Nonlinear equations

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Nonlinear equations

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

inputs outputs

using decomposition to solve high degree polynomials


    solve(x^8-8*x^7+34*x^6-92*x^5+175*x^4-236*x^3+226*x^2-140*x+46, x);

          sqrt(- sqrt(4 sqrt(3) + 3) %i - 3) - sqrt(2)
   [x = - --------------------------------------------,
                            sqrt(2)

       sqrt(- sqrt(4 sqrt(3) + 3) %i - 3) + sqrt(2)
   x = --------------------------------------------,
                         sqrt(2)

         sqrt(sqrt(4 sqrt(3) + 3) %i - 3) - sqrt(2)
   x = - ------------------------------------------,
                          sqrt(2)

       sqrt(sqrt(4 sqrt(3) + 3) %i - 3) + sqrt(2)
   x = ------------------------------------------,
                        sqrt(2)

         sqrt(sqrt(4 sqrt(3) - 3) + 3) %i - sqrt(2)
   x = - ------------------------------------------,
                          sqrt(2)

       sqrt(sqrt(4 sqrt(3) - 3) + 3) %i + sqrt(2)
   x = ------------------------------------------,
                        sqrt(2)

         sqrt(3 - sqrt(4 sqrt(3) - 3)) %i - sqrt(2)
   x = - ------------------------------------------,
                          sqrt(2)

       sqrt(3 - sqrt(4 sqrt(3) - 3)) %i + sqrt(2)
   x = ------------------------------------------]
                        sqrt(2)

multiple use of inversion functions

    assume(b > 0);

                               [b > 0]

solve(log(acos(asin(x^(2/3)-b)-1))+2, x);

                      - 2       3/2   1/3                        - 2
  [x = (b + sin(cos(%e   ) + 1))   , x    = - sqrt(b + sin(cos(%e   ) + 1))]

forget(b > 0)$

Richard Liska