max -- the maximum of numbers
Introductionmax(x1, x2, ...) returns the maximum of
the numbers x1,x2,....
Call(s)max(x1, x2, ...)
Parametersx1, x2, ... |
- | arbitrary MuPAD objects |
Returnsone of the arguments, or a symbolic max call.
x1, x2, ,
...
Related
Functions_leequal, _less, min, sysorder
Detailsmax are either integers, rational numbers,
or floating point numbers, then
max returns the numerical maximum of these arguments.max() is illegal and leads to an
error message. If there is only one argument x1, then
max evaluates x1 and returns it (see example
2).infinity, then max
returns infinity. If
an argument is -infinity, then it is removed from the
argument list (see example 3).max returns an error when one of its arguments is a complex number (see example 2).max call with the maximum of the numerical
arguments and the remaining evaluated arguments is returned (see
example 1).
Nested max calls with symbolic arguments are rewritten
as a single max call, i.e., they are flattened; see example 4.
max does not react to properties of identifiers set via
assume. Use simplify to handle this (see
example 4).max is a function of the system kernel.
Example
1max computes the maximum of integers,
rational numbers, and floating point values:
>> max(-3/2, 7, 1.4)
7
If the argument list contains symbolic expressions, then
a symbolic max call is returned:
>> delete b: max(-4, b + 2, 1, 3)
max(b + 2, 3)
>> max(sqrt(2), 1)
1/2
max(2 , 1)
Use simplify to simplify
max expressions with constant symbolic arguments:
>> simplify(%)
1/2
2
Example
2max with one argument returns the evaluated
argument:
>> delete a: max(a), max(sin(2*PI)), max(2)
a, 0, 2
Complex numbers lead to an error message:
>> max(0, 1, I)
Error: Illegal argument [max]
Example
3infinity is always the maximum of
arbitrary arguments:
>> delete x: max(100000000000, infinity, x)
infinity
-infinity is
removed from the argument list:
>> max(100000000000, -infinity, x)
max(x, 100000000000)
Example
4max does not take into account properties of identifiers set via
assume:
>> delete a, b, c: assume(a > 0): assume(b > a, _and): assume(c > b, _and): max(a, max(b, c), 0)
max(a, b, c, 0)
An application of simplify yields the desired
result:
>> simplify(%)
c