ABSTRACT

Resultants can be defined starting from a graded polynomial algebra Q ( T ) = Q [ T 0 , … , T n ] , https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429064265/c3969f1f-00ca-4e1d-a8e4-12dce1f567fb/content/unequ8_60_1.tif"/> where T 0,…,Tn are indeterminates of positive degrees γ0,…,γ n which are called weights, and generic homogeneous polynomials F 0,…,Fn of positive degrees δ 0,…,δn . That is, the Fj are polynomials F j = ∑ v ∈ N j U j v T v https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429064265/c3969f1f-00ca-4e1d-a8e4-12dce1f567fb/content/unequ8_60_2.tif"/> where Nj is a finite set of tuples ν = (v 0,…,vn ) ∊ ℕ n +1\{0} such that 〈 v , γ 〉       ≔       v 0 γ 0 + ⋯ + v n γ n = δ j https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429064265/c3969f1f-00ca-4e1d-a8e4-12dce1f567fb/content/unequ8_60_3.tif"/> and where U are independent indeterminates over ℤ: the ground ring is the polynomial ring Q = ℤ [ U j v ] j , v . https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429064265/c3969f1f-00ca-4e1d-a8e4-12dce1f567fb/content/unequ8_60_4.tif"/> .