Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Composition and inverse of multivariate functions and algebraic system
  of equations   Every one knows that an equation is equivalent to a multivariate function.
Generally speaking, there are more than one unknown x in this multivariate
function and it is not easy to reduce the number of unknown x to one. In this
paper we achieve this by introducing function promotion which can converse a
function of less variables to one of more variables and by introducing
multivariate function composition developed from unary function composition. We
introduced inverse multivariate functions extended from inverse unary functions
then we can express the solution by an inverse multivariate function if this
equivalent multivariate function is invertible. For an equivalent irreversible
multivariate function we introduced relation and consider the equivalent
multivariate function as a special multivariate relation then we can express
the solution by an inverse multivariate relation which always exists. No one
will belief that every one is familiar with multivariate function composition
after their reading this paper and knowing the importance of multivariate
function composition to express the solution of a general equation. Further
more we discuss the possibility of expressing the solution, a multivariate
function or multivariate relation, for a general equation by superposition of
unary ones. This will involve Hilbert's 13th problem. The topic shown in this
paper can be new directions for many mathematicians because the topic is so
basic.

19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat