D.8.3.1 parametrize

Procedure from library paramet.lib (see paramet_lib).

Usage:

parametrize(I); I ideal in an arbitrary number of variables, whose radical is prime, in a 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 containing the parametrization ideal resp. the original ideal, the number of variables needed for the parametrization resp. 0, and 1 resp. 0 depending on whether the parametrization was successful or not

Example:

LIB "paramet.lib";
ring RING=0,(x,y,z),dp;
ideal I=z2-y2x2+x3;
parametrize(I);
→ [1]:
→    _[1]=s2-t2
→    _[2]=s
→    _[3]=s2t-t3
→ [2]:
→    2
→ [3]:
→    1

See also: normal; parametrizepd; primdecGTZ; radical.