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 .000382061 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use minprimes) .00408501 seconds idlizer1: .00596778 seconds idlizer2: .0109863 seconds minpres: .00753869 seconds time .0399225 sec #fractions 4] [step 1: radical (use minprimes) .00497128 seconds idlizer1: .00695189 seconds idlizer2: .0348611 seconds minpres: .0113565 seconds time .0704306 sec #fractions 4] [step 2: radical (use minprimes) .00514878 seconds idlizer1: .00957103 seconds idlizer2: .0201258 seconds minpres: .00957246 seconds time .0816239 sec #fractions 5] [step 3: radical (use minprimes) .00582313 seconds idlizer1: .00800261 seconds idlizer2: .0308453 seconds minpres: .0234735 seconds time .101345 sec #fractions 5] [step 4: radical (use minprimes) .00593271 seconds idlizer1: .0140948 seconds idlizer2: .0757361 seconds minpres: .0117335 seconds time .125456 sec #fractions 5] [step 5: radical (use minprimes) .00611638 seconds idlizer1: .0102251 seconds time .0231261 sec #fractions 5] -- used 0.445202 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 |
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