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 .000333046 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00258196 seconds idlizer1: .0053549 seconds idlizer2: .0107634 seconds minpres: .0074434 seconds time .0378514 sec #fractions 4] [step 1: radical (use decompose) .00303637 seconds idlizer1: .00682267 seconds idlizer2: .0197192 seconds minpres: .0334709 seconds time .0756642 sec #fractions 4] [step 2: radical (use decompose) .00294393 seconds idlizer1: .00835274 seconds idlizer2: .0215694 seconds minpres: .00980658 seconds time .0557395 sec #fractions 5] [step 3: radical (use decompose) .00301206 seconds idlizer1: .0302674 seconds idlizer2: .0330079 seconds minpres: .0448422 seconds time .130933 sec #fractions 5] [step 4: radical (use decompose) .0033948 seconds idlizer1: .0139669 seconds idlizer2: .0877849 seconds minpres: .0119708 seconds time .136055 sec #fractions 5] [step 5: radical (use decompose) .00336963 seconds idlizer1: .0304763 seconds time .0394988 sec #fractions 5] -- used 0.478773 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 |