NAME
    min - minimum, or minimum of defined minima

SYNOPSIS
    min(x_1, x_2, ...)

TYPES
    x_1, x_2, ...	any

    return		any

DESCRIPTION
    If an argument x_i is a list with elements e_1, e_2, ..., e_n, it
    is treated as if x_i were replaced by e_1, e_2, ..., e_n; this may
    continue recurively if any of the e_j is a list.

    If an argument x_i is an object of type xx, then x_i is replaced by
    xx_min(x_i) if the function xx_min() has been defined.  If the
    type xx has been defined by:

		obj xx = {x, y, z},

    an appropriate definition of xx_min(a) is sometimes min(a.x, a.y, a.z).
    min(a) then returns the minimum of the elements of a.

    If x_i has the null value, it is ignored.  Thus, sum(a, , b, , c)

    If x_i has the null value, it is ignored.  Thus, min(a, , b, , c)
    will return the same as min(a, b, c).

    Assuming the above replacements, and that the x_1, x_2, ..., are
    of sufficently simple ordered types (e.g. real numbers or strings),
    or, if some are objects, the relevant xx_rel(a,b) has been defined
    and returns a real-number value for any comparison that has to be made,
    min(x_1, x_2, ...) returns the value determined by min(x_1) = x_1,
    and succesively for later arguments, by the use of the equivalent of
    min(a,b) = (a < b) ? a : b.	 If the ordering determined by < is total,
    min(x_1, ...) will be the minimum value among the arguments.  For a
    preorder relation it may be one of several minimal values.	For other
    relations, it may be difficult to predict the result.

EXAMPLE
    ; print min(2), min(5, 3, 7, 2, 9), min(3.2, -0.5, 8.7, -1.2, 2.5)
    2 2 -1.2

    ; print min(list(3,5), 7, list(6, list(7,8), 2))
    2

    ; print min("one", "two", "three", "four")
    four

    ; obj point {x, y}
    ; define point_rel(a,b) = sgn(a.x - b.x)
    ; obj point A = {1, 5}
    ; obj point B = {1, 4}
    ; obj point C = {3, 3}
    ; print min(A, B, C)
    obj point {1, 5}

    ; define point_min(a) = a.x
    ; print min(A, B, C)
    1

LIMITS
    The number of arguments is not to exceed 1024.

LINK LIBRARY
    NUMBER *qmin(NUMBER *x1, NUMBER *x2)

SEE ALSO
    max, obj, sum, ssq

## Copyright (C) 1999-2006  Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL.  You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: min,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/bin/calc/help/RCS/min,v $
##
## Under source code control:	1995/10/05 04:52:27
## File existed as early as:	1995
##
## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
