*Delassus--Gunther Solver
#History764#
In order to present the solver proposed by Delassus--Gunther we must slightly adapt the notation used; we assume #math143##tex2html_wrap_inline3683#⊂#tex2html_wrap_inline3684#Q = K[Z1,…, Zr] to be homogeneous and we denote, for each #math144#d∈#tex2html_wrap_inline3686#N,
#math145#
#tex2html_wrap_indisplay3690#Wd : = {τ∈#tex2html_wrap_indisplay3691#W, deg(τ) = d}<#1#> and<#1#>tex2html_image_mark>#tex2html_wrap_indisplay3698# : = #tex2html_wrap_indisplay3699#∩#tex2html_wrap_indisplay3700#(#tex2html_wrap_indisplay3703#Wd).
We assume to have performed a generic change of coordinates and we
consider the (deg)-revlex ordering ;SPMlt; induced by #math146#Z1 ;SPMlt; Z2 ;SPMlt; … ;SPMlt; Zr and for each (homogeneous) polynomial #math147#f = #tex2html_wrap_inline3707#c(f, t)t∈#tex2html_wrap_inline3708#Q we denote
#math148#
#tex2html_wrap_indisplay3712#(f ): = #tex2html_wrap_indisplay3713#(t∈#tex2html_wrap_indisplay3714#W : c(f, t)≠0)
and, for each (homogeneous) set #math149#F⊂#tex2html_wrap_inline3716#Q,
#math150#
#tex2html_wrap_indisplay3720#{F} : = {#tex2html_wrap_indisplay3723#(f ): f∈F}#tex2html_wrap_indisplay3724##tex2html_wrap_indisplay3727#(F) : = {τ#tex2html_wrap_indisplay3730#(f ): f∈F, τ∈#tex2html_wrap_indisplay3731#W}.
#Remark843#
#Theorem923#
#proof967#