documentation:master:ideal

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 — documentation:master:ideal [2019/12/05 16:19] (current) Line 1: Line 1: + ====== 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]] + + + ----
• documentation/master/ideal.txt