NF

[leonada@…]

ring R=2,(f,t,y,x),(ds(2),lp(2)); ideal I=std(x28+ft); NF(ftx29+x27,I);

x27

NF(x27+ftx29,I);

x27

NF(f6t6x27+ftx29,I);

f2t2x

NF(f6t6x29+ftx27,I);

ftx27

NF(f6t6yx29+ftx27,I);

ftx27

NF(f6t6yx29+fty4x27,I);

fty4x27+f7t7yx

NF(f6t6yx29+ftyx27,I);

ftyx27

[leonada@…]

What do I use to produce NormalForm? given this erratic behaviour?

[Oleksandr]

Hello leonada,

could You please explain: what exactly seems "erratic" to you and why?

thx.

[Oleksandr]

As a side remark, please note that you are working with a mixed ordering (e.g. y > x > 1 > f > t), which means that you are dealing with a localization of the polynomial ring, where p = x27 + ftx29 = x27 * u for u = 1 + ftx2 which is a unit in the localization, and since NF computes a weak polynomial normal form (in this case) you can check that p - u * NF(p, I) = 0 is in I.

Oleksandr