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)                                                                    # needs sage.symbolic
x
sage: max_symbolic(x, x^2)                                                           # needs sage.symbolic
max(x, x^2)
sage: f(x) = max_symbolic(x, x^2); f(1/2)                                            # needs sage.symbolic
1/2

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

This works as expected for more than two entries:

sage: # needs sage.symbolic
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)

# needs sage.symbolic
max(3, 5, x)
min(3, 5, x)
max_symbolic(3, 5, x)
min_symbolic(3, 5, x)
>>> from sage.all import *
>>> # needs sage.symbolic
>>> 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[source]#

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: # needs sage.symbolic
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)

# needs sage.symbolic
max_symbolic(3, x)
max_symbolic(3, x).subs(x=5)
max_symbolic(3, 5, x)
max_symbolic([3, 5, x])
>>> from sage.all import *
>>> # needs sage.symbolic
>>> 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[source]#

Bases: BuiltinFunction

eval_helper(this_f, builtin_f, initial_val, args)[source]#

EXAMPLES:

sage: # needs sage.symbolic
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

# needs sage.symbolic
max_symbolic(3, 5, x)  # indirect doctest
max_symbolic([5.0r])   # indirect doctest
min_symbolic(3, 5, x)
min_symbolic([5.0r])   # indirect doctest
>>> from sage.all import *
>>> # needs sage.symbolic
>>> 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[source]#

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: # needs sage.symbolic
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)

# needs sage.symbolic
min_symbolic(3, x)
min_symbolic(3, x).subs(x=5)
min_symbolic(3, 5, x)
min_symbolic([3, 5, x])
>>> from sage.all import *
>>> # needs sage.symbolic
>>> 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)