Difference between revisions of "Predefined Functions and Operators"

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(Lambert's W function)
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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>
To create numbers, coordinates, or equations using the [[Input Bar]] you may also use the following pre-defined functions and operations.
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To create numbers, coordinates, or equations using the [[Input Bar]] you may also use the following pre-defined functions and operations. Logic operators and functions are listed in article about [[Boolean values]].
  
{{Note|The pre-defined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.}}
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{{Note|The predefined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.}}
  
 
   
 
   
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!Operation / Function
 
!Operation / Function
 
!Input
 
!Input
 +
|-
 +
|ℯ ([[w:E_(mathematical_constant)|Euler's number]])
 +
| {{KeyCode|Alt+e}}
 +
|-
 +
|ί ([[w:Imaginary unit|Imaginary unit]])
 +
| {{KeyCode|Alt+i}}
 +
|-
 +
 +
| {{KeyCode|Alt+p}} or pi
 +
|-
 +
|° ([[w:Degree symbol|Degree symbol]])
 +
| {{KeyCode|Alt+o}} or deg
 
|-
 
|-
 
|Addition
 
|Addition
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|* or Space key
 
|* or Space key
 
|-
 
|-
|Vector product
+
|Vector product(see [[Points and Vectors#Vector Product|Points and Vectors]])
|⊗
+
|⊗  
 
|-
 
|-
 
|Division
 
|Division
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|y-coordinate
 
|y-coordinate
 
|y( )
 
|y( )
 +
|-
 +
|z-coordinate
 +
|z( )
 +
|-
 +
|Argument (also works for 3D points / vectors)
 +
|arg( )
 +
|-
 +
|Conjugate
 +
|conjugate( )
 +
|-
 +
|[[Real_Function|Real]]
 +
|real( )
 +
|-
 +
|[[Imaginary_Function|Imaginary]]
 +
|imaginary( )
 
|-
 
|-
 
|Absolute value
 
|Absolute value
 
|abs( )
 
|abs( )
 +
|-
 +
|Altitude angle (for 3D points / vectors)
 +
|alt( )
 
|-
 
|-
 
|Sign
 
|Sign
|sgn( )
+
|sgn( ) or sign()
 +
|-
 +
|Greatest integer less than or equal
 +
|floor( )
 +
|-
 +
|Least integer greater than or equal
 +
|ceil( )
 +
|-
 +
|Round
 +
|round( )
 
|-
 
|-
 
|Square root
 
|Square root
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|Cubic root
 
|Cubic root
 
|cbrt( )
 
|cbrt( )
 +
|-
 +
| The nth root of x
 +
| nroot(x, n)
 
|-
 
|-
 
|Random number between 0 and 1
 
|Random number between 0 and 1
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|Logarithm to base 10
 
|Logarithm to base 10
 
|lg( )
 
|lg( )
 +
|-
 +
|Logarithm of ''x'' to base ''b''
 +
|log(b, x )
 
|-
 
|-
 
|Cosine
 
|Cosine
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|tan( )
 
|tan( )
 
|-
 
|-
|Arc cosine
+
|Secant
|acos( )
+
|sec()
 +
|-
 +
|Cosecant
 +
|cosec()
 +
|-
 +
|Cotangent
 +
|cot() or cotan()
 
|-
 
|-
|Arc sine
+
|Arc cosine (answer in radians)
|asin( )
+
|acos( ) or arccos( )
 
|-
 
|-
|Arc tangent
+
|Arc cosine (answer in degrees)
|atan( )
+
|acosd( )
 +
|-
 +
|Arc sine (answer in radians)
 +
|asin( ) or arcsin( )
 +
|-
 +
|Arc sine (answer in degrees)
 +
|asind( )
 +
|-
 +
|Arc tangent (answer in radians, between -π/2 and π/2)
 +
|atan( ) or arctan( )
 +
|-
 +
|Arc tangent (answer in degrees, between -90° and 90°)
 +
|atand( )
 +
|-
 +
|[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in radians, between -π and π)]
 +
|atan2(y, x) or arcTan2(y, x)
 +
|-
 +
|[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in degrees, between -180° and 180°)]
 +
|atan2d(y, x)
 
|-
 
|-
 
|Hyperbolic cosine
 
|Hyperbolic cosine
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|Hyperbolic tangent
 
|Hyperbolic tangent
 
|tanh( )
 
|tanh( )
 +
|-
 +
|Hyperbolic secant
 +
|sech( )
 +
|-
 +
|Hyperbolic cosecant
 +
|cosech( )
 +
|-
 +
|Hyperbolic cotangent
 +
|coth( ) or cotanh()
 
|-
 
|-
 
|Antihyperbolic cosine
 
|Antihyperbolic cosine
|acosh( )
+
|acosh( ) or arccosh( )
 
|-
 
|-
 
|Antihyperbolic sine
 
|Antihyperbolic sine
|asinh( )
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|asinh( ) or arcsinh( )
 
|-
 
|-
 
|Antihyperbolic tangent
 
|Antihyperbolic tangent
|atanh( )
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|atanh( ) or arctanh( )
|-
 
|Greatest integer less than or equal
 
|floor( )
 
|-
 
|Least integer greater than or equal
 
|ceil( )
 
|-
 
|Round
 
|round( )
 
 
|-
 
|-
 
|[http://mathworld.wolfram.com/BetaFunction.html Beta function] Β(a, b)
 
|[http://mathworld.wolfram.com/BetaFunction.html Beta function] Β(a, b)
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|betaRegularized(a, b, x)
 
|betaRegularized(a, b, x)
 
|-
 
|-
|[[w:Gamma function|Gamma function]]
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|[[w:Gamma function|Gamma function Γ(x)]]
 
|gamma( x)
 
|gamma( x)
 
|-
 
|-
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|gamma(a, x)
 
|gamma(a, x)
 
|-
 
|-
|(Lower)  [http://mathworld.wolfram.com/RegularizedGammaFunction.html incomplete regularized gamma function]  
+
|(Lower)  [http://mathworld.wolfram.com/RegularizedGammaFunction.html incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) ]  
 
|gammaRegularized(a, x)
 
|gammaRegularized(a, x)
 +
|-
 +
|[[w:Error_function|Gaussian Error Function]]
 +
|erf(x)
 +
|-
 +
| [[w:Digamma_function|Digamma function]]
 +
| psi(x)
 +
|-
 +
| The [http://en.wikipedia.org/wiki/Polygamma_function Polygamma function] is the (m+1)th derivative of the natural logarithm of the [http://en.wikipedia.org/wiki/Gamma_function Gamma function, gamma(x)] (m=0,1)
 +
| polygamma(m, x)
 +
|-
 +
| The [http://mathworld.wolfram.com/SineIntegral.html Sine Integral] function
 +
| sinIntegral(x)
 +
|-
 +
| The [http://mathworld.wolfram.com/CosineIntegral.html Cosine Integral] function
 +
| cosIntegral(x)
 +
|-
 +
| The [http://mathworld.wolfram.com/ExponentialIntegral.html Exponential Integral] function
 +
| expIntegral(x)
 +
|-
 +
| The [http://en.wikipedia.org/wiki/Riemann_zeta_function Riemann-Zeta] function ζ(x)
 +
| zeta(x)
 +
|-
 +
| [https://en.wikipedia.org/wiki/Lambert_W_function Lambert's W function] LambertW(x, branch)
 +
| LambertW(x, 0), LambertW(x, -1)
 
|}
 
|}
 +
{{note|The x, y, z operators can be used to get corresponding coefficients of a line.}}

Revision as of 12:46, 14 January 2019


To create numbers, coordinates, or equations using the Input Bar you may also use the following pre-defined functions and operations. Logic operators and functions are listed in article about Boolean values.

Note: The predefined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.


Operation / Function Input
ℯ (Euler's number) Alt + e
ί (Imaginary unit) Alt + i
π Alt + p or pi
° (Degree symbol) Alt + o or deg
Addition +
Subtraction -
Multiplication * or Space key
Scalar product * or Space key
Vector product(see Points and Vectors)
Division /
Exponentiation ^ or superscript (x^2 or x2)
Factorial !
Parentheses ( )
x-coordinate x( )
y-coordinate y( )
z-coordinate z( )
Argument (also works for 3D points / vectors) arg( )
Conjugate conjugate( )
Real real( )
Imaginary imaginary( )
Absolute value abs( )
Altitude angle (for 3D points / vectors) alt( )
Sign sgn( ) or sign()
Greatest integer less than or equal floor( )
Least integer greater than or equal ceil( )
Round round( )
Square root sqrt( )
Cubic root cbrt( )
The nth root of x nroot(x, n)
Random number between 0 and 1 random( )
Exponential function exp( ) or ℯx
Logarithm (natural, to base e) ln( ) or log( )
Logarithm to base 2 ld( )
Logarithm to base 10 lg( )
Logarithm of x to base b log(b, x )
Cosine cos( )
Sine sin( )
Tangent tan( )
Secant sec()
Cosecant cosec()
Cotangent cot() or cotan()
Arc cosine (answer in radians) acos( ) or arccos( )
Arc cosine (answer in degrees) acosd( )
Arc sine (answer in radians) asin( ) or arcsin( )
Arc sine (answer in degrees) asind( )
Arc tangent (answer in radians, between -π/2 and π/2) atan( ) or arctan( )
Arc tangent (answer in degrees, between -90° and 90°) atand( )
Arc tangent (answer in radians, between -π and π) atan2(y, x) or arcTan2(y, x)
Arc tangent (answer in degrees, between -180° and 180°) atan2d(y, x)
Hyperbolic cosine cosh( )
Hyperbolic sine sinh( )
Hyperbolic tangent tanh( )
Hyperbolic secant sech( )
Hyperbolic cosecant cosech( )
Hyperbolic cotangent coth( ) or cotanh()
Antihyperbolic cosine acosh( ) or arccosh( )
Antihyperbolic sine asinh( ) or arcsinh( )
Antihyperbolic tangent atanh( ) or arctanh( )
Beta function Β(a, b) beta(a, b)
Incomplete beta function Β(x;a, b) beta(a, b, x)
Incomplete regularized beta function I(x; a, b) betaRegularized(a, b, x)
Gamma function Γ(x) gamma( x)
(Lower) incomplete gamma function γ(a, x) gamma(a, x)
(Lower) incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) gammaRegularized(a, x)
Gaussian Error Function erf(x)
Digamma function psi(x)
The Polygamma function is the (m+1)th derivative of the natural logarithm of the Gamma function, gamma(x) (m=0,1) polygamma(m, x)
The Sine Integral function sinIntegral(x)
The Cosine Integral function cosIntegral(x)
The Exponential Integral function expIntegral(x)
The Riemann-Zeta function ζ(x) zeta(x)
Lambert's W function LambertW(x, branch) LambertW(x, 0), LambertW(x, -1)
Note: The x, y, z operators can be used to get corresponding coefficients of a line.
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