Difference between revisions of "Math Module"

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m (wikified... phew!)
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==math:pi==  
 
==math:pi==  
 
{|  
 
{|  
  | '''Signatures'''
+
  | width="90" | <b>Signatures</b>
  | <code> '''math:pi'''() as xs:double</code>   
+
  | <code> <b>math:pi'''() as xs:double</code>   
 
  |-
 
  |-
  | '''Summary'''
+
  | <b>Summary</b>
 
  |Returns the value of the mathematical constant π.
 
  |Returns the value of the mathematical constant π.
 
  |-
 
  |-
  | '''Rules'''
+
  | <b>Rules</b>
 
  |This function returns the <code>xs:double</code> value whose lexical representation is 3.141592653589793.  
 
  |This function returns the <code>xs:double</code> value whose lexical representation is 3.141592653589793.  
 
  |-
 
  |-
  | '''Examples'''
+
  | <b>Examples</b>
 
  |The expression <code>2*math:pi()</code> returns <code>6.283185307179586e0</code>.The expression <code>60 * (math:pi() div 180)</code> converts an angle of 60 degrees to radians.  
 
  |The expression <code>2*math:pi()</code> returns <code>6.283185307179586e0</code>.The expression <code>60 * (math:pi() div 180)</code> converts an angle of 60 degrees to radians.  
 
|}
 
|}
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==math:e==  
 
==math:e==  
 
{|  
 
{|  
| '''Signatures'''
+
| width="90" | <b>Signatures</b>
| <code> '''math:e'''() as xs:double</code>  
+
| <code> <b>math:e'''() as xs:double</code>  
 
|-
 
|-
| '''Summary'''
+
| <b>Summary</b>
 
|Returns the value of the mathematical constant <i>e</i>.
 
|Returns the value of the mathematical constant <i>e</i>.
 
|-
 
|-
| '''Rules'''
+
| <b>Rules</b>
 
|This function returns the <code>xs:double</code> value whose lexical representation is 2.718281828459045.  
 
|This function returns the <code>xs:double</code> value whose lexical representation is 2.718281828459045.  
 
|-
 
|-
| '''Examples'''
+
| <b>Examples</b>
 
|The expression <code>5*math:e()</code> returns <code>13.591409142295225</code>.  
 
|The expression <code>5*math:e()</code> returns <code>13.591409142295225</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:sqrt'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:sqrt'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the square root of the argument.
 
|Returns the square root of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:sin'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:sin'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the sine of the argument, expressed in radians.
 
|Returns the sine of the argument, expressed in radians.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:cos'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:cos'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the cosine of the argument, expressed in radians.
 
|Returns the cosine of the argument, expressed in radians.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:tan'''($ as xs:double?) as xs:double?</code>  
+
| <code> <b>math:tan'''($ as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the tangent of the argument, expressed in radians.
 
|Returns the tangent of the argument, expressed in radians.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:asin'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:asin'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the arc sine of the argument.
 
|Returns the arc sine of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:acos'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:acos'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the arc cosine of the argument.
 
|Returns the arc cosine of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:atan'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:atan'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the arc tangent of the argument.
 
|Returns the arc tangent of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:atan2'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code>  
+
| <code> <b>math:atan2'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians.
 
|Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π.  
 
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:pow'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code>  
+
| <code> <b>math:pow'''($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the first argument raised to the power of the second argument.
 
|Returns the first argument raised to the power of the second argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>.  
 
|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:pow(2, 3)</code> returns <code>8</code>.  
 
|The expression <code>math:pow(2, 3)</code> returns <code>8</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:exp'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:exp'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns <i>e</i> raised to the power of the argument.
 
|Returns <i>e</i> raised to the power of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:exp(1)</code> returns <i>e</i>.  
 
|The expression <code>math:exp(1)</code> returns <i>e</i>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:log'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:log'''($arg as xs:double?) as xs:double?</code>  
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the natural logarithm of the argument.
 
|Returns the natural logarithm of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:log(math:e())</code> returns <code>1</code>.  
 
|The expression <code>math:log(math:e())</code> returns <code>1</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:log10'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:log10'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the base 10 logarithm of the argument.
 
|Returns the base 10 logarithm of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:log(100)</code> returns <code>2</code>.  
 
|The expression <code>math:log(100)</code> returns <code>2</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:random'''() as xs:double?</code>  
+
| <code> <b>math:random'''() as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns a random value.
 
|Returns a random value.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|This function returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>.  
 
|This function returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:sinh'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:sinh'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the hyperbolic sine of the argument.
 
|Returns the hyperbolic sine of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:sinh(0)</code> returns <code>0</code>.  
 
|The expression <code>math:sinh(0)</code> returns <code>0</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
| <code> '''math:cosh'''($arg as xs:double?) as xs:double?</code>  
+
| <code> <b>math:cosh'''($arg as xs:double?) as xs:double?</code>  
 
        
 
        
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the hyperbolic cosine of the argument.
 
|Returns the hyperbolic cosine of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:cosh(0)</code> returns <code>1</code>.  
 
|The expression <code>math:cosh(0)</code> returns <code>1</code>.  
 
|}  
 
|}  
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{|  
 
{|  
 
   |-
 
   |-
|'''Signatures'''
+
|width="90" | <b>Signatures</b>
|      <code> '''math:tanh'''($arg as xs:double?) as xs:double?</code>  
+
|      <code> <b>math:tanh'''($arg as xs:double?) as xs:double?</code>  
 
|-
 
|-
|'''Summary'''
+
|<b>Summary</b>
 
|Returns the hyperbolic tangent of the argument.
 
|Returns the hyperbolic tangent of the argument.
 
|-
 
|-
|'''Rules'''
+
|<b>Rules</b>
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of <code>$arg</code>.  
 
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of <code>$arg</code>.  
 
|-
 
|-
|'''Examples'''
+
|<b>Examples</b>
 
|The expression <code>math:tanh(100)</code> returns <code>1</code>.  
 
|The expression <code>math:tanh(100)</code> returns <code>1</code>.  
 
|}  
 
|}  
 
 
 
[[Category:XQuery]]
 
[[Category:XQuery]]

Revision as of 16:25, 12 December 2010

Math Module

The math module defines extension functions to perform mathematical operations, such as pi, asin and acos. All functions are preceded by the math: prefix. Some of the functions have also been specified in the Functions and Operators Specification of the upcoming XQuery 1.1 Recommendation.

math:pi

Signatures math:pi() as xs:double
Summary Returns the value of the mathematical constant π.
Rules This function returns the xs:double value whose lexical representation is 3.141592653589793.
Examples The expression 2*math:pi() returns 6.283185307179586e0.The expression 60 * (math:pi() div 180) converts an angle of 60 degrees to radians.

math:e

Signatures math:e() as xs:double
Summary Returns the value of the mathematical constant e.
Rules This function returns the xs:double value whose lexical representation is 2.718281828459045.
Examples The expression 5*math:e() returns 13.591409142295225.

math:sqrt

Signatures math:sqrt($arg as xs:double?) as xs:double?
Summary Returns the square root of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the xs:double value of the mathematical square root of $arg.

math:sin

Signatures math:sin($arg as xs:double?) as xs:double?
Summary Returns the sine of the argument, expressed in radians.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the sine of $arg, treated as an angle in radians.

math:cos

Signatures math:cos($arg as xs:double?) as xs:double?
Summary Returns the cosine of the argument, expressed in radians.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the cosine of $arg, treated as an angle in radians.

math:tan

Signatures math:tan($ as xs:double?) as xs:double?
Summary Returns the tangent of the argument, expressed in radians.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the tangent of $arg, treated as an angle in radians.

math:asin

Signatures math:asin($arg as xs:double?) as xs:double?
Summary Returns the arc sine of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc sine of $arg, returned as an angle in radians in the range -π/2 to +π/2.

math:acos

Signatures math:acos($arg as xs:double?) as xs:double?
Summary Returns the arc cosine of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc cosine of $arg, returned as an angle in radians in the range 0 to +π.

math:atan

Signatures math:atan($arg as xs:double?) as xs:double?
Summary Returns the arc tangent of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of $arg, returned as an angle in radians in the range -π/2 to +π/2.

math:atan2

Signatures math:atan2($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?
Summary Returns the arc tangent of the first argument divided by the second argument, the result being in the range -π/2 to +π/2 radians.
Rules If $arg1 is the empty sequence, the function returns the empty sequence.Otherwise the result is the arc tangent of $arg1 divided by $arg2, returned as an angle in radians in the range -π to +π.

math:pow

Signatures math:pow($arg1 as xs:double?, $arg2 as xs:double?) as xs:double?
Summary Returns the first argument raised to the power of the second argument.
Rules If $arg1 is the empty sequence, the function returns the empty sequence.Otherwise the result is the $arg1 raised to the power of $arg2.
Examples The expression math:pow(2, 3) returns 8.

math:exp

Signatures math:exp($arg as xs:double?) as xs:double?
Summary Returns e raised to the power of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the value of e raised to the power of $arg.
Examples The expression math:exp(1) returns e.

math:log

Signatures math:log($arg as xs:double?) as xs:double?
Summary Returns the natural logarithm of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the natural logarithm (base e) of $arg.
Examples The expression math:log(math:e()) returns 1.

math:log10

Signatures math:log10($arg as xs:double?) as xs:double?
Summary Returns the base 10 logarithm of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the base 10 logarithm of $arg.
Examples The expression math:log(100) returns 2.

math:random

Signatures math:random() as xs:double?
Summary Returns a random value.
Rules This function returns a random xs:double value between 0.0 and 1.0.

math:sinh

Signatures math:sinh($arg as xs:double?) as xs:double?
Summary Returns the hyperbolic sine of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic sine of $arg.
Examples The expression math:sinh(0) returns 0.

math:cosh

Signatures math:cosh($arg as xs:double?) as xs:double?
Summary Returns the hyperbolic cosine of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic cosine of $arg.
Examples The expression math:cosh(0) returns 1.

math:tanh

Signatures math:tanh($arg as xs:double?) as xs:double?
Summary Returns the hyperbolic tangent of the argument.
Rules If $arg is the empty sequence, the function returns the empty sequence.Otherwise the result is the hyperbolic tangent of $arg.
Examples The expression math:tanh(100) returns 1.