Hi all, Sorry for my long absence from the discussion here. I was busy improving my knowledge base on Diophantine equations and Group Theory, and getting familiar to the sympy module. I tried implementing the issues listed in https://github.com/sympy/sympy/issues?labels=Diophantine&page=1&state=open but realized I need to improve my knowledge first. Now I am pretty confident that it can be implemented. As for extension of the module I was thinking of using properties of group theory and applying it to extend it. I am looking forward to a response.
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