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D.6.10.3 CurveParam
Procedure from library curvepar.lib (see curvepar_lib).
- Usage:
- CurveParam(I);
I ideal
- Assume:
- I is an ideal of a curve C with a singular point 0.
- Compute:
- Parametrization for algebraic branches of the curve C.
- Return:
- list L of size 1.
L[1] is a ring ring rt=0,(t,a),ds;
Ring R contains a list Param
Param is a list of algebraic branches
Each Param[i] is a list of size 3
Param[i][1] is a list of polynomials
Param[i][2] is an irredusible polynomial f\in k[a].It is a minimal polynomial for
the parameter a.
Param[i][3] is an integer b--upper bound for the conductor of Weierstrass semigroup
Example:
| LIB "curvepar.lib";
ring r=0,(x,y,z),dp;
ideal i=x2-y3,z2-y5;
def s=CurveParam(i);
setring s;
Param;
==> [1]:
==> [1]:
==> [1]:
==> t3
==> [2]:
==> t2
==> [3]:
==> -t5
==> [2]:
==> a
==> [3]:
==> 38
==> [2]:
==> [1]:
==> [1]:
==> t3
==> [2]:
==> t2
==> [3]:
==> t5
==> [2]:
==> a
==> [3]:
==> 38
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