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D.12.3.6 divisor
Procedure from library hyperel.lib (see hyperel_lib).
- Usage:
- divisor(a,b,h,f); optional: divisor(a,b,h,f,s); s=0,1
- Return:
- list P
- Note:
- P[1][3]*(P[1][1], P[1][2]) +...+ P[size(P)][3]*
*(P[size(P)][1], P[size(P)][2]) - (*)infty=div(a(x)-b(x)y)
if there is an optional parameter s!=0, then divisor additionally
returns a parameter, which says, whether irreducible polynomials
occurred during computations or not. Otherwise only warnings are
displayed on the monitor. For s=0 nothing happens.
Curve C: y^2+h(x)y=f(x) is defined over 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;
poly a=(x-1)^2*(x-6);
poly b=0;
divisor(a,b,h,f,1);
==> [1]:
==> [1]:
==> -1
==> [2]:
==> -3
==> [3]:
==> 2
==> [2]:
==> [1]:
==> 1
==> [2]:
==> -2
==> [3]:
==> 2
==> [3]:
==> [1]:
==> 1
==> [2]:
==> 1
==> [3]:
==> 2
==> 0
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