When the computation takes a considerable time, this function can be used to decide if it will ever finish, or to get a feel for what is happening during the computation.
i1 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i2 : time R' = integralClosure(R, Verbosity => 2) [jacobian time .000598832 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00784161 seconds idlizer1: .0113766 seconds idlizer2: .0878736 seconds minpres: .00785249 seconds time .198269 sec #fractions 4] [step 1: radical (use minprimes) .00425758 seconds idlizer1: .00636851 seconds idlizer2: .244665 seconds minpres: .0545438 seconds time .395416 sec #fractions 4] [step 2: radical (use minprimes) .00818124 seconds idlizer1: .0510824 seconds idlizer2: .137447 seconds minpres: .0502063 seconds time .453991 sec #fractions 5] [step 3: radical (use minprimes) .0445743 seconds idlizer1: .0459355 seconds idlizer2: .156444 seconds minpres: .143333 seconds time .63746 sec #fractions 5] [step 4: radical (use minprimes) .0421228 seconds idlizer1: .0927 seconds idlizer2: .455656 seconds minpres: .0539921 seconds time .706165 sec #fractions 5] [step 5: radical (use minprimes) .0104408 seconds idlizer1: .0855818 seconds time .140862 sec #fractions 5] -- used 2.5376 seconds o2 = R' o2 : QuotientRing |
i3 : trim ideal R' 3 2 2 2 4 4 o3 = ideal (w z - x , w x - w , w x - y z - z - z, w x - w z, 4,0 4,0 1,1 1,1 4,0 1,1 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 3 2 4 2 2 4 2 w w - x y z - x z - x , w + w x y - x*y z - x*y z - 2x*y z 4,0 1,1 4,0 4,0 ------------------------------------------------------------------------ 3 3 2 6 2 6 2 - x*z - x, w x - w + x y + x z ) 4,0 1,1 o3 : Ideal of QQ[w , w , x, y, z] 4,0 1,1 |
i4 : icFractions R 3 2 2 4 x y z + z + z o4 = {--, -------------, x, y, z} z x o4 : List |
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