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 .000479309 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00375656 seconds idlizer1: .00716252 seconds idlizer2: .0129474 seconds minpres: .00937699 seconds time .0474761 sec #fractions 4] [step 1: radical (use decompose) .00399166 seconds idlizer1: .00861996 seconds idlizer2: .0227483 seconds minpres: .0146497 seconds time .0652814 sec #fractions 4] [step 2: radical (use decompose) .00397533 seconds idlizer1: .0113546 seconds idlizer2: .025841 seconds minpres: .0112201 seconds time .0676473 sec #fractions 5] [step 3: radical (use decompose) .00402309 seconds idlizer1: .00934965 seconds idlizer2: .038493 seconds minpres: .0301146 seconds time .154113 sec #fractions 5] [step 4: radical (use decompose) .0040923 seconds idlizer1: .0173543 seconds idlizer2: .0783325 seconds minpres: .013984 seconds time .135783 sec #fractions 5] [step 5: radical (use decompose) .00388783 seconds idlizer1: .0109733 seconds time .0219794 sec #fractions 5] -- used 0.496036 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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