@c Copyright (C) 1996, 1997 John W. Eaton
@c This is part of the Octave manual.
@c For copying conditions, see the file gpl.texi.

@node Arithmetic, Linear Algebra, Matrix Manipulation, Top
@chapter Arithmetic

Unless otherwise noted, all of the functions described in this chapter
will work for real and complex scalar or matrix arguments.

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

@node Utility Functions, Complex Arithmetic, Arithmetic, Arithmetic
@section Utility Functions

The following functions are available for working with complex numbers.
Each expects a single argument.  They are called @dfn{mapping functions}
because when given a matrix argument, they apply the given function to
each element of the matrix.

@DOCSTRING(ceil)

@DOCSTRING(exp)

@DOCSTRING(fix)

@DOCSTRING(floor)

@DOCSTRING(gcd)

@DOCSTRING(lcm)

@DOCSTRING(log)

@DOCSTRING(log10)

@DOCSTRING(log2)

@DOCSTRING(max)

@DOCSTRING(min)

@DOCSTRING(nextpow2)

@DOCSTRING(pow2)

@DOCSTRING(rem)

@DOCSTRING(round)

@DOCSTRING(sign)

@DOCSTRING(sqrt)

@node Complex Arithmetic, Trigonometry, Utility Functions, Arithmetic
@section Complex Arithmetic

The following functions are available for working with complex
numbers.  Each expects a single argument.  Given a matrix they work on
an element by element basis.  In the descriptions of the following
functions,
@iftex
@tex
$z$ is the complex number $x + iy$, where $i$ is defined as
$\sqrt{-1}$.
@end tex
@end iftex
@ifinfo
@var{z} is the complex number @var{x} + @var{i}@var{y}, where @var{i} is
defined as @code{sqrt (-1)}.
@end ifinfo

@DOCSTRING(abs)

@DOCSTRING(arg)

@DOCSTRING(conj)

@DOCSTRING(imag)

@DOCSTRING(real)

@node Trigonometry, Sums and Products, Complex Arithmetic, Arithmetic
@section Trigonometry

Octave provides the following trigonometric functions.  Angles are
specified in radians.  To convert from degrees to radians multipy by
@iftex
@tex
$\pi/180$
@end tex
@end iftex
@ifinfo
@code{pi/180}
@end ifinfo
 (e.g. @code{sin (30 * pi/180)} returns the sine of 30 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(scsh)
@DOCSTRING(coth)

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

Each of these functions expect a single argument.  For matrix arguments,
they work on an element by element basis.  For example,

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

@DOCSTRING(atan2)


@node Sums and Products, Special Functions, Trigonometry, Arithmetic
@section Sums and Products

@DOCSTRING(sum)

@DOCSTRING(prod)

@DOCSTRING(cumsum)

@DOCSTRING(cumprod)

@DOCSTRING(sumsq)

@node Special Functions, Mathematical Constants, Sums and Products, Arithmetic
@section Special Functions

@DOCSTRING(bessel)

@DOCSTRING(beta)

@DOCSTRING(betai)

@DOCSTRING(bincoeff)

@DOCSTRING(erf)

@DOCSTRING(erfc)

@DOCSTRING(erfinv)

@DOCSTRING(gamma)

@DOCSTRING(gammai)

@DOCSTRING(lgamma)

@DOCSTRING(cross)

@DOCSTRING(commutation_matrix)

@DOCSTRING(duplication_matrix)

@node Mathematical Constants,  , Special Functions, Arithmetic
@section Mathematical Constants

@DOCSTRING(I)

@DOCSTRING(Inf)

@DOCSTRING(NaN)

@DOCSTRING(pi)

@DOCSTRING(e)

@DOCSTRING(eps)

@DOCSTRING(realmax)

@DOCSTRING(realmin)