Macaulay2, version 1.6.0.1
with packages: ConwayPolynomials, Elimination, IntegralClosure, LLLBases, PrimaryDecomposition,
               ReesAlgebra, TangentCone

i1 : R=QQ[a,b,c]

o1 = R

o1 : PolynomialRing

i2 : i1=ideal(a+b+c-3,a^2+b^2+c^2-5,a^3+b^3+c^3-7)

                            2    2    2       3    3    3
o2 = ideal (a + b + c - 3, a  + b  + c  - 5, a  + b  + c  - 7)

o2 : Ideal of R

i3 : S=R/i1

o3 = S

o3 : QuotientRing

i4 : phi=map(S,R)

o4 = map(S,R,{- b - c + 3, b, c})

o4 : RingMap S <--- R

i6 : use R

o6 = R

o6 : PolynomialRing

i7 : phi(a^5+b^5+c^5)

     29
o7 = --
      3

o7 : S