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D.4.5.7 sat
Procedure from library elim.lib (see 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+y4
==> [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+y4
==> [2]:
==> 2
printlevel = p;
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See also:
modSat.
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