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 .000517972 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00522555 seconds idlizer1: .00747176 seconds idlizer2: .0138387 seconds minpres: .0093407 seconds time .0500218 sec #fractions 4] [step 1: radical (use minprimes) .00618389 seconds idlizer1: .00836699 seconds idlizer2: .0423921 seconds minpres: .0129379 seconds time .0845138 sec #fractions 4] [step 2: radical (use minprimes) .00541421 seconds idlizer1: .0104786 seconds idlizer2: .0253814 seconds minpres: .0112345 seconds time .113774 sec #fractions 5] [step 3: radical (use minprimes) .0065464 seconds idlizer1: .00892297 seconds idlizer2: .0386044 seconds minpres: .0294096 seconds time .126219 sec #fractions 5] [step 4: radical (use minprimes) .00611556 seconds idlizer1: .0158234 seconds idlizer2: .0933627 seconds minpres: .0133463 seconds time .148839 sec #fractions 5] [step 5: radical (use minprimes) .00631906 seconds idlizer1: .0104976 seconds time .0236622 sec #fractions 5] -- used 0.551256 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, 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 |
The exact information displayed may change.