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I have some trouble understanding the attached section of my book. Basically I can't see why the marked equations are equivalent - that is the first two are contained in the last one. I can follow the derivation but when I do an example for myself where I just have two variables (q,p) being transformed to (Q,P). I get the condition from the symplectic condition that some determinant (actually the Jacobian defined in my last thread) equal 1 which does not seem equivalent to the equations 9.48. If the reader does not remember the matrix J I have attached that too on my own example. I am right in assuming that eqs. 9.48 should follow from the symplectic condition right? It certainly seems from the book that this condition is just a nicer way of writing eqs. 9.48 (although they look pretty nice to me already? - is there a sum or something?) so I would think so.