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 .000379886 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .0031419 seconds idlizer1: .00584932 seconds idlizer2: .0110937 seconds minpres: .00805119 seconds time .0396932 sec #fractions 4] [step 1: radical (use decompose) .0035365 seconds idlizer1: .00734819 seconds idlizer2: .020221 seconds minpres: .0126502 seconds time .0561505 sec #fractions 4] [step 2: radical (use decompose) .00325267 seconds idlizer1: .0346665 seconds idlizer2: .0224566 seconds minpres: .0100006 seconds time .0830106 sec #fractions 5] [step 3: radical (use decompose) .00375287 seconds idlizer1: .0086659 seconds idlizer2: .0354755 seconds minpres: .0245943 seconds time .0907933 sec #fractions 5] [step 4: radical (use decompose) .00345247 seconds idlizer1: .021789 seconds idlizer2: .0605528 seconds minpres: .0129518 seconds time .11687 sec #fractions 5] [step 5: radical (use decompose) .00397276 seconds idlizer1: .0105299 seconds time .0215478 sec #fractions 5] -- used 0.410999 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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