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7.5.23.0. allExtOfRight
Procedure from library purityfiltration.lib (see purityfiltration_lib).
- Usage:
- allExtOfRight(R), R matrix representing the right Module M=D^q/RD^p over a ring D
M module with finite right projective dimension n
- Return:
- list, entries are ext-modules
- Purpose:
- computes a list T, which entries are representations of the left modules ext^i(M,D)
T[i] gives the repr. matrix of ext^(i-1)(M,D), i=1,..,n+1
Example:
| | LIB "purityfiltration.lib";
ring D = 0,(x,y,z),dp;
matrix R[6][4]=
0,-2*x,z-2*y-x,-1,
0,z-2*x,2*y-3*x,1,
z,-6*x,-2*y-5*x,-1,
0,y-x,y-x,0,
y,-x,-y-x,0,
x,-x,-2*x,0;
// coker(R) considered as right module
projectiveDimension(R,1)[2];
==> 1
list T=allExtOfRight(R);
print(T[1]);
==> 4x,
==> -4y,
==> -z,
==> z
print(T[2]);
==> 1,0,0, 0,0, 0,
==> 0,0,4y-z,0,4x-z,0,
==> 0,z,0, y,0, x
// left modules coker(.T[i])!!
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