Difference between revisions of "Predefined Functions and Operators"
From GeoGebra Manual
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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]]. | 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]]. | ||
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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}} | ||
+ | |- | ||
+ | |π | ||
+ | | {{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( ) | |y( ) | ||
|- | |- | ||
− | |Argument | + | |z-coordinate |
− | |arg() | + | |z( ) |
+ | |- | ||
+ | |Argument (also works for 3D points / vectors) | ||
+ | |arg( ) | ||
|- | |- | ||
|Conjugate | |Conjugate | ||
− | |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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|- | |- | ||
|Cotangent | |Cotangent | ||
− | |cot() | + | |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 | + | |Arc tangent (answer in degrees, between -90° and 90°) |
− | | | + | |atand( ) |
|- | |- | ||
− | |Arc | + | |[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in radians, between -π and π)] |
− | | | + | |atan2(y, x) or arcTan2(y, x) |
|- | |- | ||
− | |Arc tangent | + | |[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 secant | |Hyperbolic secant | ||
− | |sech() | + | |sech( ) |
|- | |- | ||
|Hyperbolic cosecant | |Hyperbolic cosecant | ||
− | |cosech() | + | |cosech( ) |
|- | |- | ||
|Hyperbolic cotangent | |Hyperbolic cotangent | ||
− | |coth() | + | |coth( ) or cotanh() |
|- | |- | ||
|Antihyperbolic cosine | |Antihyperbolic cosine | ||
− | |acosh( ) | + | |acosh( ) or arccosh( ) |
|- | |- | ||
|Antihyperbolic sine | |Antihyperbolic sine | ||
− | |asinh( ) | + | |asinh( ) or arcsinh( ) |
|- | |- | ||
|Antihyperbolic tangent | |Antihyperbolic tangent | ||
− | |atanh( ) | + | |atanh( ) or arctanh( ) |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
|[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]] | + | |[[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]] | |[[w:Error_function|Gaussian Error Function]] | ||
|erf(x) | |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 13:46, 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.