CHW Example 2.4 (Example 3 of AS08)

Loads the chemJac command file, which contains all commands used below

\(\(\(\ \)\( (*\ 
      SetDirectory["C:\CHEMmma"]\ *) \)\(\ \)\(
\)\(<< "chemJac.m"\)\)\)

The RHS of the ODE and the list of species concentrations 'vars'. 
Here the notation fj, j=1,...6, hj, j=1,2,3,5,6 is consistent with AS08. We use -H4, -H7 in place of h4, h7  so that all of the functions, f1, ..., f6, h1, h2, h3, h5, h6, H4, H7 are increasing.

f = {-f1[x1] - H4[x4] - H7[x6], -f2[x2] + h1[x1], -f3[x3] + 
          h2[x2], -f4[x4] + h3[x3], -f5[x5] + h5[x2], -f6[x6] + 
          h6[x5]}

vars = {x1, x2, x3, x4, x5, 
        x6}

The Jacobian of the RHS of the ODE, and its Craciun-Feinberg determinant

j = jac[f,  vars]
j // MatrixForm

det = Det[j]

coeffs[det]