# 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.

## Version

This documentation describes version 0.2 of RandomObjects.

## Source code

The source code from which this documentation is derived is in the file RandomObjects.m2.

## Exports

• Types
• Functions and commands
• Methods
• 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 .