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

Synopsis

• 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

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

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.