D.8.3.2 parametrizepd

Procedure from library paramet.lib (see paramet_lib).

Usage:

parametrizepd(I); I ideal in a polynomial ring with global ordering

Create:

If the parametrization is successful, the basering will be changed to the parametrization ring, that is to the ring PR=0,(s,t),dp; respectively PR=0,t(1..d),dp;, depending on the dimension of the parametrized variety.

Return:

a list of lists, where each entry contains the parametrization of a primary component of I resp. 0, the number of variables resp. 0, and 1 resp. 0 depending on whether the parametrization of the component was successful or not

Example:

LIB "paramet.lib";
ring RING=0,(x,y,z),dp;
ideal I=(x2-y2z2+z3)*(x2-z2-z3),(x2-y2z2+z3)*yz;
parametrizepd(I);
→ [1]:
→    [1]:
→       _[1]=s2t-t3
→       _[2]=s
→       _[3]=s2-t2
→    [2]:
→       2
→    [3]:
→       1
→ [2]:
→    [1]:
→       _[1]=0
→       _[2]=s
→       _[3]=0
→    [2]:
→       1
→    [3]:
→       1
→ [3]:
→    [1]:
→       _[1]=s3-s
→       _[2]=0
→       _[3]=s2-1
→    [2]:
→       1
→    [3]:
→       1

See also: normal; parametrize; primdecGTZ.