Hi Sandeep, What background do you have? It would be good to now a quite little bit of algebra though the project is mostly programming and would require good skills in OOP and in Sage's class hierarchy and category framework. The point is that the current polynomial classes hierarchy in Sage is ill designed. And many methods currently existing should be split and dispatched into different/new classes or into the category framework. You could have a look at how roots are computed right now and suggest some improvements.
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