Yogesh Swami axelexic
axelexic
/ Schoof.sage
Last active
January 27, 2021 07:28
Schoof algorithm (without Elkies/Atkins improvements) to compute number of points on a curve
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| from sage.all_cmdline import * | |
| def curve_fx(e: EllipticCurve): | |
| a4 = e.a4() | |
| a6 = e.a6() | |
| X,Y=e.multiplication_by_m(1) | |
| return X**3 + a4*X + a6 | |
| def trace_mod_2(e: EllipticCurve): | |
| (X,Y) = e.multiplication_by_m(1) |
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| from sage.all_cmdline import * | |
| Fq=GF(11) | |
| E=EllipticCurve(Fq, [3,7]) | |
| G0=(E.gens()[0]) | |
| R = PolynomialRing(Fq, 'X,Y'); R.inject_variables() | |
| def normalize_rational_map(rational_map, curve : EllipticCurve): | |
| def reduce_y2(poly, fx): | |
| xterms = 0 |
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| alias n next ;; list | |
| alias c continue ;; list | |
| alias s step ;; list | |
| alias finish up ;; list | |
| alias f up ;; list | |
| alias fini up ;; list | |
| alias d down ;; list | |
| alias u until ;; list |
axelexic
/ nTorsonIsogeny
Created
January 28, 2019 06:04
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| def normalize(polyList, fx): | |
| const_term = 0 | |
| y_term = 0 | |
| for i, v in enumerate(polyList): | |
| xterm = polyList[i] | |
| if i % 2 == 0: | |
| expo = int(i/2) | |
| const_term = const_term + xterm * (fx ^ expo) | |
| else: |
axelexic
/ gist:01c7eef0cd7972598737
Created
March 24, 2016 02:49
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