Home
Language syntax
Variables and iteration
- For
- ForElement
- Repeat
- Step
- Fun
- Where
- Def
Booleans and logic
- Equal
- NotEqual
- True
- False
- Not
- And
- Or
- Equivalent
- Implies
- Exists
- All
- Cases
- Otherwise
Tuples, lists and sets
- Tuple
- List
- Set
- Item
- Element
- NotElement
- Length
- Cardinality
- Concatenation
- Union
- Intersection
- SetMinus
- Subset
- SubsetEqual
- CartesianProduct
- CartesianPower
- Sets
- PowerSet
- Tuples
- Universe
- Undefined
Numbers and arithmetic
- Sets of numbers
  - ZZ
  - QQ
  - RR
  - CC
  - PP
  - AlgebraicNumbers
- Particular numbers
  - Decimal
  - Pi
  - ConstI
  - ConstE
  - ConstGamma
  - GoldenRatio
  - ConstCatalan
- Arithmetic operations
  - Pos
  - Neg
  - Add
  - Sub
  - Mul
  - Div
  - Pow
  - Sqrt
- Inequalities
  - Less
  - LessEqual
  - Greater
  - GreaterEqual
- Ranges and intervals
- Infinities
  - Infinity
  - UnsignedInfinity
Operators and calculus
- Sums and products
  - Sum
  - Product
  - PrimeSum
  - PrimeProduct
  - DivisorSum
  - DivisorProduct
- Solutions and zeros
- Extreme values
  - Supremum
  - Infimum
  - Minimum
  - Maximum
  - ArgMin
  - ArgMax
  - ArgMinUnique
  - ArgMaxUnique
- Limits
- Derivatives
- Integrals
  - Integral
- Complex analysis
Matrices and linear algebra
- Matrix
- Matrix2x2
- Matrix2x1
- IdentityMatrix
- Det
- Spectrum
- SingularValues
- Matrices
- SL2Z
- SpecialLinearGroup
- GeneralLinearGroup
- HilbertMatrix
Special functions
- Number parts and step functions
  - Abs
  - Sign
  - Re
  - Im
  - Arg
  - Conjugate
  - Csgn
  - RealAbs
  - Max
  - Min
  - Floor
  - Ceil
  - KroneckerDelta
- Primes and divisibility
  - Odd
  - Even
  - CongruentMod
  - Divides
  - GCD
  - LCM
  - XGCD
  - PrimeNumber
  - PrimePi
  - DivisorSigma
  - MoebiusMu
  - Totient
  - DiscreteLog
  - LegendreSymbol
  - JacobiSymbol
  - KroneckerSymbol
  - SquaresR
  - LiouvilleLambda
- Elementary functions
  - Exp
  - Log
  - Sin
  - Cos
  - Tan
  - Cot
  - Sec
  - Csc
  - Sinh
  - Cosh
  - Tanh
  - Coth
  - Sech
  - Csch
  - Asin
  - Acos
  - Atan
  - Acot
  - Asec
  - Acsc
  - Asinh
  - Acosh
  - Atanh
  - Acoth
  - Asech
  - Acsch
  - Atan2
  - Sinc
  - LambertW
  - LambertWPuiseuxCoefficient
- Combinatorial functions
- Gamma and factorials
- Orthogonal polynomials
- Exponential integrals
- Bessel and Airy functions
  - AiryAi
  - AiryBi
  - AiryAiZero
  - AiryBiZero
  - BesselJ
  - BesselI
  - BesselY
  - BesselK
  - HankelH1
  - HankelH2
  - BesselJZero
  - BesselYZero
  - CoulombF
  - CoulombG
  - CoulombH
  - CoulombC
  - CoulombSigma
- Hypergeometric functions
- Zeta and L-functions
- Elliptic integrals
- Elliptic, theta and modular functions
Polynomials, series and rings
- Pol
- Ser
- PolX
- SerX
- Coefficient
- PolynomialDegree
- Polynomials
- PolynomialFractions
- FormalPowerSeries
- FormalLaurentSeries
- FormalPuiseuxSeries
- Zero
- One
- Characteristic
- Rings
- CommutativeRings
- Fields
- QuotientRing

GoldenRatio

Input: GoldenRatio

\varphi

The golden ratio (1.618...).

Numerical evaluation examples

Input: GoldenRatio

\varphi

Output: RealBall(Decimal("1.6180339887498948482"), Decimal("4.59e-21")) (evaluated by pygrim in 0.0001 s)

\left[1.6180339887498948482 \pm 4.59 \cdot 10^{-21}\right]

Last updated: 2020-03-06 00:22:16