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@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
@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::
* Coordinate Transformations::
* Mathematical Constants::
@end menu
@node Utility Functions
@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(mod)
@DOCSTRING(nextpow2)
@DOCSTRING(pow2)
@DOCSTRING(rem)
@DOCSTRING(round)
@DOCSTRING(sign)
@DOCSTRING(sqrt)
@node Complex 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
@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(csch)
@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
@section Sums and Products
@DOCSTRING(sum)
@DOCSTRING(prod)
@DOCSTRING(cumsum)
@DOCSTRING(cumprod)
@DOCSTRING(sumsq)
@node Special Functions
@section Special Functions
@DOCSTRING(besselj)
@DOCSTRING(airy)
@DOCSTRING(beta)
@DOCSTRING(betainc)
@DOCSTRING(bincoeff)
@DOCSTRING(erf)
@DOCSTRING(erfc)
@DOCSTRING(erfinv)
@DOCSTRING(gamma)
@DOCSTRING(gammainc)
@DOCSTRING(lgamma)
@DOCSTRING(cross)
@DOCSTRING(commutation_matrix)
@DOCSTRING(duplication_matrix)
@node Coordinate Transformations
@section Coordinate Transformations
@DOCSTRING(cart2pol)
@DOCSTRING(pol2cart)
@DOCSTRING(cart2sph)
@DOCSTRING(sph2cart)
@node Mathematical Constants
@section Mathematical Constants
@DOCSTRING(I)
@DOCSTRING(Inf)
@DOCSTRING(NaN)
@DOCSTRING(pi)
@DOCSTRING(e)
@DOCSTRING(eps)
@DOCSTRING(realmax)
@DOCSTRING(realmin)
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