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— | documentation:master:ideal [2023/01/27 16:59] (current) – created - external edit 127.0.0.1 | ||
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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 ' | ||
+ | |||
+ | imports from: | ||
+ | * application [[.: | ||
+ | |||
+ | ===== Objects ===== | ||
+ | ** '' | ||
+ | ** '' | ||
+ | ** '' | ||
+ | |||
+ | ===== 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: | ||
+ | ? **'' | ||
+ | :: Generates the ideal of all Grassmann-Plücker relations of the given matroid. For the algorithm see Sturmfels: Algorithms in invariant theory, Springer, 2nd ed., 2008 | ||
+ | ? Parameters: | ||
+ | :: '' | ||
+ | ? Returns: | ||
+ | :'' | ||
+ | |||
+ | |||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: 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: | ||
+ | :: '' | ||
+ | :: '' | ||
+ | ? Returns: | ||
+ | :'' | ||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | ==== Singular interface ==== | ||
+ | | ||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: Loads a SINGULAR library | ||
+ | ? Parameters: | ||
+ | :: '' | ||
+ | ? from extension: | ||
+ | : [[: | ||
+ | |||
+ | |||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: Executes given string with Singular | ||
+ | ? Parameters: | ||
+ | :: '' | ||
+ | ? from extension: | ||
+ | : [[: | ||
+ | |||
+ | |||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: Retrieves a variable from ' | ||
+ | ? Parameters: | ||
+ | :: '' | ||
+ | ? Returns: | ||
+ | :'' | ||
+ | ? from extension: | ||
+ | : [[: | ||
+ | |||
+ | |||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: 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:// | ||
+ | ? from extension: | ||
+ | : [[: | ||
+ | |||
+ | |||
+ | ---- | ||
+ | |||
+ | ===== Small Object Types ===== | ||
+ | |||
+ | ==== Singular interface ==== | ||
+ | | ||
+ | ---- | ||
+ | {{anchor: | ||
+ | ? **'' | ||
+ | :: An intermediate object wrapping the ideal on the Singular side and providing its methods. | ||
+ | ? from extension: | ||
+ | : [[: | ||
+ | |||
+ | |||
+ | ---- | ||