Functional decomposition of polynomials: The wild case

Joachim von zur Gathen
1990 Journal of symbolic computation  
If g and h are polynomials of degrees r and s over a field, their functional composition f = #(h) has degree n = rs. The functional decomposition problem is: given f of degree n = rs, determine whether such g and h exist, and, in the affirmative case, compute them. An apparently difficult case is when the characteristic p of the ground field divides r. This paper presents a polynomial-time partial solution for this "wild" case; it works, e.g., when p2 t r.
doi:10.1016/s0747-7171(08)80054-5 fatcat:6xlsmeh2wfaztcty2hp65xocrq