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std(Plural) and liftstd(Plural)
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1838		 Page 1 of 1
Author:  akishi [ Thu Jul 01, 2010 3:27 am ]
Post subject:  std(Plural) and liftstd(Plural)
Hello,

I am in trouble interpreting the results produced by
"std(Plural)" and "liftstd(Plural)".

As far as I understand, they both return a left Groebner basis
of an ideal or a module.

In the following example, their results do not agree
with each other; the variable T appears in one Groebner basis,
but not in the other.

I would appreciate your help.
Thank you.

---------------------------------------------------

> LIB "nctools.lib";
> option(redSB);
> option(redTail);
> ring r=(0,q),(U,V,S,T),lp;
> matrix C[4][4];
C[1,2]=1/q;
C[1,3]=1;
C[1,4]=1;
C[2,3]=1;
C[2,4]=1;
C[3,4]=1/q;
> def R=nc_algebra(C,0);
> setring R;
> R;
// characteristic : 0
// 1 parameter : q
// minpoly : 0
// number of vars : 4
// block 1 : ordering lp
// : names U V S T
// block 2 : ordering C
// noncommutative relations:
// VU=1/(q)*UV
// TS=1/(q)*ST
> ideal I=U*V+S-V-1,U-V-V*T,U+V-V*S;
> I;
I[1]=UV-V+S-1
I[2]=U-VT-V
I[3]=U-VS+V
> ideal G=std(I);
> matrix M;
> ideal H=liftstd(I,M);
> G;
G[1]=T
G[2]=S-1
G[3]=V
G[4]=U
> std(G);
_[1]=T
_[2]=S-1
_[3]=V
_[4]=U
> H;
H[1]=(q7-q6-3q5+5q4-2q3)*S+(-q7+q6+3q5-5q4+2q3)
H[2]=(-q11+2q10+2q9-8q8+7q7-2q6)*V
H[3]=(q6-3q4+2q3)*U
> std(H);
_[1]=S-1
_[2]=V
_[3]=U
Author:  malex [ Thu Aug 12, 2010 5:31 pm ]
Post subject:  Re: std(Plural) and liftstd(Plural)
Hello akishi,

It looks very strange and seems to be a bug. Ticket for this: http://www.singular.uni-kl.de:8002/trac/ticket/251

Thanks for reporting!
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