probabilitySumIdeal -- ideal enforcing that a probability distribution sums to 1

Usage:

probabilitySumIdeal R
Inputs:
- R, a ring, a ring typically from probabilityRing
Outputs:
- an ideal, the ideal generated by the sum of all probabilities minus 1

Description

Constructs the ideal expressing normalization of a joint probability distribution. If given a list, it first calls probabilityRing with default options.

i1 : R = probabilityRing {2,3,4};

i2 : probabilitySumIdeal R

o2 = ideal(p          + p          + p          + p          + p          +
            {0, 0, 0}    {0, 0, 1}    {0, 0, 2}    {0, 0, 3}    {0, 1, 0}  
     ------------------------------------------------------------------------
     p          + p          + p          + p          + p          + p      
      {0, 1, 1}    {0, 1, 2}    {0, 1, 3}    {0, 2, 0}    {0, 2, 1}    {0, 2,
     ------------------------------------------------------------------------
        + p          + p          + p          + p          + p          +
     2}    {0, 2, 3}    {1, 0, 0}    {1, 0, 1}    {1, 0, 2}    {1, 0, 3}  
     ------------------------------------------------------------------------
     p          + p          + p          + p          + p          + p      
      {1, 1, 0}    {1, 1, 1}    {1, 1, 2}    {1, 1, 3}    {1, 2, 0}    {1, 2,
     ------------------------------------------------------------------------
        + p          + p          - 1)
     1}    {1, 2, 2}    {1, 2, 3}

o2 : Ideal of R

Ways to use probabilitySumIdeal:

probabilitySumIdeal(Ring)

For the programmer

The object probabilitySumIdeal is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GameTheory.m2:1577:0.

probabilitySumIdeal -- ideal enforcing that a probability distribution sums to 1

Description

See also

Ways to use probabilitySumIdeal:

For the programmer