Using Sparse Interpolation in Hensel Lifting

Speeding up polynomial GCD, a crucial operation in Maple

“…For example, for 𝑓 in Figure 1, 𝑏 = 16. The first monomial 𝑥𝑦 3 𝑧 of degree 𝑑 = 5 is encoded as 5 • 2 48 + 1 • 2 32 + 3 • 2 16 + 1. This is depicted as 5131 in Figure 1.…”

“…If the time for gcd is slower than factor then something is wrong as we could simply use the factorization of 𝐴 and 𝐵 to determine the gcd 𝐺. The factor code Maple has been using since Maple2019 is the work of Monagan and Tuncer [16,17,18]. As the reader can see Maple's factor command is faster than our GCD1 timings when #𝐺 ≫ # Ā.…”

“…R := rand(0..d); # generate random exponents on [0,d] f := 0; while numterms(f) < t do s := t-numterms(f); g := add( C()*getmon(R,X,D), i=1..s ); f := f + g; end do; return f; end: gcddegs := [ [5,10,15], [4,8,12,16], [4,7,10,13,16], [3,6,9,11,14,17]]; cofdegs := [ [15,10,5], [16,12,8,4], [16,13,10,7,4], [17,14,11,9,6,3] [5,10,15], [4,8,12,16], [4,7,10,13,16], [3,6,…”