next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
MinimalPrimes :: MinimalPrimes

MinimalPrimes -- experimental package: minimal primes of an ideal


Find the minimal primes of an ideal in a polynomial ring over a prime field, or a quotient ring of that. These are the geometric components of the corresponding algebraic set.

The main routine is minprimes, although in a future release this will be renamed to minimalPrimes.

Use installMinprimes to replace the system versions of ’decompose Ideal’, ’minimalPrimes Ideal’ and ’isPrime Ideal’. In many cases the new function is much faster, although there are cases when the older, current, version is faster.


Only works for ideals in (commutative)polynomial rings or quotients of polynomial rings over a prime field, might have bugs in small characteristic and larger degree (although, many of these cases are caught correctly).

See also



This documentation describes version 0.9 of MinimalPrimes.

Source code

The source code from which this documentation is derived is in the file MinimalPrimes.m2. The auxiliary files accompanying it are in the directory MinimalPrimes/.


  • Functions and commands
    • installMinprimes -- install experimental functions into Macaulay2
    • minprimes -- minimal primes in a polynomial ring over a field
    • newIsPrime (missing documentation)
  • Symbols
    • Verbosity -- optional argument describing how verbose the output should be