min
-- the minimum of numbersmin(
x1, x2, ...)
returns the minimum of
the numbers x1,x2,....
min(x1, x2, ...)
x1, x2, ... |
- | arbitrary MuPAD objects |
one of the arguments, or a symbolic min
call.
x1
, x2
, ,
...
_leequal
, _less
, min
, sysorder
min
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.min
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
min
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]
-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)
min
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