# Operators

## Extreme values

Symbol: Supremum $\mathop{\operatorname{sup}}\limits_{P\left(x\right)} f\!\left(x\right)$ Supremum of a set or function
Symbol: Infimum $\mathop{\operatorname{inf}}\limits_{P\left(x\right)} f\!\left(x\right)$ Infimum of a set or function
Symbol: Minimum $\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right)$ Minimum value of a set or function
Symbol: Maximum $\mathop{\max}\limits_{P\left(x\right)} f\!\left(x\right)$ Maximum value of a set or function
Symbol: ArgMin $\mathop{\operatorname{arg\,min}}\limits_{P\left(x\right)} f\!\left(x\right)$ Locations of minimum value
Symbol: ArgMax $\mathop{\operatorname{arg\,max}}\limits_{P\left(x\right)} f\!\left(x\right)$ Locations of maximum value
Symbol: ArgMinUnique $\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right)$ Unique location of minimum value
Symbol: ArgMaxUnique $\mathop{\operatorname{arg\,max*}}\limits_{P\left(x\right)} f\!\left(x\right)$ Unique location of maximum value

## Limits

Symbol: Limit $\lim_{x \to a} f\!\left(x\right)$ Limiting value
Symbol: SequenceLimit $\lim_{n \to a} f\!\left(n\right)$ Limiting value of sequence
Symbol: RealLimit $\lim_{x \to a} f\!\left(x\right)$ Limiting value, real variable
Symbol: LeftLimit $\lim_{x \to {a}^{-}} f\!\left(x\right)$ Limiting value, from the left
Symbol: RightLimit $\lim_{x \to {a}^{+}} f\!\left(x\right)$ Limiting value, from the right
Symbol: ComplexLimit $\lim_{z \to a} f\!\left(z\right)$ Limiting value, complex variable
Symbol: MeromorphicLimit $\lim_{z \to a} f\!\left(z\right)$ Limiting value, allowing poles

## Derivatives

Symbol: Derivative $\frac{d}{d z}\, f\!\left(z\right)$ Derivative
Symbol: RealDerivative $\frac{d}{d x}\, f\!\left(x\right)$ Real derivative
Symbol: ComplexDerivative $\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
Symbol: ComplexBranchDerivative $\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative, allowing branch cuts
Symbol: MeromorphicDerivative $\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative, allowing poles

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC