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D.6.6.5 primparam
Procedure from library curvepar.lib (see curvepar_lib).
- Usage:
- MultiplicitySequence(x,y,c); x poly, y poly, c integer
- Assume:
- x and y are polynomials in k(a)[t] such that (x,y) is a primitive parametrization of
a plane curve branch and ord(x)<ord(y).
- Return:
- Hamburger-Noether Matrix of the curve branch given parametrically by (x,y).
Example:
| | LIB "curvepar.lib";
ring r=(0,a),t,ds;
poly x=t6;
poly y=t8+t11;
int c=15;
primparam(x,y,c);
==> _[1,1]=0
==> _[1,2]=t
==> _[1,3]=0
==> _[1,4]=0
==> _[1,5]=0
==> _[1,6]=0
==> _[1,7]=0
==> _[1,8]=0
==> _[1,9]=0
==> _[1,10]=0
==> _[1,11]=0
==> _[1,12]=0
==> _[1,13]=0
==> _[1,14]=0
==> _[1,15]=0
==> _[2,1]=0
==> _[2,2]=0
==> _[2,3]=1
==> _[2,4]=0
==> _[2,5]=t
==> _[2,6]=0
==> _[2,7]=0
==> _[2,8]=0
==> _[2,9]=0
==> _[2,10]=0
==> _[2,11]=0
==> _[2,12]=0
==> _[2,13]=0
==> _[2,14]=0
==> _[2,15]=0
==> _[3,1]=0
==> _[3,2]=1/9
==> _[3,3]=0
==> _[3,4]=0
==> _[3,5]=-7/243
==> _[3,6]=0
==> _[3,7]=0
==> _[3,8]=250/19683
==> _[3,9]=0
==> _[3,10]=0
==> _[3,11]=-3625/531441
==> _[3,12]=0
==> _[3,13]=0
==> _[3,14]=58351/14348907
==> _[3,15]=0
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