m1 is a polynomial function in variable t2=s2 of degree (maximum power with nonzero coefficient) t3 interpreted by rules m2
m2 can include (but is not limited to) information about the underlying formal polynomial and/or ring of definition, steps of addition series (which terms are being summed), and input domain of the function. t2 is a variable of input (no longer an indeterminant, as it is for the underlying formal polynomial). See also: cpolinomi'a