Singular

D.6.6.3 CurveParam

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

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