Difference between revisions of "Predefined Functions and Operators"
From GeoGebra Manual
m (Text replace - "<div class="box info"> 48px|left This page is part of the official manual for print and pdf. For structural reasons normal users can't edit this page. If you found any errors on this page please contact ) |
(log₂() ,log₁₀( )) |
||
(18 intermediate revisions by 4 users not shown) | |||
Line 1: | Line 1: | ||
− | <noinclude>{{Manual Page|version= | + | <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. 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]]. | ||
Line 20: | Line 20: | ||
|- | |- | ||
|° ([[w:Degree symbol|Degree symbol]]) | |° ([[w:Degree symbol|Degree symbol]]) | ||
− | | {{KeyCode|Alt+o}} | + | | {{KeyCode|Alt+o}} or deg |
|- | |- | ||
|Addition | |Addition | ||
Line 34: | Line 34: | ||
|* or Space key | |* or Space key | ||
|- | |- | ||
− | |Vector product | + | |Vector product(see [[Points and Vectors#Vector Product|Points and Vectors]]) |
|⊗ | |⊗ | ||
|- | |- | ||
Line 55: | Line 55: | ||
|y( ) | |y( ) | ||
|- | |- | ||
− | |Argument | + | |z-coordinate |
+ | |z( ) | ||
+ | |- | ||
+ | |Argument (also works for 3D points / vectors) | ||
|arg( ) | |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( ) or sign() | |sgn( ) or sign() | ||
+ | |- | ||
+ | |Greatest integer less than or equal | ||
+ | |floor( ) | ||
+ | |- | ||
+ | |Least integer greater than or equal | ||
+ | |ceil( ) | ||
+ | |- | ||
+ | |Round | ||
+ | |round(x) or round(x, y) | ||
|- | |- | ||
|Square root | |Square root | ||
Line 72: | Line 93: | ||
|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 | ||
Line 80: | Line 104: | ||
|- | |- | ||
|Logarithm (natural, to base e) | |Logarithm (natural, to base e) | ||
− | |ln | + | |ln( ) |
|- | |- | ||
|Logarithm to base 2 | |Logarithm to base 2 | ||
− | |ld( ) | + | |log₂() or ld( ) |
|- | |- | ||
|Logarithm to base 10 | |Logarithm to base 10 | ||
− | |lg( ) | + | |log₁₀( ) or log( ) or lg( ) |
|- | |- | ||
|Logarithm of ''x'' to base ''b'' | |Logarithm of ''x'' to base ''b'' | ||
Line 104: | Line 128: | ||
|- | |- | ||
|Cosecant | |Cosecant | ||
− | |cosec() | + | |csc() or cosec() |
|- | |- | ||
|Cotangent | |Cotangent | ||
− | |cot() | + | |cot() or cotan() |
|- | |- | ||
− | |Arc cosine | + | |Arc cosine (answer in radians) |
|acos( ) or arccos( ) | |acos( ) or arccos( ) | ||
|- | |- | ||
− | |Arc sine | + | |Arc cosine (answer in degrees) |
+ | |acosd( ) | ||
+ | |- | ||
+ | |Arc sine (answer in radians) | ||
|asin( ) or arcsin( ) | |asin( ) or arcsin( ) | ||
|- | |- | ||
− | |Arc tangent ( | + | |Arc sine (answer in degrees) |
+ | |asind( ) | ||
+ | |- | ||
+ | |Arc tangent (answer in radians, between -π/2 and π/2) | ||
|atan( ) or arctan( ) | |atan( ) or arctan( ) | ||
|- | |- | ||
− | |[http://en.wikipedia.org/wiki/Atan2 Arc tangent ( | + | |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) | |atan2(y, x) | ||
+ | |- | ||
+ | |[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in degrees, between -180° and 180°)] | ||
+ | |atan2d(y, x) | ||
|- | |- | ||
|Hyperbolic cosine | |Hyperbolic cosine | ||
Line 134: | Line 170: | ||
|- | |- | ||
|Hyperbolic cosecant | |Hyperbolic cosecant | ||
− | | | + | |csch( ) |
|- | |- | ||
|Hyperbolic cotangent | |Hyperbolic cotangent | ||
− | |coth( ) | + | |coth( ) or cotanh() |
|- | |- | ||
|Antihyperbolic cosine | |Antihyperbolic cosine | ||
Line 147: | Line 183: | ||
|Antihyperbolic tangent | |Antihyperbolic tangent | ||
|atanh( ) or arctanh( ) | |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) | ||
Line 177: | Line 204: | ||
|[[w:Error_function|Gaussian Error Function]] | |[[w:Error_function|Gaussian Error Function]] | ||
|erf(x) | |erf(x) | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|- | |- | ||
| [[w:Digamma_function|Digamma function]] | | [[w:Digamma_function|Digamma function]] | ||
Line 198: | Line 219: | ||
| The [http://mathworld.wolfram.com/ExponentialIntegral.html Exponential Integral] function | | The [http://mathworld.wolfram.com/ExponentialIntegral.html Exponential Integral] function | ||
| expIntegral(x) | | 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 11:17, 9 September 2020
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(x) or round(x, y) |
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( ) |
Logarithm to base 2 | log₂() or ld( ) |
Logarithm to base 10 | log₁₀( ) or log( ) or lg( ) |
Logarithm of x to base b | log(b, x ) |
Cosine | cos( ) |
Sine | sin( ) |
Tangent | tan( ) |
Secant | sec() |
Cosecant | csc() or 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) |
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 | csch( ) |
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.