"Is" vs. "Are" when using the word "Pair" in a mathematical setting

If the mathematical statement is about the two objects in the pair then "are" is appropriate, however if it is about the pair as a mathematical object of itself then "is" is in place. Thus "The pair of polynomials (f,g) are related by the reciprocity law" but "The pair of polynomials (f,g) is equal to the pair (h,q)".

You should use the singular, because it refers to "Pair" and not to "polynomials". The pair in this case is one, so "is".

If it was "three pairs of polynomials...", for example, then you would have used "are".

Like:

A pair of shoes is in my bedroom. - VS - Two (three, four, five, etc) pairs of shoes are in my bedroom.

answer is 'is' according to me, because pair represents a collective noun or verb of something, and there is a single pair of polynomials