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Results tagged with algebraic-systems
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user 18739
Algebraic systems, relational structures. As considered in model theory, a structure (or a model) is a set endowed with a family of finitary relations and functions (operations). In some contexts, these can be represented by relational structures with some of the $(n+1)$-ary relations being viewed as $n$-ary functions. As considered in universal algebra, an algebraic structure is a structure with operations only.
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Expected number of solutions of a random quadratic polynomial system over a finite field
The expected number of $N$ is $q^{n-m}$. One can either argue as in the comments by Command Master, or perform a simple double counting argument: Let $S$ be the set of polynomial systems with the give …
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