Answering my own question -- but as a cautionary tale for others. I mistakenly thought that if I define a power series ring with some default precision, say 200, and create an object in it out of a vector of 200 coefficients, then it would automatically have +O(q^200) added, but that is not the case -- the object is treated just as if it is a polynomial of degree 199 with no truncation. This was causing a problem since I was multiplying 39 such things together, and the results ended up with "degree" almost 8000. And the later coefficients are enormous, which makes matters worse.
When I manually add +O(q^200) after creating the objects the running time goes from hours to seconds, as I always thought it should. Maybe I am just stupid, but I think that it would be good for this behaviour to be documented more clearly! After all, if I define R=RealField(200) and mutiply elements of R together the results will still only have 200 bits of precision. (And yes, I do know the difference between archimedean and non-archimedean valuations, but still!) John On 25 March 2013 15:15, John Cremona <john.crem...@gmail.com> wrote: > In a current project I have to compute quite a lot of monomial > expressions of the form X^i*Y^j*Z^k where i+j+k=39 and X,Y,Z are power > series in one variable over a cubic number field. This takes a *very* > long time once the coefficients of the intermediate expressions get > large. (I tried to optimize by first computing the first 39 powers of > each of X,Y,Z and only then compute their products; it was very > noticeable that the first few powers are quick but by the 39th they > are taking a minute or more to multiply by another X.) > > By contrast after cutting-and-pasting into Magma the monomial > evaluations take seconds (to do all of them). > > Any idea what makes Sage so very uncompetitive here? Is it the basic > arithmetic in the number field, rather than anything to do with the > power series? > > John > > PS On the other hand the linear algebra step which followed was > instantaneous in Sage (finding the 1-d kernel of a 155x600 matrix over > Q) and slower in Magma. But before I restricted scalars and had a > 155x200 matrix over the cubic field, Sage took hours. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
