MathDB

We say that a function

f:\mathbb{R}^k \rightarrow \mathbb{R}

is a metapolynomial if, for some positive integers

m

and

n

, it can be represented in the form

f(x_1,\cdots , x_k )=\max_{i=1,\cdots , m} \min_{j=1,\cdots , n}P_{i,j}(x_1,\cdots , x_k),

where

P_{i,j}

are multivariate polynomials. Prove that the product of two metapolynomials is also a metapolynomial.

A7