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Results tagged with elimination-theory
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user 7076
Elimination theory is the study of necessary and sufficient conditions for polynomial equations (E) to have solutions.In the homogeneous case, if the number of variables is equal to the number of equations, this leads to the study of the Resultant (polynomial in the coefficients of (E), obtained by "eliminating" the variables ). In the general case, one get a Resultant ideal, generated by polynomial relations in the coefficients of the equations (E).
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Conditions for resultants of bivariate quadratics to be perfect squares
At very least it is necessary that each of the following three numbers is a square:
$$a_{02}^2 b_{20}^2-a_{02} a_{11} b_{11} b_{20}-2 a_{02} a_{20} b_{02} b_{20}+a_{02} a_{20} b_{11}^2+a_{11}^2 b_{02} …
- 34.3k
6
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Useful software for variable elimination
This can be done, e.g., in SageMath - here are documentation and examples. The code can be run online at SageMathCell.
- 34.3k
3
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Library/Database of parametric polynomial systems
There is a database of polynomial systems, which comes with PHCpack by Jan Verschelde.
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