Macaulay2 » Documentation
Packages » RandomObjects :: RandomObjects
next | previous | forward | backward | up | index | toc

# 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

- Hans-Christian Graf v. Bothmer <bothmer@uni-math.gwdg.de>
- Florian Geiss <fg@math.uni-sb.de>
- Daniel R. Grayson <dan@math.uiuc.edu>
- Frank-Olaf Schreyer <schreyer@math.uni-sb.de>

## Version

This documentation describes version 0.2 of RandomObjects, released June 19, 2011.

## 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/stable/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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RandomObjects.m2:193:0.