# Revision history [back]

You can also solve it more directly without explicitly computing the Groebner basis.

sage: R.<a,b,c> = PolynomialRing(QQ,order='lex')
sage: f1 = a+b+c - 3
sage: f2 = a^2+b^2+c^2 - 5
sage: f3 = a^3+b^3+c^3 - 7
sage: Rel = ideal(f1,f2,f3)
sage: Rel.reduce(a^5+b^5+c^5)
29/3


(I came up with this solution after reading the solution to Exercise 37 from the book "Calcul Mathematique avec Sage", given on page 423)

You can also solve it a bit more directly without explicitly computing invoking the Groebner basis.basis (this happens under the hood).

sage: R.<a,b,c> = PolynomialRing(QQ,order='lex')
sage: f1 = a+b+c - 3
sage: f2 = a^2+b^2+c^2 - 5
sage: f3 = a^3+b^3+c^3 - 7
sage: Rel = ideal(f1,f2,f3)
sage: Rel.reduce(a^5+b^5+c^5)
29/3


(I came up with this solution after reading the solution to Exercise 37 from the book "Calcul Mathematique avec Sage", given on page 423)