# 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