A new general algorithmic method in reaction syntheses using linear algebra

We discuss here a new general linear algebraic method (both model and algor ithm) for describing and generating (among others) minimal reactions and al so minimal mechanisms in stoichiometry, or dimensionless groups in physics as well. (Further applications in process network syntheses will be discuss ed in [1].) With some minor modifications of the input this method can be e xtended for several related questions: for generating direct and overall re actions, direct (steady state) mechanisms, for finding the possible resulti ng (overall) reactions among all possible mechanisms, etc. Computational results in section 4 show the speed of our algorithm. We give also mathematical background and results in sections 3, 5 and 6. Ho wever, we do not restrict ourselves to mathematics only, we also talk on th e language of chemistry, too. The theoretical results in sections 3.2, 3.3, 5 and the computational examp les in section 4 are completely new, further theoretical results will appea r in [1,2] and in [3].