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D.12.5.11 pairset
Procedure from library teachstd.lib (see teachstd_lib).
- Usage:
- pairset(G); G ideal or module
- Return:
- list L,
L[1] = the pairset of G as list (not containing pairs for
which the product or the chain criterion applies),
L[2] = intvec v, v[1]= # product criterion, v[2]= # chain criterion
Example:
| | LIB "teachstd.lib";
ring r=0,(x,y,z),dp;
ideal G = x2y+x2,y3+xyz,xyz2+z4;
pairset(G);"";
==> [1]:
==> [1]:
==> _[1]=x2y+x2
==> _[2]=y3+xyz
==> [2]:
==> _[1]=x2y+x2
==> _[2]=xyz2+z4
==> [3]:
==> _[1]=y3+xyz
==> _[2]=xyz2+z4
==> [2]:
==> 0,0
==>
module T = [x2y3-z2,x2y],[x2y2+z2,x2-y2],[x2y4+z3,x2+y2];
pairset(T);
==> [1]:
==> [1]:
==> _[1]=x2y3*gen(1)+x2y*gen(2)-z2*gen(1)
==> _[2]=x2y2*gen(1)+x2*gen(2)-y2*gen(2)+z2*gen(1)
==> [2]:
==> _[1]=x2y3*gen(1)+x2y*gen(2)-z2*gen(1)
==> _[2]=x2y4*gen(1)+z3*gen(1)+x2*gen(2)+y2*gen(2)
==> [2]:
==> 0,1
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