Hi,
I have an algebra defined over the Laurent polynomial ring Z[x,x**-1] which
has three bases: F, P and C, for an algebra. The transition matrices
between any two of these bases is unitriangular.
I have an expensive (cached) function which writes
P(t)=F(t) + \sum_{s<t} r_sx^_{a_s}F(s), for a_s, r_s\in Z.
The element C(t) is determined by starting with F(P(s))=F(s) + smaller
terms, and then ensuring that the coefficient of F(s) is always of the form
r_s'x^{a_s} where a_s<0. To compute this I am currently using the function
@cached_method
def _C_to_F_on_basis(self, t):
F=self.realization_of().F()
P=self.realization_of().P()
ct=F(P.term(t))
k=1
terms=ct._monomial_coefficients.items()
terms.sort(cmp=lambda a,b: my_cmp(a[0],b[0]))
while k<len(terms):
if terms[k][1].valuation()<0: k+=1
else:
ct -= C.term(term[k][0],term[k][1]) # removes
c_s, doesn't change higher terms, may change lower terms
terms=ct._monomial_coefficients.items() # need to update
terms
terms.sort(cmp=lambda a,b: my_cmp(a[0],b[0]))
return ct
For reasons I don't understand this is ridiculously slow even when the
number of terms is small. Is there a way to improve on this?
I'm not sure if it's necessary to continually resort the indices in terms
as my algebra does have a indices_cmp method.
On the other hand, from some tracking messages that I have added it is
beginning to look to me that the problem might be caused by my coercion set
up. I have defined all of these coercions using triangular morphisms like
C_to_F = Psi.module_morphism(C._C_to_F_on_basis,
codomain=F,
triangular = 'lower', unitriangular = True,
cmp = my_cmp
)
C_to_F.register_as_coercion()
(~C_to_F).register_as_coercion()
It looks to me as by calling F(C(t)) I am automatically triggering all of
the expensive conversions F(P(s)) whenever F(s) appears in P(t) even though
these conversions may not be necessary in order to compute F(C(t)). For
example, this seems to happen even in the case where C(t)==P(t) so that
only F(P(t)) is needed to compute C(t).
Is some one able to tell me whether I am imaging this, or whether I have
set things up badly and so am deserving of it! :)
Cheers,
Andrew
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