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ReactionNetworks :: stoichSubspaceKer

stoichSubspaceKer -- Computes the kernel of the stoichiometric matrix of a Reaction Network.

Synopsis

Description

Computes the left kernel of the stoichiometric matrix of a Reaction Network.

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

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

o1 : ReactionNetwork
i2 : Z = stoichSubspaceKer N

o2 = | 1 |
     | 1 |

              2        1
o2 : Matrix ZZ  <--- ZZ
i3 : S = stoichiometricMatrix N

o3 = | -1 1  |
     | 1  -1 |

              2        2
o3 : Matrix ZZ  <--- ZZ
i4 : K = ker transpose S

o4 = image | 1 |
           | 1 |

                               2
o4 : ZZ-module, submodule of ZZ

A bigger example:

i5 : N = oneSiteModificationA()

o5 = S_0+E-->X
     X-->S_0+E
     X-->E+S_1
     S_1+F-->Y
     Y-->S_1+F
     Y-->S_0+F

o5 : ReactionNetwork
i6 : Z = stoichSubspaceKer N

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

              6        3
o6 : Matrix ZZ  <--- ZZ
i7 : S = stoichiometricMatrix N

o7 = | -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
o7 : Matrix ZZ  <--- ZZ
i8 : K = ker transpose S

o8 = image | 0 -1 1 |
           | 1 1  0 |
           | 1 0  1 |
           | 0 -1 1 |
           | 0 1  0 |
           | 0 0  1 |

                               6
o8 : ZZ-module, submodule of ZZ

See also

Ways to use stoichSubspaceKer :

For the programmer

The object stoichSubspaceKer is a method function.