Singular

D.15.11.3 evaluatepfd

Usage:

evaluatepfd(dec, values[, mode]); dec list, values ideal, mode int

Return:

the number gotten by substituting the numbers generating the ideal values for the variables in the partial fraction decomposition dec. The list dec has to have the same structure as the output of pfd.
mode=1: raise Error in case of division by 0 (default)
mode=2: return a second integer which is 1 if the denominator becomes 0, and 0 otherwise.

LIB "pfd.lib";
ring R = 0,(x,y),dp;
poly f = x+2*y;
poly g = x^2-y^2;
// partial fraction decomposition of f/g:
list dec = pfd(f,g);
==>   (-1/2) / (q2)
==> + (3/2) / (q1)
==> where
==> q1 = x-y
==> q2 = x+y
==> (2 terms)
==> 
displaypfd_long(dec);
==>   (-1/2)/((x+y))
==> + (3/2)/((x-y))
==> (2 terms)
==> 
// evaluation at x=2, y=1:
ideal values = 2,1;
evaluatepfd(dec,values);
==> 4/3
// compare: f(2,1)/g(2,1) = (2+2*1)/(2^2-1^1) = 4/3