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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

application ideal

This application allows to define ideals and enables other applications to use these. For example we can compute the tropical variety of an ideal via gfan in the application 'tropical'. Using this application with the bundled extension Singular adds a lot more commutative algebra power.

imports from:

  • Groebner:
    The Groebner object collects information about an ideal depending on the monomial ordering of the ambient ring.

  • Ideal:
    An ideal in a polynomial ring.

Producing an ideal from scratch

With these clients you can create ideals belonging to various parameterized families which occur frequently in comumutative algebra.


pluecker_ideal(Int d, Int n)

Generates the ideal of all Grassmann-Plücker relations of dxd minors of an dxn matrix. For the algorithm see Sturmfels: Algorithms in invariant theory, Springer, 2nd ed., 2008

Parameters:

Int d

Int n

Returns:

Singular interface

Functions, methods and objects and attached from/to Singular.


load_singular_library(String s)

Loads a SINGULAR library

Parameters:

String s

from extension:

quotient(Ideal I, Ideal J)

Computes an ideal quotient via SINGULAR

Parameters:

Ideal I

Ideal J

Returns:
from extension:

singular_eval(String s)

Executes given string with Singular

Parameters:

String s

from extension:

singular_get_int(String s)

Retrieves an int variable from 'Singular'

Parameters:

String s

from extension:

singular_get_var(String s)

Retrieves a variable from 'Singular'

Parameters:

String s: variable name

Returns:
from extension:

slack_ideal_non_saturated

Computes the non-saturated slack ideal of a polytope, as described in > João Gouveia, Antonio Macchia, Rekha R. Thomas, Amy Wiebe: > The Slack Realization Space of a Polytope > (https://arxiv.org/abs/1708.04739)

from extension:

Singular interface

Functions, methods and objects and attached from/to Singular.


SingularIdeal

An intermediate object wrapping the ideal on the Singular side and providing its methods.

from extension:

  • documentation/latest/ideal.txt
  • Last modified: 2019/11/15 22:01
  • (external edit)