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documentation:master:ideal [2019/12/05 16:19] (current)
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 +====== 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:
 +    * application [[.:​common|common]]
 +
 +===== Objects =====
 +  ** ''​[[.:​ideal:​Groebner |Groebner]]'':​\\ ​ The Groebner object collects information about an ideal depending on the monomial ordering of the ambient ring.
 +  ** ''​[[.:​ideal:​Ideal |Ideal]]'':​\\ ​ An ideal in a polynomial ring.
 +
 +===== Functions =====
 +
 +==== Producing an ideal from scratch ====
 + With these clients you can create ideals belonging to various parameterized families which occur frequently in comumutative algebra.
 +----
 +{{anchor:​pluecker_ideal:​}}
 +  ?  **''​pluecker_ideal([[.:​common#​Int |Int]] d, [[.:​common#​Int |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:
 +    :: ''​[[.:​common#​Int |Int]]''​ ''​d''​
 +    :: ''​[[.:​common#​Int |Int]]''​ ''​n''​
 +    ? Returns:
 +    :''​[[.:​ideal:​Ideal |Ideal]]''​
 +
 +
 +----
 +
 +==== Singular interface ====
 + ​Functions,​ methods and objects and attached from/to Singular.
 +----
 +{{anchor:​load_singular_library:​}}
 +  ?  **''​load_singular_library([[.:​common#​String |String]] s)''​**
 +  :: Loads a SINGULAR library
 +    ? Parameters:
 +    :: ''​[[.:​common#​String |String]]''​ ''​s''​
 +    ? from extension:
 +    : [[:​external_software|bundled:​singular]]
 +
 +
 +----
 +{{anchor:​singular_eval:​}}
 +  ?  **''​singular_eval([[.:​common#​String |String]] s)''​**
 +  :: Executes given string with Singular
 +    ? Parameters:
 +    :: ''​[[.:​common#​String |String]]''​ ''​s''​
 +    ? from extension:
 +    : [[:​external_software|bundled:​singular]]
 +
 +
 +----
 +{{anchor:​singular_get_var:​}}
 +  ?  **''​singular_get_var([[.:​common#​String |String]] s)''​**
 +  :: Retrieves a variable from '​Singular'​
 +    ? Parameters:
 +    :: ''​[[.:​common#​String |String]]''​ ''​s'':​ variable name
 +    ? Returns:
 +    :''​[[.:​common#​List |List]]''​
 +    ? from extension:
 +    : [[:​external_software|bundled:​singular]]
 +
 +
 +----
 +{{anchor:​slack_ideal_non_saturated:​}}
 +  ?  **''​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:
 +    : [[:​external_software|bundled:​singular]]
 +
 +
 +----
 +
 +===== Small Object Types =====
 +
 +==== Singular interface ====
 + ​Functions,​ methods and objects and attached from/to Singular.
 +----
 +{{anchor:​singularideal:​}}
 +  ?  **''​SingularIdeal''​**
 +  :: An intermediate object wrapping the ideal on the Singular side and providing its methods.
 +    ? from extension:
 +    : [[:​external_software|bundled:​singular]]
 +
 +
 +----
  
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