Singular Manual: ncrepGetRegularMinimal

| #### 7.10.6.31 ncrepGetRegularMinimal Procedure from library `ncrat.lib` (see ncrat_lib). Usage: ncrep q = ncrepGetRegularMinimal(f, vars, point); Return: q is a representation of f with minimal dimension Assumption: f is regular at point, i.e., f(point) has to be defined Note: list vars = list(x1, ..., xn) has to consist exactly of the nc variables occurring in f and list point = (p1, ..., pn) of scalars such that f(point) is defined Example:
    LIB "ncrat.lib";
    // We want to prove the Hua's identity, telling that for two
    // invertible elements x,y from a division ring, one has
    // inv(x+x*inv(y)*x)+inv(x+y) = inv(x)
    // where inv(t) stands for the two-sided inverse of t
    ncInit(list("x", "y"));
    ncrat f = ncratFromString("inv(x+x*inv(y)*x)+inv(x+y)-inv(x)");
    print(f);
    ==> inv(x+x*inv(y)*x)+inv(x+y)-inv(x)
    ncrep r = ncrepGet(f);
    ncrepDim(r);
    ==> 18
    ncrep s = ncrepGetRegularMinimal(f, list(x, y), list(1, 1));
    ncrepDim(s);
    ==> 0
    print(s);
    ==> lvec=
    ==> 0
    ==>
    ==> mat=
    ==> 1
    ==>
    ==> rvec=
    ==> 0
    // since s represents the zero element, Hua's identity holds.

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