高次方程式・恒等式関連の問題を Julia の SymPy で解く

1.　高校数学の「高次方程式・恒等式」関連の問題をPythonで解く

https://qiita.com/code0327/items/66efb7ac56cdea5b0b0d

Julia の SymPy でやってみる。

  
  using SymPy
  @syms x
  f = x^3 - 1;

  # (1)
  f.(x => 2) |> string

  "7"

  # (2)
  f.(x => 1) |> string

  "0"

  # (3)
  factor(f) |> string

  "(x - 1)*(x^2 + x + 1)"

  # (4)
  solve(f) |> string

  "Sym[1, -1/2 - sqrt(3)*I/2, -1/2 + sqrt(3)*I/2]"

  # (1)
  solve(x^4 - 10x^3 +35x^2 - 50x + 24) |> string

  "Sym[1, 2, 3, 4]"

  # なお，
  factor(x^4 - 10x^3 +35x^2 - 50x + 24) |> string

  "(x - 4)*(x - 3)*(x - 2)*(x - 1)"

  # (2)
  solve(x^4 - 10x^2 +9) |> string

  "Sym[-3, -1, 1, 3]"

  # なお，
  factor(x^4 - 10x^2 +9) |> string

  "(x - 3)*(x - 1)*(x + 1)*(x + 3)"

  # (1)
  @syms a, b, c, x
  solve(Eq(x^2, a*(x - 2)^2 + b*(x - 2) + c), [a, b, c]) |> string

  "Dict{Any, Any}(c => 4, b => 4, a => 1)"

  # (2)
  @syms a, b, x
  solve(Eq((3x- 4) / ((x + 2) * (x - 3)), a / (x + 2) + b / (x - 3)), [a, b])

  Dict{Any, Any} with 2 entries:
    b => 1
    a => 2

  # (1)
  solve(Eq(3 / (x + 2) + 3 / (x - 2), 2)) |> string

  "Sym[-1, 4]"

  # (2)
  solve(Eq(3 / (x + 2) + 3 / (x - 2), 0)) |> string

  "Sym[0]"

  # (3)
  solve(Eq(sqrt(x + 3), x + 1)) |> string

  "Sym[1]"

  # (4)
  solve(Eq(-sqrt(x + 3), x + 1)) |> string

  "Sym[-2]"