Nils Bruin wrote:
> polynomial aritmetic over ZZ and QQ is so much more optimized than
> over number fields,

Yes, polynomial arithmetic over number fields is painfully slow. The 
branch trac:u/mmezzarobba/speed_up_generic_polynomials (not fully tested 
yet) may help a little.

Another trick you can use if you are creating the polynomial rings 
yourself and only need to do basic arithmetic is to define them by

PolynomialRing_field(base, var, element_class=Polynomial_generic_dense)

instead of PolynomialRing(base, var). You then loose a few features 
specific to polynomial rings over fields, but you're basically saving a 
call to Polynomial_absolute_number_field_dense.__init__() after every 
operation, which can make basic arithmetic operations quite a bit 
faster.

-- 
Marc

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