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Let $x \in \mathbb{R}^n$ be a variable, and $f_1, \ldots , f_n : \mathbb{R}^n \mapsto \mathbb{R}$ be a sequence of functions, each having a closed form expression. Assume that we want to solve the system $f_i(x) = 0$ where $1 \leq i \leq n$. Is there a specific name for such a system? I am in need of a "name", because I will be continually referring to this setting in writing. I tried to come up with things of the form "a system of _____ equations", but I couldn't find a good one.

Remark: Initially, I considered using the adjective "non-differential", but it sounded weird to me. I am currently using "algebraical" equations, but this is probably a bad choice. The term "algebraic" has a well defined meaning, and $f_i$ need not be algebraic in general. I can say "transcendental", but $f_i$ need not always include transcendental terms either.

Note: There are no restrictions on $f_i$, other than the stipulation that each have a closed form expression. In summary, I require $f_i$ to have finitely many terms, each involving elementary functions.


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What do you mean by a function $f:\mathbb{R}^n \to \mathbb{R}$ being a closed form expression. It's obvious when $n=1$, but for $n>1$ it is unclear imho. – Nate Iverson Jun 1 '14 at 5:14
@NateIverson : How is it obvious for $n=1$? – Patrick Da Silva Jun 1 '14 at 5:17
@PatrickDaSilva: – Nate Iverson Jun 1 '14 at 5:19
@NateIverson I know, but still, this remains very ad-hoc. – Patrick Da Silva Jun 1 '14 at 5:21
@NateIverson: Does my edits clarify the question? – iheap Jun 1 '14 at 5:22

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