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.

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`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), "."))