5.7.4 Polynomial division

The two functions

ex quo(const ex & a, const ex & b, const ex & x);
ex rem(const ex & a, const ex & b, const ex & x);

compute the quotient and remainder of univariate polynomials in the variable ‘x’. The results satisfy a = b*quo(a, b, x) + rem(a, b, x).

The additional function

ex prem(const ex & a, const ex & b, const ex & x);

computes the pseudo-remainder of ‘a’ and ‘b’ which satisfies c*a = b*q + prem(a, b, x), where c = b.lcoeff(x) ^ (a.degree(x) - b.degree(x) + 1).

Exact division of multivariate polynomials is performed by the function

bool divide(const ex & a, const ex & b, ex & q);

If ‘b’ divides ‘a’ over the rationals, this function returns true and returns the quotient in the variable q. Otherwise it returns false in which case the value of q is undefined.