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# Symbolic Minimum and Maximum

Sage provides a symbolic maximum and minimum due to the fact that the Python builtin max and min are not able to deal with variables as users might expect. These functions wait to evaluate if there are variables.

Here you can see some differences:

    sage: max(x,x^2)
    x
    sage: max_symbolic(x,x^2)
    max(x, x^2)
    sage: f(x) = max_symbolic(x,x^2); f(1/2)
    1/2

This works as expected for more than two entries:

    sage: max(3,5,x)
    5
    sage: min(3,5,x)
    3
    sage: max_symbolic(3,5,x)
    max(x, 5)
    sage: min_symbolic(3,5,x)
    min(x, 3)

class `sage.functions.min_max.``MaxSymbolic`

  Bases: `sage.functions.min_max.MinMax_base`

  Symbolic \(\max\) function.

  The Python builtin \(\max\) function doesn’t work as expected when symbolic expressions are given as arguments. This function delays evaluation until all symbolic arguments are substituted with values.

  EXAMPLES:

      sage: max_symbolic(3, x)
      max(3, x)
      sage: max_symbolic(3, x).subs(x=5)
      5
      sage: max_symbolic(3, 5, x)
      max(x, 5)
      sage: max_symbolic([3,5,x])
      max(x, 5)

  TESTS:

      sage: loads(dumps(max_symbolic(x,5)))
      max(x, 5)
      sage: latex(max_symbolic(x,5))
      \max\left(x, 5\right)
      sage: max_symbolic(x, 5)._sympy_()
      Max(5, x)

class `sage.functions.min_max.``MinMax_base`

  Bases: `sage.symbolic.function.BuiltinFunction`

  TESTS:

      sage: from sage.functions.trig import Function_cot
      sage: c = Function_cot() # indirect doctest
      sage: c(pi/2)
      0

  `eval_helper`(this_f, builtin_f, initial_val, args)

    EXAMPLES:

        sage: max_symbolic(3,5,x) # indirect doctest
        max(x, 5)
        sage: min_symbolic(3,5,x)
        min(x, 3)

class `sage.functions.min_max.``MinSymbolic`

  Bases: `sage.functions.min_max.MinMax_base`

  Symbolic \(\min\) function.

  The Python builtin \(\min\) function doesn’t work as expected when symbolic expressions are given as arguments. This function delays evaluation until all symbolic arguments are substituted with values.

  EXAMPLES:

      sage: min_symbolic(3, x)
      min(3, x)
      sage: min_symbolic(3, x).subs(x=5)
      3
      sage: min_symbolic(3, 5, x)
      min(x, 3)
      sage: min_symbolic([3,5,x])
      min(x, 3)

  TESTS:

      sage: loads(dumps(min_symbolic(x,5)))
      min(x, 5)
      sage: latex(min_symbolic(x,5))
      \min\left(x, 5\right)
      sage: min_symbolic(x, 5)._sympy_()
      Min(5, x)

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