-eps, 1, 0],
[1, 0, -1],
[0, 0, -1]])
#5
Updated by John Abbott about 2 months ago
- Related to Design #984: GroebnerFanIdeals: order matrices sometimes have "large" entries added