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$F$: a function with $F(z)=A(f_1(z),f_2(z),...,f_n(z))$

$A$: an algebraic function

$f_1$, $f_2$, ..., $f_n$: transcendental functions, pairwise algebraically independent

$z\in\mathbb{C}$

What, or what kind of relation, is the inverse relation (the reverse) $A^{-1}$ of $A$? The terms "multivalued function" and "multifunction" are outdated. But by what terms are they replaced? "Correspondence" corresponds to the term "relation".

I want somehow express that $A^{-1}$ is a set(?)/a tuple(?) of algebraic functions. Is there a suitable term or a suitable description for $A^{-1}$?

user405214
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2 Answers2

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$A^{-1}(z)=\{(z1,...,z_n):A(z1,...,z_n)=z\}$
or
$A^{-1}(z)=\{u:A(f1(u),...,f_n(u))=z\}$

depending by what you want for $A^{-1}$.

user405214
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William Elliot
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  • I can imagine that you are affirming that $A^{-1}(z)$ is a set, though refusing to use $\LaTeX$ makes the response hard to read. However the OP seems to want advice about terminology for $A^{-1}$ itself, not the inverse image of a point. – hardmath Aug 08 '17 at 04:47
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The word you're looking for is probably "relation." Given a function $f : A \rightarrow B$, we get a corresponding relation $f : A \nrightarrow B$ which has a converse $f^\dagger : B \nrightarrow A$. See here about the category of sets and relations, and here about allegory theory. See also here about multivalued maps in complex analysis (no answers yet, unfortunately.)

goblin GONE
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