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speed up construction of kernel polynomial for Vélu isogeny using product tree #40948

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Oct 6, 2025
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speed up construction of kernel polynomial for Vélu isogeny using product tree #40948

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7 changes: 3 additions & 4 deletions src/sage/schemes/elliptic_curves/ell_curve_isogeny.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2244,11 +2244,10 @@ def __init_kernel_polynomial_velu(self):
else:
invX = x

psi = poly_ring.one()
for xQ in self.__kernel_mod_sign.keys():
psi *= x - invX(xQ)
from sage.misc.misc_c import prod
psi = prod([x - invX(xQ) for xQ in self.__kernel_mod_sign.keys()]) # building the list is not redundant; this is slightly faster
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really? prod delegates to iterator_prod if the input is a generator. Where does the overhead come from?

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actually the overhead might be because Python can inline the list comprehension, but not the generator expression.

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doesnt prod use a binary tree for the product when given a list?

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Last time I checked, the difference was that passing an iterator makes it use a different (suboptimal) tree structure since the total length is not a priori known.

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Looking at it again, I'm not sure if that is the reason: iterator_prod() does promise that the tree will be balanced... So you might be right, @user202729.


self.__kernel_polynomial = psi
self.__kernel_polynomial = poly_ring(psi)

###################################
# Kohel's Variant of Velu's Formula
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