The following example appeared in Maxima mailing list (Maxima could not do it). Here we solve it using FriCAS. First we form system of equations: fricas (1) -> -- Form system of equations eqn1 := a1*x1^5 + a2*x2^5 + a3*x3^5 = 1 / 6
Type: Equation(Polynomial(Fraction(Integer)))fricas eqn2 := a1*x1^4 + a2*x2^4 + a3*x3^4 = 1 / 5
Type: Equation(Polynomial(Fraction(Integer)))fricas eqn3 := a1*x1^3 + a2*x2^3 + a3*x3^3 = 1 / 4
Type: Equation(Polynomial(Fraction(Integer)))fricas eqn4 := a1*x1^2 + a2*x2^2 + a3*x3^2 = 1 / 3
Type: Equation(Polynomial(Fraction(Integer)))fricas eqn5 := a1*x1 + a2*x2 + a3*x3 = 1 / 2
Type: Equation(Polynomial(Fraction(Integer)))fricas eqn6 := a1 + a2 + a3 = 1
Type: Equation(Polynomial(Integer))fricas eqns := [eqn1, Type: List(Equation(Polynomial(Fraction(Integer))))Now we solve it fricas solve(eqns,
Type: List(List(Equation(Fraction(Polynomial(Integer)))))The solution above is not fully explicit, in first solotion we need to solve
quadratic equation in fricas radicalSolve(eqns,
Type: List(List(Equation(Expression(Integer))))Note: not all equations have solutions in radicals and FriCAS can find solutions in radicals only in relatively simple cases. But system above has simple solution in radicals and FriCAS can find it. |