possibly incorrect result of toric_ideal()

[Dumitru]

Hello,

I've been experimenting the various algorithms that may be chosen as a second argument in toric_ideal(...,..) and it seems that I get different results.

I needed the relations defining the semigroup ring associated to the semigroup H= <3504, 3510, 3516, 3520>. When I use the "blr" or the "hs" algorithms I obtain the same ideal, but it is different from the one obtained with the "pt" method. This is not the only semigroup where I noticed different ideals being returned by "blr" and "pt".

I tend to believe that "blr" and "hs" are correct, but maybe there is a bug somewhere that could be fixed.

The code is below.

I would appreciate an answer from you. Thank you!

Dumitru Stamate,

dumitrustamate@…

LIB "sing.lib"; LIB "toric.lib"; ring r=0, (x,y,z,t), dp; /*degrevlex*/

ideal I1, G1, I2,G2, I3, G3; intvec gensemi= 3504, 3510, 3516, 3520;

intmat M[1][4]= transpose(gensemi); M;

I1= toric_ideal(M, "pt");

/* other options: ect, pt, blr, hs, du */

G1=groebner(I1); G1; /* G1[1]=y2-xz G1[2]=z4-xt3 G1[3]=x220t12-t231 G1[4]=x220z3t9-z3t228 */

I2= toric_ideal(M, "blr"); I2; ideal G2=groebner(I2); /* G2[1]=y2-xz G2[2]=z4-xt3 G2[3]=x220-t219 */

reduce(G1,G2); /* _[1]=0 _[2]=0 _[3]=0 _[4]=0 therefore I1 is included in I2 */

reduce(G2,G1); /* _[1]=0 _[2]=0 _[3]=x220-t219 therefore I2 is not included in I1 */

I3= toric_ideal(M, "hs");

I3; ideal G3=groebner(I3); reduce(G2,G3); reduce(G3,G2); /* _[1]=0 _[2]=0 _[3]=0 _[1]=0 _[2]=0 _[3]=0 */ G3 and G2 are the same, hence I3==I2