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 .00086762 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00721692 seconds idlizer1: .0135675 seconds idlizer2: .0271959 seconds minpres: .0189962 seconds time .0920994 sec #fractions 4] [step 1: radical (use decompose) .0077349 seconds idlizer1: .0158991 seconds idlizer2: .0469521 seconds minpres: .0289472 seconds time .173577 sec #fractions 4] [step 2: radical (use decompose) .0078927 seconds idlizer1: .0224484 seconds idlizer2: .055959 seconds minpres: .0245472 seconds time .141591 sec #fractions 5] [step 3: radical (use decompose) .00848458 seconds idlizer1: .0194403 seconds idlizer2: .0849064 seconds minpres: .061444 seconds time .220201 sec #fractions 5] [step 4: radical (use decompose) .00837974 seconds idlizer1: .0359492 seconds idlizer2: .172099 seconds minpres: .0302509 seconds time .339475 sec #fractions 5] [step 5: radical (use decompose) .00799752 seconds idlizer1: .0225752 seconds time .0446422 sec #fractions 5] -- used 1.01873 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 |