-- -*- M2-comint -*- hash: -1663871215

i1 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : S = {x+y+z-1, x^2+y^2, x+y-z-3}

                      2    2
o2 = {x + y + z - 1, x  + y , x + y - z - 3}

o2 : List

i3 : L = solveSystem(S)

o3 = {{1-ii, 1+ii, -1}, {1+ii, 1-ii, -1}}

o3 : List

i4 : oneSoln = L_0

o4 = oneSoln

o4 : Point

i5 : peek oneSoln

o5 = Point{cache => CacheTable{...3...}   }
           Coordinates => {1-ii, 1+ii, -1}

i6 : system = {y-x^2, z-x^3, x+y+z-1, x+y+ x^3 -1}

         2         3                      3
o6 = {- x  + y, - x  + z, x + y + z - 1, x  + x + y - 1}

o6 : List

i7 : #system > numcols vars R --overdetermined system

o7 = true

i8 : solns = solveSystem(system);
*** after parseSolutions, ring has {x, y, z} ***

i9 : numSolns = #solns

o9 = 3

i10 : 
