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 .000606057 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .0560377 seconds idlizer1: .00920049 seconds idlizer2: .0172122 seconds minpres: .0117357 seconds time .112427 sec #fractions 4] [step 1: radical (use minprimes) .00302538 seconds idlizer1: .0146819 seconds idlizer2: .029856 seconds minpres: .017956 seconds time .0845186 sec #fractions 4] [step 2: radical (use minprimes) .00284699 seconds idlizer1: .0149222 seconds idlizer2: .0315637 seconds minpres: .0140225 seconds time .106567 sec #fractions 5] [step 3: radical (use minprimes) .00280971 seconds idlizer1: .0151859 seconds idlizer2: .0464662 seconds minpres: .0360944 seconds time .126654 sec #fractions 5] [step 4: radical (use minprimes) .00286785 seconds idlizer1: .0458744 seconds idlizer2: .104363 seconds minpres: .0201312 seconds time .200934 sec #fractions 5] [step 5: radical (use minprimes) .00331829 seconds idlizer1: .0124338 seconds time .0271454 sec #fractions 5] -- used 0.663326 seconds o2 = R' o2 : QuotientRing |
i3 : trim ideal R' 3 2 2 2 4 4 2 2 2 3 2 3 2 3 2 o3 = ideal (w z - x , w x - w , w x - y z - z - z, w x - w z, w w - x y z - x z - x , w + w x y - 4,0 4,0 1,1 1,1 4,0 1,1 4,0 1,1 4,0 4,0 ---------------------------------------------------------------------------------------------------------------------------- 4 2 2 4 2 3 3 2 6 2 6 2 x*y z - x*y z - 2x*y z - x*z - x, w x - w + x y + x z ) 4,0 1,1 o3 : Ideal of QQ[w , w , x..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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