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

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

Python

>>> from sage.all import *
>>> max(x, x**Integer(2))
x
>>> max_symbolic(x, x**Integer(2))
max(x, x^2)
>>> __tmp__=var("x"); f = symbolic_expression(max_symbolic(x, x**Integer(2))).function(x); f(Integer(1)/Integer(2))
1/2

This works as expected for more than two entries:

Sage

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)

[Python]

>>> from sage.all import *
>>> max(Integer(3), Integer(5), x)
5
>>> min(Integer(3), Integer(5), x)
3
>>> max_symbolic(Integer(3), Integer(5), x)
max(x, 5)
>>> min_symbolic(Integer(3), Integer(5), x)
min(x, 3)

class sage.functions.min_max.MaxSymbolic

Bases: MinMax_base

Symbolic \(\max\) function.

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

EXAMPLES:

Sage

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)

Python

>>> from sage.all import *
>>> max_symbolic(Integer(3), x)
max(3, x)
>>> max_symbolic(Integer(3), x).subs(x=Integer(5))
5
>>> max_symbolic(Integer(3), Integer(5), x)
max(x, 5)
>>> max_symbolic([Integer(3), Integer(5), x])
max(x, 5)

class sage.functions.min_max.MinMax_base

Bases: BuiltinFunction

eval_helper(this_f, builtin_f, initial_val, args)

EXAMPLES:

Sage

sage: max_symbolic(3, 5, x)  # indirect doctest
max(x, 5)
sage: max_symbolic([5.0r])   # indirect doctest
5.0
sage: min_symbolic(3, 5, x)
min(x, 3)
sage: min_symbolic([5.0r])   # indirect doctest
5.0

Python

>>> from sage.all import *
>>> max_symbolic(Integer(3), Integer(5), x)  # indirect doctest
max(x, 5)
>>> max_symbolic([5.0])   # indirect doctest
5.0
>>> min_symbolic(Integer(3), Integer(5), x)
min(x, 3)
>>> min_symbolic([5.0])   # indirect doctest
5.0

class sage.functions.min_max.MinSymbolic

Bases: MinMax_base

Symbolic \(\min\) function.

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

EXAMPLES:

Sage

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)

Python

>>> from sage.all import *
>>> min_symbolic(Integer(3), x)
min(3, x)
>>> min_symbolic(Integer(3), x).subs(x=Integer(5))
3
>>> min_symbolic(Integer(3), Integer(5), x)
min(x, 3)
>>> min_symbolic([Integer(3), Integer(5), x])
min(x, 3)