Comment on Chemical equation balancing: An integer programming approachComments−jamessb10yA while ago I saw a paper in the SIAM Review - just one and a half pages of maths, followed by"Remark 2. The theorem proved here gives a completely new general method. It generalizes all known results for balancing chemical equations cited chronologically in references [1]–[125]." http://www.siam.org/journals/problems/downloadfiles/71-025s....Reference 125 is to this paper.−octonion10yThis appears to be essentially equivalent to solving a linear system using the Moore-Penrose pseudoinverse. https://en.m.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudo...−_delirium10yIt's interesting that despite being long open, both the problem and the solution are stated using only elementary linear algebra.−GFK_of_xmaspast10yIn fairness, this paper is looking for integer solutions instead of SiRev's real ones.
Comments
A while ago I saw a paper in the SIAM Review - just one and a half pages of maths, followed by
"Remark 2. The theorem proved here gives a completely new general method. It generalizes all known results for balancing chemical equations cited chronologically in references [1]–[125]." http://www.siam.org/journals/problems/downloadfiles/71-025s....
Reference 125 is to this paper.
This appears to be essentially equivalent to solving a linear system using the Moore-Penrose pseudoinverse. https://en.m.wikipedia.org/wiki/Moore%E2%80%93Penrose_pseudo...
It's interesting that despite being long open, both the problem and the solution are stated using only elementary linear algebra.
In fairness, this paper is looking for integer solutions instead of SiRev's real ones.