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D.4.2.5 sat

Procedure from library elim.lib (see section elim_lib).

Usage:

sat(id,j); id=ideal/module, j=ideal

Return:

list of an ideal/module [1] and an integer [2]:
[1] = saturation of id with respect to j (= union_(k=1...) of id:j^k) [2] = saturation exponent (= min( k | id:j^k = id:j^(k+1) ))

Note:

[1] is a standard basis in the basering

Display:

saturation exponent during computation if printlevel >=1

Example:

LIB "elim.lib";
int p      = printlevel;
ring r     = 2,(x,y,z),dp;
poly F     = x5+y5+(x-y)^2*xyz;
ideal j    = jacob(F);
sat(j,maxideal(1));
→ [1]:
→    _[1]=x3+x2y+xy2+y3
→    _[2]=y4+x2yz+y3z
→    _[3]=x2y2+x2yz+y3z
→ [2]:
→    4
printlevel = 2;
sat(j,maxideal(2));
→ // compute quotient 1
→ // compute quotient 2
→ // compute quotient 3
→ // saturation becomes stable after 2 iteration(s)
→ 
→ [1]:
→    _[1]=x3+x2y+xy2+y3
→    _[2]=y4+x2yz+y3z
→    _[3]=x2y2+x2yz+y3z
→ [2]:
→    2
printlevel = p;

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            User manual for Singular version 2-0-4, October 2002, generated by texinfo.