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Bivariate polynomial resultants over the integers are now
computed using the following modular method.
For 
word size prime moduli 
the resultant
is computed in 
and then combined
using the Chinese remainder theorem.
Each resultant calculation in 
is
reduced to 
resultant calculations in 
by
polynomial evaluation and interpolation.
This method (due to George Collins)
gives better performance for polynomials of large degree.