### 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)

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