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D.4.2.5 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+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; |