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

## Synopsis

• Usage:
Z = stoichSubspaceKer N
• Inputs:
• Outputs:
• Z, , whose columns span the left kernel of the stoichiometric matrix.

## 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