@c Copyright (C) 1996, 1997, 1999, 2000, 2001, 2002, 2007, 2008,
@c               2009 John W. Eaton
@c
@c This file is part of Octave.
@c
@c Octave is free software; you can redistribute it and/or modify it
@c under the terms of the GNU General Public License as published by the
@c Free Software Foundation; either version 3 of the License, or (at
@c your option) any later version.
@c 
@c Octave is distributed in the hope that it will be useful, but WITHOUT
@c ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
@c FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
@c for more details.
@c 
@c You should have received a copy of the GNU General Public License
@c along with Octave; see the file COPYING.  If not, see
@c <http://www.gnu.org/licenses/>.

@node Arithmetic
@chapter Arithmetic

Unless otherwise noted, all of the functions described in this chapter
will work for real and complex scalar, vector, or matrix arguments.  Functions
described as @dfn{mapping functions} apply the given operation individually to 
each element when given a matrix argument.  For example,

@example
@group
sin ([1, 2; 3, 4])
     @result{}  0.84147   0.90930
         0.14112  -0.75680
@end group
@end example

@menu
* Exponents and Logarithms::
* Complex Arithmetic::          
* Trigonometry::                
* Sums and Products::           
* Utility Functions::           
* Special Functions::           
* Coordinate Transformations::
* Mathematical Constants::      
@end menu

@node Exponents and Logarithms
@section Exponents and Logarithms

@DOCSTRING(exp)

@DOCSTRING(expm1)

@DOCSTRING(log)

@DOCSTRING(log1p)

@DOCSTRING(log10)

@DOCSTRING(log2)

@DOCSTRING(nextpow2)

@DOCSTRING(nthroot)

@DOCSTRING(pow2)

@DOCSTRING(reallog)

@DOCSTRING(realpow)

@DOCSTRING(realsqrt)

@DOCSTRING(sqrt)

@node Complex Arithmetic
@section Complex Arithmetic

In the descriptions of the following functions,
@tex
$z$ is the complex number $x + iy$, where $i$ is defined as
$\sqrt{-1}$.
@end tex
@ifnottex
@var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is
defined as @code{sqrt (-1)}.
@end ifnottex

@DOCSTRING(abs)

@DOCSTRING(arg)

@DOCSTRING(conj)

@DOCSTRING(cplxpair)

@DOCSTRING(imag)

@DOCSTRING(real)

@node Trigonometry
@section Trigonometry

Octave provides the following trigonometric functions where angles are
specified in radians.  To convert from degrees to radians multiply by
@tex
$\pi/180$
@end tex
@ifnottex
@code{pi/180}
@end ifnottex
(e.g., @code{sin (30 * pi/180)} returns the sine of 30 degrees).  As
an alternative, Octave provides a number of trigonometric functions
which work directly on an argument specified in degrees.  These functions
are named after the base trigonometric function with a @samp{d} suffix.  For
example, @code{sin} expects an angle in radians while @code{sind} expects an
angle in degrees.

@DOCSTRING(sin)
@DOCSTRING(cos)
@DOCSTRING(tan)
@DOCSTRING(sec)
@DOCSTRING(csc)
@DOCSTRING(cot)

@DOCSTRING(asin)
@DOCSTRING(acos)
@DOCSTRING(atan)
@DOCSTRING(asec)
@DOCSTRING(acsc)
@DOCSTRING(acot)

@DOCSTRING(sinh)
@DOCSTRING(cosh)
@DOCSTRING(tanh)
@DOCSTRING(sech)
@DOCSTRING(csch)
@DOCSTRING(coth)

@DOCSTRING(asinh)
@DOCSTRING(acosh)
@DOCSTRING(atanh)
@DOCSTRING(asech)
@DOCSTRING(acsch)
@DOCSTRING(acoth)

@DOCSTRING(atan2)

Octave provides the following trigonometric functions where angles are
specified in degrees.  These functions produce true zeros at the appropriate
intervals rather than the small roundoff error that occurs when using
radians.  For example:
@example
@group
cosd (90)
     @result{} 0
cos (pi/2)
     @result{} 6.1230e-17
@end group
@end example

@DOCSTRING(sind)
@DOCSTRING(cosd)
@DOCSTRING(tand)
@DOCSTRING(secd)
@DOCSTRING(cscd)
@DOCSTRING(cotd)

@DOCSTRING(asind)
@DOCSTRING(acosd)
@DOCSTRING(atand)
@DOCSTRING(asecd)
@DOCSTRING(acscd)
@DOCSTRING(acotd)

@node Sums and Products
@section Sums and Products

@DOCSTRING(sum)

@DOCSTRING(prod)

@DOCSTRING(cumsum)

@DOCSTRING(cumprod)

@DOCSTRING(sumsq)

@DOCSTRING(accumarray)

@node Utility Functions
@section Utility Functions

@DOCSTRING(ceil)

@DOCSTRING(cross)

@DOCSTRING(del2)

@DOCSTRING(factor)

@DOCSTRING(factorial)

@DOCSTRING(fix)

@DOCSTRING(floor)

@DOCSTRING(fmod)

@DOCSTRING(gcd)

@DOCSTRING(gradient)

@DOCSTRING(hypot)

@DOCSTRING(lcm)

@DOCSTRING(list_primes)

@DOCSTRING(max)

@DOCSTRING(min)

@DOCSTRING(cummax)

@DOCSTRING(cummin)

@DOCSTRING(mod)

@DOCSTRING(primes)

@DOCSTRING(rem)

@DOCSTRING(round)

@DOCSTRING(roundb)

@DOCSTRING(sign)

@node Special Functions
@section Special Functions

@DOCSTRING(airy)

@DOCSTRING(besselj)

@DOCSTRING(beta)

@DOCSTRING(betainc)

@DOCSTRING(betaln)

@DOCSTRING(bincoeff)

@DOCSTRING(commutation_matrix)

@DOCSTRING(duplication_matrix)

@DOCSTRING(erf)

@DOCSTRING(erfc)

@DOCSTRING(erfinv)

@DOCSTRING(gamma)

@DOCSTRING(gammainc)

@DOCSTRING(legendre)

@anchor{doc-gammaln}
@DOCSTRING(lgamma)

@node Coordinate Transformations
@section Coordinate Transformations

@DOCSTRING(cart2pol)

@DOCSTRING(pol2cart)

@DOCSTRING(cart2sph)

@DOCSTRING(sph2cart)

@node Mathematical Constants
@section Mathematical Constants

@DOCSTRING(e)

@DOCSTRING(pi)

@DOCSTRING(I)

@DOCSTRING(Inf)

@DOCSTRING(NaN)

@DOCSTRING(eps)

@DOCSTRING(realmax)

@DOCSTRING(realmin)