RandomObjects -- a Framework for the construction of random points of unirational moduli spaces

Description

This package provides the framework for the implementation of unirationality constructions.

A moduli space $M$ of objects is unirational if there exists a dominant rational map $\phi:\mathbb{P}^n --> M$. If the function $\phi$ is explicitly given it can be translated into a construction function that computes $\phi(P)$ for a given $P \in \mathbb{P}^n$. If $P$ is chosen randomly (over a finite field $F_q$ or over a subset of $\mathbb{Q}$ limited by a given height) it may not lie in the open subset of $\mathbb{P}^n$ where $\phi$ is defined. This can be remedied by calling the function several times, i.e. allowing a certain number of Attempts. One is also interested in certifying the constructed object meaning that it satisfies certain reasonable properties.

Authors

Version

This documentation describes version 0.2 of RandomObjects.

Citation

If you have used this package in your research, please cite it as follows:

@misc{RandomObjectsSource,
  title = {{RandomObjects: a framework for making random objects in algebraic geometry. Version~0.2}},
  author = {Hans-Christian Graf v. Bothmer and Florian Geiss and Daniel R. Grayson and Frank-Olaf Schreyer},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Types
- RandomObject -- framework for creation of random objects
Functions and commands
- randomObjectTemplate -- a template for the implementation of a random object
Methods
- random(RandomObject) -- returns a function that constructs a random object
- randomObjectTemplate(String) (missing documentation)
Symbols
- Attempts -- number of attempts in the construction of a random object
- Certify -- whether to certify the object
- Construction -- key of randomObject that contains the construction function

For the programmer

The object RandomObjects is a package, defined in RandomObjects.m2.

The source of this document is in RandomObjects.m2:193:0.