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<H2><A NAME="s6">6. Mathematical Functions</A></H2>
<P>
<H2><A NAME="Conj"></A> <A NAME="ss6.1">6.1 <B>Conj</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the complex conjugate of a number
<DT><B> Usage </B><DD><P><CODE>z1 = Conj (z)</CODE>
<DT><B> Description </B><DD><P>The <CODE>Conj</CODE> function returns the complex conjugate of a number.
If its argument is an array, the <CODE>Conj</CODE> function will be applied to each
element and the result returned as an array.
<DT><B> See Also </B><DD><P><CODE>Real, Imag, abs</CODE>
</DL>
<P>
<P>
<H2><A NAME="Imag"></A> <A NAME="ss6.2">6.2 <B>Imag</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the imaginary part of a number
<DT><B> Usage </B><DD><P><CODE>i = Imag (z)</CODE>
<DT><B> Description </B><DD><P>The <CODE>Imag</CODE> function returns the imaginary part of a number.
If its argument is an array, the <CODE>Imag</CODE> function will be applied to each
element and the result returned as an array.
<DT><B> See Also </B><DD><P><CODE>Real, Conj, abs</CODE>
</DL>
<P>
<P>
<H2><A NAME="Real"></A> <A NAME="ss6.3">6.3 <B>Real</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the real part of a number
<DT><B> Usage </B><DD><P><CODE>r = Real (z)</CODE>
<DT><B> Description </B><DD><P>The <CODE>Real</CODE> function returns the real part of a number. If its
argument is an array, the <CODE>Real</CODE> function will be applied to
each element and the result returned as an array.
<DT><B> See Also </B><DD><P><CODE>Imag, Conj, abs</CODE>
</DL>
<P>
<P>
<H2><A NAME="abs"></A> <A NAME="ss6.4">6.4 <B>abs</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the absolute value of a number
<DT><B> Usage </B><DD><P><CODE>y = abs(x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>abs</CODE> function returns the absolute value of an arithmetic
type. If its argument is a complex number (<CODE>Complex_Type</CODE>),
then it returns the modulus. If the argument is an array, a new
array will be created whose elements are obtained from the original
array by using the <CODE>abs</CODE> function.
<DT><B> See Also </B><DD><P><CODE>sign, sqr</CODE>
</DL>
<P>
<P>
<H2><A NAME="acos"></A> <A NAME="ss6.5">6.5 <B>acos</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the arc-cosine of an number
<DT><B> Usage </B><DD><P><CODE>y = acos (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>acos</CODE> function computes the arc-cosine of a number and
returns the result as an array. If its argument is an array, the
<CODE>acos</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="acosh"></A> <A NAME="ss6.6">6.6 <B>acosh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the inverse cosh of an number
<DT><B> Usage </B><DD><P><CODE>y = acosh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>acosh</CODE> function computes the inverse cosh of a number and
returns the result as an array. If its argument is an array, the
<CODE>acosh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="asin"></A> <A NAME="ss6.7">6.7 <B>asin</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the arc-sine of an number
<DT><B> Usage </B><DD><P><CODE>y = asin (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>asin</CODE> function computes the arc-sine of a number and
returns the result as an array. If its argument is an array, the
<CODE>asin</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="asinh"></A> <A NAME="ss6.8">6.8 <B>asinh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the inverse-sinh of an number
<DT><B> Usage </B><DD><P><CODE>y = asinh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>asinh</CODE> function computes the inverse-sinh of a number and
returns the result as an array. If its argument is an array, the
<CODE>asinh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="atan"></A> <A NAME="ss6.9">6.9 <B>atan</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the arc-tangent of an number
<DT><B> Usage </B><DD><P><CODE>y = atan (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>atan</CODE> function computes the arc-tangent of a number and
returns the result as an array. If its argument is an array, the
<CODE>atan</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="atanh"></A> <A NAME="ss6.10">6.10 <B>atanh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the inverse-tanh of an number
<DT><B> Usage </B><DD><P><CODE>y = atanh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>atanh</CODE> function computes the inverse-tanh of a number and
returns the result as an array. If its argument is an array, the
<CODE>atanh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="cos"></A> <A NAME="ss6.11">6.11 <B>cos</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the cosine of an number
<DT><B> Usage </B><DD><P><CODE>y = cos (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>cos</CODE> function computes the cosine of a number and
returns the result as an array. If its argument is an array, the
<CODE>cos</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="cosh"></A> <A NAME="ss6.12">6.12 <B>cosh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the hyperbolic cosine of an number
<DT><B> Usage </B><DD><P><CODE>y = cosh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>cosh</CODE> function computes the hyperbolic cosine of a number and
returns the result as an array. If its argument is an array, the
<CODE>cosh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="exp"></A> <A NAME="ss6.13">6.13 <B>exp</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the exponential of an number
<DT><B> Usage </B><DD><P><CODE>y = exp (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>exp</CODE> function computes the exponential of a number and
returns the result as an array. If its argument is an array, the
<CODE>exp</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="log"></A> <A NAME="ss6.14">6.14 <B>log</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the logarithm of an number
<DT><B> Usage </B><DD><P><CODE>y = log (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>log</CODE> function computes the logarithm of a number and
returns the result as an array. If its argument is an array, the
<CODE>log</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="log10"></A> <A NAME="ss6.15">6.15 <B>log10</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the base-10 logarithm of an number
<DT><B> Usage </B><DD><P><CODE>y = log10 (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>log10</CODE> function computes the base-10 logarithm of a number and
returns the result as an array. If its argument is an array, the
<CODE>log10</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="mul2"></A> <A NAME="ss6.16">6.16 <B>mul2</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Multiply a number by 2
<DT><B> Usage </B><DD><P><CODE>y = mul2(x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>mul2</CODE> function multiplies an arithmetic type by two and
returns the result. If its argument is an array, a new array will
be created whose elements are obtained from the original array by
using the <CODE>mul2</CODE> function.
<DT><B> See Also </B><DD><P><CODE>sqr, abs</CODE>
</DL>
<P>
<P>
<H2><A NAME="polynom"></A> <A NAME="ss6.17">6.17 <B>polynom</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Evaluate a polynomial
<DT><B> Usage </B><DD><P><CODE>Double_Type polynom(Double_Type a, b, ...c, Integer_Type n, Double_Type x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>polynom</CODE> function returns the value of the polynomial expression:
<BLOCKQUOTE><CODE>
<PRE>
ax^n + bx^(n - 1) + ... c
</PRE>
</CODE></BLOCKQUOTE>
<DT><B> Notes </B><DD><P>The <CODE>polynom</CODE> function should be extended to work with complex
and array data types. The current implementation is limited to
<CODE>Double_Type</CODE> quantities.
<DT><B> See Also </B><DD><P><CODE>exp</CODE>
</DL>
<P>
<P>
<H2><A NAME="set_float_format"></A> <A NAME="ss6.18">6.18 <B>set_float_format</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Set the format for printing floating point values.
<DT><B> Usage </B><DD><P><CODE>set_float_format (String_Type fmt)</CODE>
<DT><B> Description </B><DD><P>The <CODE>set_float_format</CODE> function is used to set the floating
point format to be used when floating point numbers are printed.
The routines that use this are the traceback routines and the
<CODE>string</CODE> function. The default value is <CODE>"%f"</CODE>
<DT><B> Example </B><DD><P>
<BLOCKQUOTE><CODE>
<PRE>
s = string (PI); % --> s = "3.14159"
set_float_format ("%16.10f");
s = string (PI); % --> s = "3.1415926536"
set_float_format ("%10.6e");
s = string (PI); % --> s = "3.141593e+00"
</PRE>
</CODE></BLOCKQUOTE>
<DT><B> See Also </B><DD><P><CODE>string, sprintf, double</CODE>
</DL>
<P>
<P>
<H2><A NAME="sign"></A> <A NAME="ss6.19">6.19 <B>sign</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the sign of a number
<DT><B> Usage </B><DD><P><CODE>y = sign(x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>sign</CODE> function returns the sign of an arithmetic type. If
its argument is a complex number (<CODE>Complex_Type</CODE>), it returns
the sign of the imaginary part of the number. If the argument is an
array, a new array will be created whose elements are obtained from
the original array by using the <CODE>sign</CODE> function.
<P>When applied to a real number or an integer, the <CODE>sign</CODE> function
returns <CODE>-1</CODE>, <CODE>0</CODE>, or <CODE>+1</CODE> according to whether the number is
less than zero, equal to zero, or greater than zero, respectively.
<DT><B> See Also </B><DD><P><CODE>abs</CODE>
</DL>
<P>
<P>
<H2><A NAME="sin"></A> <A NAME="ss6.20">6.20 <B>sin</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the sine of an number
<DT><B> Usage </B><DD><P><CODE>y = sin (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>sin</CODE> function computes the sine of a number and
returns the result as an array. If its argument is an array, the
<CODE>sin</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="sinh"></A> <A NAME="ss6.21">6.21 <B>sinh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the hyperbolic sine of an number
<DT><B> Usage </B><DD><P><CODE>y = sinh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>sinh</CODE> function computes the hyperbolic sine of a number and
returns the result as an array. If its argument is an array, the
<CODE>sinh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="sqr"></A> <A NAME="ss6.22">6.22 <B>sqr</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the square of a number
<DT><B> Usage </B><DD><P><CODE>y = sqr(x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>sqr</CODE> function returns the square of an arithmetic type. If its
argument is a complex number (<CODE>Complex_Type</CODE>), then it returns
the square of the modulus. If the argument is an array, a new array
will be created whose elements are obtained from the original array
by using the <CODE>sqr</CODE> function.
<DT><B> See Also </B><DD><P><CODE>abs, mul2</CODE>
</DL>
<P>
<P>
<H2><A NAME="sqrt"></A> <A NAME="ss6.23">6.23 <B>sqrt</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the square root of an number
<DT><B> Usage </B><DD><P><CODE>y = sqrt (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>sqrt</CODE> function computes the square root of a number and
returns the result as an array. If its argument is an array, the
<CODE>sqrt</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>sqr, cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="tan"></A> <A NAME="ss6.24">6.24 <B>tan</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the tangent of an number
<DT><B> Usage </B><DD><P><CODE>y = tan (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>tan</CODE> function computes the tangent of a number and
returns the result as an array. If its argument is an array, the
<CODE>tan</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<H2><A NAME="tanh"></A> <A NAME="ss6.25">6.25 <B>tanh</B></A>
</H2>
<P>
<DL>
<DT><B> Synopsis </B><DD><P>Compute the hyperbolic tangent of an number
<DT><B> Usage </B><DD><P><CODE>y = tanh (x)</CODE>
<DT><B> Description </B><DD><P>The <CODE>tanh</CODE> function computes the hyperbolic tangent of a number and
returns the result as an array. If its argument is an array, the
<CODE>tanh</CODE> function will be applied to each element and the result returned
as an array.
<DT><B> See Also </B><DD><P><CODE>cos, atan, acosh, cosh</CODE>
</DL>
<P>
<P>
<P>
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