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D.12.4.10 cantorred
Procedure from library hyperel.lib (see hyperel_lib).
- Usage:
- cantorred(D,h,f);
- Return:
- list N
- Note:
- Cantor's algorithm - reduction.
important: Divisor D has to be semireduced!
Computes reduced divisor div(N[1],N[2])= div(D[1],D[2]).
The divisors are defined over the basering.
Curve C: y^2+h(x)y=f(x) is defined over the basering.
Example:
| | LIB "hyperel.lib";
ring R=7,x,dp;
// hyperelliptic curve y^2 + h*y = f
poly h=x;
poly f=x5+5x4+6x2+x+3;
// semireduced divisor
list D=2x4+3x3-3x-2, -x3-2x2+3x+1;
cantorred(D,h,f);
==> [1]:
==> x2-2x+2
==> [2]:
==> 2x-2
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