Singular

D.4.20.5 primdecSYE

Usage:

primdecSYE(I, c); I ideal, c int (optional)

Return:

a list pr of primary ideals and their associated primes:

pr[i][1] the i-th primary component, pr[i][2] the i-th prime component.

If I is the unit ideal returns an empty list.

Note:

Algorithm of Shimoyama/Yokoyama.

if c=0, the given ordering of the variables is used, if c=1, minAssChar tries to use an optimal ordering (default), if c=2, minAssGTZ is used, if c=3, minAssGTZ and facstd are used.

For local orderings, the result is considered in the localization of the polynomial ring, not in the power series ring.
For local and mixed orderings, the decomposition in the corresponding global ring is returned if the string 'global' is specified as third argument

LIB "primdec.lib";
ring  r = 0,(x,y,z),lp;
poly  p = z2+1;
poly  q = z3+2;
ideal I = p*q^2,y-z2;
list pr = primdecSYE(I);
pr;
==> [1]:
==>    [1]:
==>       _[1]=z2+1
==>       _[2]=y-z2
==>    [2]:
==>       _[1]=z2+1
==>       _[2]=y+1
==> [2]:
==>    [1]:
==>       _[1]=z6+4z3+4
==>       _[2]=y-z2
==>    [2]:
==>       _[1]=z3+2
==>       _[2]=y-z2
ideal J = x;
list prUnit = primdecSYE(J);
prUnit;
==> [1]:
==>    [1]:
==>       _[1]=x
==>    [2]:
==>       _[1]=x