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