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


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.



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.


  • 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 a package.