Difference between revisions of "Math Module"

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|Returns the value of the mathematical constant π.
+
|Returns the <code>xs:double</code> value of the mathematical constant π whose lexical representation is 3.141592653589793.<br />
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| valign='top' | '''Rules'''
 
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|This function returns the <code>xs:double</code> value whose lexical representation is 3.141592653589793.<br />
 
 
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| valign='top' | '''Examples'''
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
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|Returns the value of the mathematical constant <i>e</i>.
+
|Returns the <code>xs:double</code> value of the mathematical constant <i>e</i> whose lexical representation is 2.718281828459045.<br />
−
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| valign='top' | '''Rules'''
 
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|This function returns the <code>xs:double</code> value whose lexical representation is 2.718281828459045.<br />
 
 
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| valign='top' | '''Examples'''
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
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|Returns the square root of the argument.
+
|Returns the square root of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>.<br />
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| valign='top' | '''Rules'''
 
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|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the <code>xs:double</code> value of the mathematical square root of <code>$arg</code>.<br />
 
 
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|-
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
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|Returns the sine of the argument, expressed in radians.
+
|Returns the sine of the <code>$arg</code>, expressed in radians.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians.<br />
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| valign='top' | '''Rules'''
 
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|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the sine of <code>$arg</code>, treated as an angle in radians.<br />
 
 
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|-
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
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|Returns the cosine of the argument, expressed in radians.
+
|Returns the cosine of <code>$arg</code>, expressed in radians.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians.<br />
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|-
 
−
| valign='top' | '''Rules'''
 
−
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the cosine of <code>$arg</code>, treated as an angle in radians.<br />
 
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
−
|Returns the tangent of the argument, expressed in radians.
+
|Returns the tangent of <code>$arg</code>, expressed in radians.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians.<br />
−
|-
 
−
| valign='top' | '''Rules'''
 
−
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the tangent of <code>$arg</code>, treated as an angle in radians.<br />
 
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
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|Returns the arc sine of the argument.
+
|Returns the arc sine of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />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.<br />
−
|-
 
−
| valign='top' | '''Rules'''
 
−
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the arc sine of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.<br />
 
 
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|-
 
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| valign='top' | '''Summary'''
 
| valign='top' | '''Summary'''
−
|Returns the arc cosine of the argument.
+
|Returns the arc cosine of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π.<br />
−
|-
 
−
| valign='top' | '''Rules'''
 
−
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the arc cosine of <code>$arg</code>, returned as an angle in radians in the range 0 to +π.<br />
 
 
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| valign='top' | '''Summary'''
 
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|Returns the arc tangent of the argument.
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|Returns the arc tangent of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />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.<br />
−
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−
| valign='top' | '''Rules'''
 
−
|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the arc tangent of <code>$arg</code>, returned as an angle in radians in the range -π/2 to +π/2.<br />
 
 
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|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 <code>$arg1</code> divided by <code>$arg2</code>, the result being in the range -π/2 to +π/2 radians.<br/>If <code>$arg1</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π.<br />
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| valign='top' | '''Rules'''
 
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|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the arc tangent of <code>$arg1</code> divided by <code>$arg2</code>, returned as an angle in radians in the range -π to +π.<br />
 
 
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|Returns the first argument raised to the power of the second argument.
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|Returns <code>$arg1</code> raised to the power of <code>$arg2</code>.<br/>If <code>$arg1</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>.<br />
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|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the <code>$arg1</code> raised to the power of <code>$arg2</code>.<br />
 
 
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|Returns <i>e</i> raised to the power of the argument.
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|Returns <i>e</i> raised to the power of <code>$arg</code>. If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>.<br />
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|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the value of <i>e</i> raised to the power of <code>$arg</code>.<br />
 
 
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|Returns the natural logarithm of the argument.
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|Returns the natural logarithm of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>.<br />
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| valign='top' | '''Rules'''
 
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|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the natural logarithm (base <i>e</i>) of <code>$arg</code>.<br />
 
 
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|Returns the base 10 logarithm of the argument.
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|Returns the base 10 logarithm of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the base 10 logarithm of <code>$arg</code>.<br />
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|If <code>$arg1</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the base 10 logarithm of <code>$arg</code>.<br />
 
 
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|Returns a random value.
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|Returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>.<br />
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|This function returns a random <code>xs:double</code> value between <code>0.0</code> and <code>1.0</code>.<br />
 
 
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|Returns the hyperbolic sine of the argument.
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|Returns the hyperbolic sine of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic sine of <code>$arg</code>.<br />
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| valign='top' | '''Rules'''
 
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|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the hyperbolic sine of <code>$arg</code>.<br />
 
 
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|Returns the hyperbolic cosine of the argument.
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|Returns the hyperbolic cosine of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic cosine of <code>$arg</code>.<br />
−
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| valign='top' | '''Rules'''
 
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|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the hyperbolic cosine of <code>$arg</code>.<br />
 
 
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|Returns the hyperbolic tangent of the argument.
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|Returns the hyperbolic tangent of <code>$arg</code>.<br/>If <code>$arg</code> is the empty sequence, the empty sequence is returned.<br />Otherwise the result is the hyperbolic tangent of <code>$arg</code>.<br />
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|If <code>$arg</code> is the empty sequence, the function returns the empty sequence.<br />Otherwise the result is the hyperbolic tangent of <code>$arg</code>.<br />
 
 
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Revision as of 20:51, 22 April 2011

The math module defines XQuery Functions to perform mathematical operations, such as pi, asin and acos. All functions are preceded by the math: prefix, which is linked to the http://www.w3.org/2005/xpath-functions/math namespace. Some of the functions have also been specified in the Functions and Operators Specification of the upcoming XQuery 3.0 Recommendation.

math:pi

Signatures math:pi() as xs:double
Summary Returns the xs:double value of the mathematical constant π 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 xs:double value of the mathematical constant e 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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg, expressed in radians.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg1 divided by $arg2, the result being in the range -π/2 to +π/2 radians.
If $arg1 is the empty sequence, the empty sequence is returned.
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 $arg1 raised to the power of $arg2.
If $arg1 is the empty sequence, the empty sequence is returned.
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 $arg. If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
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 $arg.
If $arg is the empty sequence, the empty sequence is returned.
Otherwise the result is the hyperbolic tangent of $arg.
Examples The expression math:tanh(100) returns 1.
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