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Gröbner Bases for Left and Two-Sided Ideals
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Task: Compute left Gröbner bases for
left and two-sided ideals given by generating sets. |
Consider the algebra
U(sl2)
= < e, f, h | fe = ef - h,
he = eh + 2e, hf = fh - 2f >,
and two sets of generators
I2 = {e2, f2,
h2-1}
and
I3 = {e3, f3,
h3-4h}
.
Solution: first we set up the algebra
ring r=0,(e,f,h),Dp;
matrix C[3][3];
matrix D[3][3];
C[1,2]=1; C[1,3]=1; C[2,3]=1;
D[1,2]=-h; D[1,3]=2e; D[2,3]=-2f;
system("PLURAL",C,D);
r;
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==>
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// characteristic : 0
// number of vars : 3
// block 1 : ordering Dp
// : names e f h
// block 2 : ordering C
// noncommutative relations:
// fe=ef-h
// he=eh+2e
// hf=fh-2f
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