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# stoichiometricConeKer -- Computes a matrix whose columns are the rays of the cone non-negative kernel of the stoichiometric matrix of a Reaction Network.

- Usage:
    `E = stoichiometricConeKer N`
- Inputs:
  - N, an instance of the type ReactionNetwork, a chemical reaction network.
- Outputs:
  - E, a matrix, whose columns are the non negative kernel of the stoichiometric matrix of N.

## Description

Computes the cone non-negative kernel of the stoichiometric matrix of N and puts its rays as columns of a matrix.

    i1 : N = reactionNetwork "A <--> B"

    o1 = A-->B
         B-->A

    o1 : ReactionNetwork

    i2 : S = stoichiometricMatrix N

    o2 = | -1 1  |
         | 1  -1 |

                  2       2
    o2 : Matrix ZZ  <-- ZZ

    i3 : E = stoichiometricConeKer N

    o3 = | 1 |
         | 1 |

                  2       1
    o3 : Matrix ZZ  <-- ZZ

A bigger example:

    i4 : N = oneSiteModificationA()

    o4 = S_0+E-->X
         X-->S_0+E
         X-->E+S_1
         S_1+F-->Y
         Y-->S_1+F
         Y-->S_0+F

    o4 : ReactionNetwork

    i5 : S = stoichiometricMatrix N

    o5 = | -1 1  0  0  0  1  |
         | -1 1  1  0  0  0  |
         | 1  -1 -1 0  0  0  |
         | 0  0  1  -1 1  0  |
         | 0  0  0  -1 1  1  |
         | 0  0  0  1  -1 -1 |

                  6       6
    o5 : Matrix ZZ  <-- ZZ

    i6 : E = stoichiometricConeKer N

    o6 = | 0 1 1 |
         | 0 0 1 |
         | 0 1 0 |
         | 1 1 0 |
         | 1 0 0 |
         | 0 1 0 |

                  6       3
    o6 : Matrix ZZ  <-- ZZ

## See also

- stoichiometricMatrix -- Computes the stoichiometric matrix of a Reaction Network.
- stoichiometricSubspace -- Computes the stoichiometric space of a Reaction Network.
- stoichSubspaceKer -- Computes the kernel of the stoichiometric matrix of a Reaction Network.
- negativeLaplacian -- Computes the negative of the Laplacian matrix of a Reaction Network.
- negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.

## Ways to use stoichiometricConeKer:

- `stoichiometricConeKer(ReactionNetwork)`

## For the programmer

The object stoichiometricConeKer is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ReactionNetworks/DocReactionNetworks.m2:860:0.