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 .000534472 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00295925 seconds idlizer1: .00960991 seconds idlizer2: .0170457 seconds minpres: .0118254 seconds time .0581463 sec #fractions 4] [step 1: radical (use minprimes) .00306744 seconds idlizer1: .0152459 seconds idlizer2: .030846 seconds minpres: .0185228 seconds time .0863177 sec #fractions 4] [step 2: radical (use minprimes) .0029684 seconds idlizer1: .0162113 seconds idlizer2: .0877113 seconds minpres: .014989 seconds time .140783 sec #fractions 5] [step 3: radical (use minprimes) .00314905 seconds idlizer1: .0175992 seconds idlizer2: .0541524 seconds minpres: .0417347 seconds time .170954 sec #fractions 5] [step 4: radical (use minprimes) .00309177 seconds idlizer1: .0190697 seconds idlizer2: .109153 seconds minpres: .0193326 seconds time .204031 sec #fractions 5] [step 5: radical (use minprimes) .0031077 seconds idlizer1: .0123343 seconds time .0250482 sec #fractions 5] -- used 0.690139 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..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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