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D.4.7.3 primdecSY
Procedure from library primdec.lib (see primdec_lib).
- Usage:
primdecSY(i); i ideal, c int
- 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.
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- 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,
if c=2, minAssGTZ is used,
if c=3, minAssGTZ and facstd are used.
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Example:
| 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 = primdecSY(i);
pr;
→ [1]:
→ [1]:
→ _[1]=z6+4z3+4
→ _[2]=y-z2
→ [2]:
→ _[1]=z3+2
→ _[2]=y-z2
→ [2]:
→ [1]:
→ _[1]=z2+1
→ _[2]=y+1
→ [2]:
→ _[1]=z2+1
→ _[2]=y+1
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