Posibility to see the intermediate results of std ?

jannis · Wed Dec 30, 2020 7:04 pm

Hey,

I have a short code example which I don't understand. Why is the Groebnerbasis getting reduced in F2 but not in F1? Is there any way to see the intermediate results of the computations? I allready used option(prot), but I don't understand where s, 1s or 1s, s comes from (although I read the Online Manual).

Code:

> ring RF1= 0, (x,t), Wp(-1,0);
> def F1=nc_algebra(1,x);
> module A1=[0,1],[-t,x];
> print(std(A1));
s
1s
product criterion:0 chain criterion:0
0,t,
1,-x

> ring RF2= 0, (x,t), Wp(0,1);
> def F2=nc_algebra(1,x);
> module A2=[0,1],[-t,x];
> print(std(A2));
1s
s
product criterion:0 chain criterion:0
0,t,
1,0

Thanks for your help,

Jannis

Re: Posibility to see the intermediate results of std ?

hannes · Tue Jan 05, 2021 4:01 pm

F1 has a local ordering (i.e. 1 is not the smallest monomial),
while F2 has a global ordering.
Complete reduction is only possible for global orderings
(with local orrderings infinite reductions could appear).

option(prot) is a progress report:
https://www.singular.uni-kl.de/Manual/4-2-0/sing_318.htm
- s means a new standard basis element is found
- 1 means: working now in degree 1

Re: Posibility to see the intermediate results of std ?

jannis · Sat Jan 09, 2021 6:30 pm

Thanks a lot. I didn't knew that fact but now it is clear.
Is there any way (comand or option) to surpress the reduction while computing groebner basis?

Thx, Jannis

Re: Posibility to see the intermediate results of std ?

hannes · Mon Jan 11, 2021 12:17 pm

Code:

option(noredTail);option(noredSB);

should do this.