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

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)
class sage.functions.min_max.MinMax_base
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

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)