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D.12.3.11 double
Procedure from library hyperel.lib (see hyperel_lib).
- Usage:
- double(D,h,f);
- Return:
- list Q=2*D
- Note:
- important: Divisor D has to be semireduced!
Special case of Cantor's algorithm.
Computes reduced divisor div(Q[1],Q[2])= 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;
// reduced divisor
list D=x2-1,2x-1;
double(D,h,f);
==> [1]:
==> x2-2x+1
==> [2]:
==> 3x-2
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