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~The~implicit~matrix~of~the~rational~surface~P~and~extraneous~factors~associate d~to~bad~base~points~and~anomalies~at~infinity.|+F&FA-F/6#QZ~~Compute~the~impli cit~matrix~of~the~rational~surface~P.|+F&FG-F/6#Qjn~~ImpMatrix(~[s^2*t,s+t,t,s* t]~)~~#The~default~last~item~is~1|+|+F&OF&@$/F+T5C-F.-F/6#Q/~~ImpCurve(P)|+F&F5 -F/6#Qbq~~P:~P~is~a~rational~planar~curve~in~affine~space~or~a~homogeneous~para metrization~in~projective~space|+F&F;-F/6#QY~~The~implicit~equation~of~the~rati onal~planar~curve~P.|+F&FA-F/6#Qjn~~Implicitization~using~the~mu-basis~of~ratio nal~planar~curve.|+F&FG-F/6#QG~~ImpCurve(~[t^5+4*t^3,~t^2+1,~t+4]~)|+F&OF&@$/F+ T7C/F.-F/6#Q7~~polyBP(~[bp],~m,~n)|+F&F5-F/6#QR~~bp:~a~series~of~points~specifi ed~as~base~point|+F&-F/6#QT~~m:~the~degree~of~rational~surface~in~parameter~s|+ F&-F/6#QT~~n:~the~degree~of~rational~surface~in~parameter~t|+F&F;-F/6#QZ~~A~rat ional~tensor~product~surface~with~base~points~bp.|+F&FA-F/6#Qho~~Generate~a~rat 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F&-F/6#QO~~ImpDegree(~[s^2*t+t,~s*t+t+1,~s+2,~t^2+s]~)|+F&-F/6#Qao~~ImpDegree(~ [(s^2*t+t)/(t^2+s),~(s*t+t+1)/(t^2+s),~(s+2))/(t^2+s)]~)|+F&OF&@$/F+T'C/F.-F/6# QH~~Impby3mp(P~,~mode=|fr"ploy","matrix"|hr)|+F&F5F8-F/6#Q^o~~mode(optional)~:~ choose~the~expression~of~output,defualt~is~ploy|+F&F;-F/6#Qeo~~The~implicit~equ ation~of~the~rational~surface~P~or~the~implicit~matrix.|+F&FA-F/6#Q]p~~Implicit ization~using~the~resultant~matrix~of~three~low~bidegree~moving~planes.|+F&FG-F /6#QN~~Impby3mp(~[s^2*t+t,~s*t+t+1,~s+2,~t^2+s]~)|+F&-F/6#Qin~~Impby3mp(~[s^2*t +t,~s*t+t+1,~s+2,~t^2+s]~,~mode~=~"matrix")|+F&OF&@$/F+T)C/F.-F/6#QJ~~ImpbyDixo nA(P,~mode=|fr"ploy","matrix"|hr)|+F&F5F8FXF;FenFA-F/6#Qdo~~Implicitization~usi ng~the~Dixon~A-resultant~of~three~obvious~syzygies.|+F&FG-F/6#QF~~ImpbyDixonA(~ [s^2*t,s+t,t^3,s*t]~)|+F&-F/6#QW~~ImpbyDixonA(~[s^2*t,s+t,t^3,s*t]~,~mode~=~"ma trix")|+F&OF&@$/F+T+C/F.-F/6#QH~~Impbympmq(P,~mode=|fr"ploy","matrix"|hr)|+F&F5 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