# Fungrim entry: 4d0e14

Symbol: Path $a \rightsquigarrow b \rightsquigarrow c$ Line path
This object represents the path formed by connecting the given points or paths by line segments. A path is a formal object, semantically different from a set of points: for a path object, the direction is significant, and it is undefined whether a path segment corresponds to an open interval or a closed interval between the points. The typical application is to represent a path of integration.
Path(1, -1) $1 \rightsquigarrow -1$ Represents the path going left from 1 to -1.
Path(a, Path(b, c)) $a \rightsquigarrow b \rightsquigarrow c$ Equivalent to Path(a, b, c).
Path(1, ConstI, -1, Neg(ConstI), 1) $1 \rightsquigarrow i \rightsquigarrow -1 \rightsquigarrow -i \rightsquigarrow 1$ Represents a diamond-shaped loop around the origin in the counterclockwise direction.
Path(Neg(Mul(ConstI, Infinity)), Mul(ConstI, Infinity)) $-i \infty \rightsquigarrow i \infty$ Represents the imaginary axis traversed upwards.
Path(1, Mul(Exp(Div(Mul(Pi, ConstI), 4)), Infinity)) $1 \rightsquigarrow {e}^{\pi i / 4} \infty$ Represents the ray from 1 to infinity along a 45 degree angle.
Path(Tuple(2, 1), Tuple(0, 0)) $\left(2, 1\right) \rightsquigarrow \left(0, 0\right)$ Represents the line segment from (2, 1) to the origin in ${\mathbb{R}}^{2}$.
Definitions:
Fungrim symbol Notation Short description
Path$a \rightsquigarrow b \rightsquigarrow c$ Line path
ConstI$i$ Imaginary unit
Infinity$\infty$ Positive infinity
Exp${e}^{z}$ Exponential function
Pi$\pi$ The constant pi (3.14...)
Pow${a}^{b}$ Power
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("4d0e14"),
SymbolDefinition(Path, Path(a, b, c), "Line path"),
Description("This object represents the path formed by connecting the given points or paths by line segments. ", "A path is a formal object, semantically different from a set of points: for a path object, the direction is significant, and it is undefined whether a path segment corresponds to an open interval or a closed interval between the points.", "The typical application is to represent a path of integration."),
CodeExample(Path(1, -1), "Represents the path going left from", 1, "to", -1, "."),
CodeExample(Path(a, Path(b, c)), "Equivalent to", SourceForm(Path(a, b, c)), "."),
CodeExample(Path(1, ConstI, -1, Neg(ConstI), 1), "Represents a diamond-shaped loop around the origin in the counterclockwise direction."),
CodeExample(Path(Neg(Mul(ConstI, Infinity)), Mul(ConstI, Infinity)), "Represents the imaginary axis traversed upwards."),
CodeExample(Path(1, Mul(Exp(Div(Mul(Pi, ConstI), 4)), Infinity)), "Represents the ray from", 1, "to infinity along a 45 degree angle."),
CodeExample(Path(Tuple(2, 1), Tuple(0, 0)), "Represents the line segment from", Tuple(2, 1), "to the origin in", Pow(RR, 2), "."))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC