Arithmetic

Constants

Symbol Value
ThreeQuarter \[ \frac{3}{4} \]
TwoThird \[ \frac{2}{3} \]
Half \[ \frac{1}{2} \]
Third \[ \frac{1}{3} \]
Quarter \[ \frac{1}{4} \]
ExponentialE \(2.7182818284\ldots\) Euler’s number
ImaginaryUnit \( \imaginaryI \) The imaginary unit, solution of \(x^2+1=0\)
MachineEpsilon \[ 2^{−52}\] The difference between 1 and the next larger floating point number.
See Machine Epsilon on Wikipedia
CatalanConstant \[ = 0.9159655941\ldots \] \[ \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2n+1)^2} \]
See Catalan’s Constant on Wikipedia
GoldenRatio \[ = 1.6180339887\ldots\] \[ \frac{1+\sqrt{5}}{2} \] See Golden Ratio on Wikipedia
EulerGamma \[ = 0.5772156649\ldots \] See Euler-Mascheroni Constant on Wikipedia

Functions

Function Operation
Add \( a + b\) Addition
Subtract \( a - b\) Subtraction
Negate \(-a\) Additive inverse
Multiply \( a\times b \) Multiplication
Power \( a^b \) Exponentiation
Root \(\sqrt[n]{x}=x^{\frac1n}\) n-th root
Sqrt \(\sqrt{x}=x^{\frac12}\) Square root
Square \(x^2\)

Function Operation
Exp \(\exponentialE^{x}\) Exponential function
Log \(\ln(x)\) Logarithm function, the inverse of Exp
Log2 \(\ln_2(x)\) Binary logarithm function, the base-2 logarithm
Log10 \(\ln_{10}(x)\) Common logarithm, the base-10 logarithm
LogOnePlus

Function Operation
Abs \(|x| \) Absolute value, magnitude
Chop Replace real numbers that are very close to 0 (less than \(10^{-10}\)) with 0
Ceil Rounds a number up to the next largest integer
Floor Round a number to the greatest integer less than the input value.
Round