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# spohnIdeal -- compute the ideal of the Spohn variety of a given game

- Usage:
    `spohnIdeal(PR,X)`
- Inputs:
  - PR, a ring, a probability ring obtained via probabilityRing(Di), where $Di$ is the format of the game
  - X, a list, a list of n tensors of format $D_i$ describing the payoffs of the game
- Outputs:
  - a list, the ideal generated by the $2\times 2$ minors of the Spohn matrices of the game $X$

## Description

It is crucial that the formats in PR and X match up. The Spohn ideal $I_X$ is the ideal defining the Spohn variety of a game $X$, which contains the dependency equilibria of the game $X$. Its generators are given by the $2\times 2$ minors of the Spohn matrices. This function uses the function spohnMatrices to compute the Spohn matrices of the given game.

    i1 : Di = {2,2,3};

    i2 : PR = probabilityRing(Di);

    i3 : X = randomGame(Di);

    i4 : I = spohnIdeal(PR,X);

    o4 : Ideal of PR

## See also

- probabilityRing -- ring of probability distributions of a game indexed by ordered multi-indices
- randomGame -- construct a game of a given format with arbitrary payoffs
- spohnMatrices -- compute the list of Spohn matrices of a given game
- konstanzMatrix -- construct the Konstanz matrix of a given game

## Ways to use spohnIdeal:

- spohnIdeal(Ring,List) (missing documentation)

## For the programmer

The object spohnIdeal is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GameTheory.m2:1695:0.