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7.5.22.0. purityTriang
Procedure from library purityfiltration.lib (see purityfiltration_lib).
- Usage:
- purityTriang(S), S matrix with entries of an Auslander regular ring D
- Return:
- a matrix T
- Purpose:
- compute a triangular block matrix T, such that M=D^p/D^q(S^t) is isomorphic to M'=D^p'/D^q(T^t)
Example:
| | LIB "purityfiltration.lib";
ring D = 0,(x1,x2,d1,d2),dp;
def S=Weyl();
setring S;
int i;
matrix R[3][3]=0,d2-d1,d2-d1,d2,-d1,-d1-d2,d1,-d1,-2*d1;
print(R);
==> 0, -d1+d2,-d1+d2,
==> d2,-d1, -d1-d2,
==> d1,-d1, -2*d1
matrix T=purityTriang(transpose(R));
// a triangular blockmatrix representing the module coker(R)
print(T);
==> 0, 1,1,-1, 0, 0, 0,
==> -1,0,1,0, -1, 0, 0,
==> 0, 0,0,-d1,-d2,-1,0,
==> 0, 0,0,-1, -1, 0, -1,
==> 0, 0,0,0, 0, 1, -d2,
==> 0, 0,0,0, 0, 1, 0,
==> 0, 0,0,0, 0, 0, d1
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