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sagemathgh-40948: speed up construction of kernel polynomial for Vélu isogeny using product tree Computing a product of a collection of linear polynomials is best done using a balanced product tree. Example: ```sage sage: E = EllipticCurve(GF(16411), [1,0]) sage: P = E.lift_x(25) sage: phi = E.isogeny(P) sage: assert phi._EllipticCurveIsogeny__algorithm == 'velu' sage: %time _ = phi.kernel_polynomial() ``` Current `develop`: ``` CPU times: user 25.6 ms, sys: 0 ns, total: 25.6 ms Wall time: 25.7 ms ``` This branch: ``` CPU times: user 13.7 ms, sys: 0 ns, total: 13.7 ms Wall time: 13.8 ms ``` URL: sagemath#40948 Reported by: Lorenz Panny Reviewer(s): Giacomo Pope, Lorenz Panny, user202729
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src/sage/schemes/elliptic_curves/ell_curve_isogeny.py

Lines changed: 3 additions & 4 deletions
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@@ -2244,11 +2244,10 @@ def __init_kernel_polynomial_velu(self):
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else:
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invX = x
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psi = poly_ring.one()
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for xQ in self.__kernel_mod_sign.keys():
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psi *= x - invX(xQ)
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from sage.misc.misc_c import prod
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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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self.__kernel_polynomial = psi
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self.__kernel_polynomial = poly_ring(psi)
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###################################
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# Kohel's Variant of Velu's Formula

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