Given an overdetermined set of quadratic multivariable polynomial equations over some finite field F_{q}, what is the best known algorithm to solve the problem and what is its complexity ?
What are the underlying assumptions leading to the given complexity ? The same questions over F_{2} ?
Is there any result regarding sets of such equations that have some structure ?
Is it true that when the number of equations m>n, where n is the number of variables, when n tends to infinity, the number of solutions tends to be 0 or 1 ?
Is there any proof or any explanation to this phenomena or is it only from observations ?
How bigger m should be in order to see this phenomena in experiments ?
Any system of polynomial equations can be reduced to a system of quadratic equations in more variables. (This is well known.) For example, if a monomial m of degree d>=3 appears in an equation, write m=m_1*m_2
where m_1, m_2 are monomials of degree
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