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D.4.28.6 minAssGTZ
Procedure from library primdec.lib (see primdec_lib).
- Usage:
- minAssGTZ(I[, l]); I ideal, l list (optional)
Optional parameters in list l (can be entered in any order):
0, "facstd" -> uses facstd to first decompose the ideal (default)
1, "noFacstd" -> does not use facstd
"GTZ" -> the original algorithm by Gianni, Trager and Zacharias is used
"SL" -> GTZ algorithm with modificiations by Laplagne is used (default)
- Return:
- a list, the minimal associated prime ideals of proper ideal I, otherwise ideal(1)
- Note:
- - Designed for characteristic 0, works also in char k > 0 based
on an algorithm of Yokoyama
- 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 second argument
Example:
| LIB "primdec.lib";
ring r = 0,(x,y,z),dp;
poly p = z2+1;
poly q = z3+2;
ideal i = p*q^2,y-z2;
list pr = minAssGTZ(i);
pr;
==> [1]:
==> _[1]=z3+2
==> _[2]=-z2+y
==> [2]:
==> _[1]=z2+1
==> _[2]=-z2+y
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