# Singular

#### 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