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mapToMarkovRing -- ring isomorphism from the given probabilityRing to the corresponding markovRing

Description

This function creates the RingMap from a given probabilityRing to its canonically isomorphic markovRing.

i1 : R = probabilityRing {2,3,4};
i2 : markovR = toMarkovRing R;
i3 : F = mapToMarkovRing R

o3 = map (markovR, R, {q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     , q     })
                        1,1,1   1,1,2   1,1,3   1,1,4   1,2,1   1,2,2   1,2,3   1,2,4   1,3,1   1,3,2   1,3,3   1,3,4   2,1,1   2,1,2   2,1,3   2,1,4   2,2,1   2,2,2   2,2,3   2,2,4   2,3,1   2,3,2   2,3,3   2,3,4

o3 : RingMap markovR <-- R
i4 : target F

o4 = markovR

o4 : PolynomialRing
i5 : source F

o5 = R

o5 : PolynomialRing
i6 : isInjective F

o6 = true
i7 : F.matrix

o7 = | q_(1,1,1) q_(1,1,2) q_(1,1,3) q_(1,1,4) q_(1,2,1) q_(1,2,2) q_(1,2,3)
     ------------------------------------------------------------------------
     q_(1,2,4) q_(1,3,1) q_(1,3,2) q_(1,3,3) q_(1,3,4) q_(2,1,1) q_(2,1,2)
     ------------------------------------------------------------------------
     q_(2,1,3) q_(2,1,4) q_(2,2,1) q_(2,2,2) q_(2,2,3) q_(2,2,4) q_(2,3,1)
     ------------------------------------------------------------------------
     q_(2,3,2) q_(2,3,3) q_(2,3,4) |

                   1            24
o7 : Matrix markovR  <-- markovR

See also

Ways to use mapToMarkovRing:

  • mapToMarkovRing(Ring)

For the programmer

The object mapToMarkovRing is a method function.


The source of this document is in GameTheory.m2:1817:0.