Singular Manual: invertLeftFraction

| ##### 7.5.19.0. invertLeftFraction Procedure from library `olga.lib` (see olga_lib). Usage: invertLeftFraction(frac, locType, locData), vector frac, int locType, list/vector/intvec locData Purpose: invert a fraction in the specified localization Assume: frac is invertible in the loc. specified by locType and locData Return: vector Note: - returns the multiplicative inverse of frac in the localization specified by locType and locData, - throws error if frac is not invertible (NOTE: this does NOT mean that the fraction is not invertible, it just means it could not be determined by the method listed above). Example:
    LIB "olga.lib";
    ring R = 0,(x,y,Dx,Dy),dp;
    def S = Weyl();
    setring S; S;
    ==> // coefficients: QQ
    ==> // number of vars : 4
    ==> //        block   1 : ordering dp
    ==> //                  : names    x y Dx Dy
    ==> //        block   2 : ordering C
    ==> // noncommutative relations:
    ==> //    Dxx=x*Dx+1
    ==> //    Dyy=y*Dy+1
    poly g1 = x+3;
    poly g2 = x*y;
    list L = g1,g2;
    vector frac = [g1*g2, 17, 0, 0];
    print(invertLeftFraction(frac, 0, L));
    ==> [17,x^2*y+3*x*y]
    ideal p = x-1, y;
    frac = [g1, x, 0, 0];
    print(invertLeftFraction(frac, 1, p));
    ==> [x,x+3]
    intvec rat = 1,2;
    frac = [g1*g2, y, 0, 0];
    print(invertLeftFraction(frac, 2, rat));
    ==> [y,x^2*y+3*x*y]

User manual for Singular version 4-1-3, 2020, generated by texi2html.