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 .00186284 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .0140248 seconds idlizer1: .0260367 seconds idlizer2: .0532106 seconds minpres: .0371976 seconds time .180942 sec #fractions 4] [step 1: radical (use decompose) .01495 seconds idlizer1: .030865 seconds idlizer2: .0995122 seconds minpres: .0598378 seconds time .263648 sec #fractions 4] [step 2: radical (use decompose) .0149631 seconds idlizer1: .0434336 seconds idlizer2: .304887 seconds minpres: .0450737 seconds time .465617 sec #fractions 5] [step 3: radical (use decompose) .0148755 seconds idlizer1: .0345395 seconds idlizer2: .164479 seconds minpres: .123986 seconds time .428346 sec #fractions 5] [step 4: radical (use decompose) .0151198 seconds idlizer1: .0694574 seconds idlizer2: .34295 seconds minpres: .0642156 seconds time .579512 sec #fractions 5] [step 5: radical (use decompose) .0148746 seconds idlizer1: .0432128 seconds time .0845294 sec #fractions 5] -- used 2.01716 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 |