D.12.3 hyperel_lib

Library:

hyperel.lib

Author:

Markus Hochstetter, markushochstetter@gmx.de

Note:

The library provides procedures for computing with divisors in the jacobian of hyperelliptic curves. In addition procedures are available for computing the rational representation of divisors and vice versa. The library is intended to be used for teaching and demonstrating purposes but not for efficient computations.

Procedures:

D.12.3.1 ishyper		test, if y^2+h(x)y=f(x) is hyperelliptic
D.12.3.2 isoncurve		test, if point P is on C: y^2+h(x)y=f(x)
D.12.3.3 chinrestp		compute polynom x, s.t. x=b[i] mod moduli[i]
D.12.3.4 norm		norm of a(x)-b(x)y in IF[C]
D.12.3.5 multi		(a(x)-b(x)y)*(c(x)-d(x)y) in IF[C] ratrep (P,h,f) returns polynomials a,b, s.t. div(a,b)=P
D.12.3.6 divisor		computes divisor of a(x)-b(x)y
D.12.3.7 gcddivisor		gcd of the divisors p and q
D.12.3.8 semidiv		semireduced divisor of the pair of polys D[1], D[2]
D.12.3.9 cantoradd		adding divisors of the hyperell. curve y^2+h(x)y=f(x)
D.12.3.10 cantorred		returns reduced divisor which is equivalent to D
D.12.3.11 double		computes 2*D on y^2+h(x)y=f(x)
D.12.3.12 cantormult		computes m*D on y^2+h(x)y=f(x)