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solutions to under- and over-determined systems

September 19 2007 by Shawn Bauldry 20

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I have a project where I'm trying to establish the identification of systems of equations (usually 10 or so equations). The systems can be under- exactly- or over-determined. If over-determined, I would like to know what constraints would need to be made to identify the system. For example, with the system: x + y = a x - y = b 2x + 2y = c Is there a way to have Maple return that c = 2a? Also, in some cases when the system is under-determined I get parametric solutions but in other cases I get {} (which is the same result returned for over-determined equations). Does anyone know why Maple will provide solutions for some under-determined systems and not others (i.e., where I might look to diagnose this problem with my systems)?
equations example

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