Singular Manual: ComplexValue

| #### D.15.4.19 ComplexValue Procedure from library `finitediff.lib` (see finitediff_lib). Usage: ComplexValue(f); f a poly in the basering; Return: type poly; gives back the formal complex-value of f, where var(1) is redarded as the imaginary unit. Does only make sense, if the proc <setinitials> is executed before -> nvars <= npars Example:
    LIB "finitediff.lib";
    list D="Ut","Ux","Uy","U";
    list V="t","x","y";
    list P="a","b";
    setinitials(V,D,P);////does not show the ring, as there is  no output
    basering;///does show the ring
    ==> // coefficients: QQ(I, T, Px, Py, Cx, Cy, Sx, Sy, a, b, dt, dx, dy)
    ==> // number of vars : 8
    ==> //        block   1 : ordering c
    ==> //        block   2 : ordering lp
    ==> //                  : names    i t x y cx cy sx sy
    ==> // quotient ring from ideal
    ==> _[1]=cy^2+sy^2-1
    ==> _[2]=cx^2+sx^2-1
    ==> _[3]=i^2+1
    poly f=t**3*cx**2-cy**2*dt+i**3*sx;
    f;
    ==> i^3*sx+t^3*cx^2+(-dt)*cy^2
    ComplexValue(f);
    ==> t^6*sx^4-2*t^6*sx^2+t^6+(-2*dt)*t^3*sx^2*sy^2+(2*dt)*t^3*sx^2+(2*dt)*t^3*\
       sy^2+(-2*dt)*t^3+sx^2+(dt^2)*sy^4+(-2*dt^2)*sy^2+(dt^2)

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