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 .000548546 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00476725 seconds idlizer1: .0098999 seconds idlizer2: .0163262 seconds minpres: .0118336 seconds time .0627666 sec #fractions 4] [step 1: radical (use decompose) .00456519 seconds idlizer1: .00873994 seconds idlizer2: .0289677 seconds minpres: .0191842 seconds time .0820956 sec #fractions 4] [step 2: radical (use decompose) .00508413 seconds idlizer1: .0140429 seconds idlizer2: .0638113 seconds minpres: .014292 seconds time .117692 sec #fractions 5] [step 3: radical (use decompose) .00520993 seconds idlizer1: .0122735 seconds idlizer2: .0494113 seconds minpres: .0405855 seconds time .139388 sec #fractions 5] [step 4: radical (use decompose) .00613119 seconds idlizer1: .0204264 seconds idlizer2: .12671 seconds minpres: .019552 seconds time .20116 sec #fractions 5] [step 5: radical (use decompose) .00568506 seconds idlizer1: .0131866 seconds time .0304654 sec #fractions 5] -- used 0.638875 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 |