Singular Manual: ncExt_R

| ##### 7.5.16.0. ncExt_R Procedure from library `nchomolog.lib` (see nchomolog_lib). Usage: ncExt_R(i, M); i int, M module Compute: a presentation of Ext^i(M',R); for M'=coker(M). Return: right module Ext, a presentation of Ext^i(M',R) Example:
    LIB "nchomolog.lib";
    ring R     = 0,(x,y),dp;
    poly F    = x2-y2;
    def A = annfs(F);  setring A; // A is the 2nd Weyl algebra
    matrix M[1][size(LD)] = LD; // ideal
    print(M);
    ==> y*Dx+x*Dy,x*Dx+y*Dy+2,x^2*Dy-y^2*Dy-2*y
    print(ncExt_R(1,M)); // hence the Ext^1 is zero
    ==> 1,0,
    ==> 0,1
    module E  = ncExt_R(2,M); // define the right module E
    print(E); // E is in the opposite algebra
    ==> 1, -x,    -y,
    ==> Dx,y*Dy+1,x*Dy
    def Aop = opposite(A);  setring Aop;
    module Eop = oppose(A,E);
    module T1  = ncExt_R(2,Eop);
    setring A;
    module T1 = oppose(Aop,T1);
    print(T1); // this is a left module Ext^2(Ext^2(M,A),A)
    ==> y*Dx+x*Dy,x*Dx+y*Dy+2,x^2*Dy-y^2*Dy-2*y
    print(M); // it is known that M holonomic implies Ext^2(Ext^2(M,A),A) iso to M
    ==> y*Dx+x*Dy,x*Dx+y*Dy+2,x^2*Dy-y^2*Dy-2*y

User manual for Singular version 4.3.2, 2023, generated by texi2html.