Doesn't there also have to be some notion of "atomic" (gcd?) reaction, otherwise you couldn't separate 2 H2 + 3 O2 + C <-> 2 H2O + CO2 into its constituent reactions 2 H2 + 2 O2 <-> 2 H2O + energy and C + O2 <-> CO2 + energy At 11:29 AM 4/25/2011, mcintosh@unam.mx wrote:

...

There must be more to it than just determinants & linear algebra, because you aren't guaranteed to get integers. Or do you simply multiply by the (integer-valued) determinant to clear the fractions?

Is there any chance that you might end up doing "integer linear programming", which is considerably harder than linear programming (because it subsumes hard problems like the knapsack problem) ?

Well, I didn't pursue it that far. But since the solution would be rational, presumably a multiple would suffice.

In truth, there is a problem of reaction kinetics involved, an there is an implicit assumption of stable compounds; otherwise the reaction could just as well be reversible. (hence your second question)

But this is all simple introductory chemistry. And I was mostly delighted that I had found a rational scheme for understanding those reaction equations.

-hvm