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 .000351056 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .003625 seconds idlizer1: .00610219 seconds idlizer2: .0187505 seconds minpres: .0092325 seconds time .049927 sec #fractions 4] [step 1: radical (use decompose) .00990615 seconds idlizer1: .00668779 seconds idlizer2: .0277267 seconds minpres: .011241 seconds time .0707961 sec #fractions 4] [step 2: radical (use decompose) .00328891 seconds idlizer1: .0187964 seconds idlizer2: .0793254 seconds minpres: .00866362 seconds time .123048 sec #fractions 5] [step 3: radical (use decompose) .00331486 seconds idlizer1: .00988299 seconds idlizer2: .0450298 seconds minpres: .0249088 seconds time .109947 sec #fractions 5] [step 4: radical (use decompose) .00330558 seconds idlizer1: .0132499 seconds idlizer2: .128106 seconds minpres: .0201424 seconds time .188279 sec #fractions 5] [step 5: radical (use decompose) .00640315 seconds idlizer1: .00972547 seconds time .0287329 sec #fractions 5] -- used 0.574167 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 |