-- -*- M2-comint -*- hash: 14744966813690843441

i1 : R = QQ[x_1..x_3]

o1 = R

o1 : PolynomialRing

i2 : f = (x_1-1)

o2 = x  - 1
      1

o2 : R

i3 : g = (x_2-2)

o3 = x  - 2
      2

o3 : R

i4 : h = (x_3^2-9)

      2
o4 = x  - 9
      3

o4 : R

i5 : I = ideal (f,g,h)

                             2
o5 = ideal (x  - 1, x  - 2, x  - 9)
             1       2       3

o5 : Ideal of R

i6 : decompose I

o6 = {ideal (x  - 3, x  - 2, x  - 1), ideal (x  + 3, x  - 2, x  - 1)}
              3       2       1               3       2       1

o6 : List

i7 : rur=msolveRUR(I)

o7 = HashTable{"degree" => 2                  }
               "denominator" => 2T
                                      2
               "findRootsUniPoly" => T  - 9
                                            2
               "numerator" => {-2T, -4T, -2T }
               "T" => x
                       3
               "var" => T

o7 : HashTable

i8 : factor rur#"findRootsUniPoly"

o8 = (T - 3)(T + 3)

o8 : Expression of class Product

i9 : sols=-1*(rur#"numerator")

                2
o9 = {2T, 4T, 2T }

o9 : List

i10 : denom= rur#"denominator"

o10 = 2T

o10 : QQ[T]

i11 : (for s in sols list sub(s,T=>3))/sub(denom,T=>3)

o11 = {1, 2, 3}

o11 : List

i12 : (for s in sols list sub(s,T=>-3))/sub(denom,T=>-3)

o12 = {1, 2, -3}

o12 : List

i13 : 
