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"Header and Footer" -1 207 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 208 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "Equation Label" -1 209 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 } {CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 208 71 "Andrew Sommese 2009: Us ing resultants to solve a system of polynomials" }{TEXT 208 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f := (x,y) -> 1+x^3+y^2+y^3; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "g := (x,y) -> x^2+x*y+y^2+y^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "deg_f := degree(expand(f(x,y)),y):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "deg_g := degree(expand(g(x,y)),y):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "A:=Matrix(deg_f+deg_g,deg_f+deg_g):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for i from 0 to deg_f do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "F[i] := coeff(expand(f(x,y)),y,i):\n" } {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for i from 0 to deg_g do\n" }{MPLTEXT 1 0 34 "G[i] :=coeff(expand(g(x,y)),y,i):\n" }{MPLTEXT 1 0 4 "od:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for i from 1 to deg_g do\n" }{MPLTEXT 1 0 31 "for j from 1 to deg_f+deg_g do\n" }{MPLTEXT 1 0 89 " if j < i then A[i,j] := 0 elif j > i + deg_f then A[i,j] := 0 else A[i ,j] := F[j-i]; fi;\n" }{MPLTEXT 1 0 7 "od;od;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 39 "for i from deg_g +1 to deg_f+deg_g do\n" }{MPLTEXT 1 0 31 "for j from 1 to deg_f+deg_g do\n" }{MPLTEXT 1 0 107 "if j+deg_ g < i then A[i,j] := 0 elif j+deg_g > i + deg_f then A[i,j] := 0 else \+ A[i,j] := G[j+deg_g-i]; fi;\n" }{MPLTEXT 1 0 7 "od;od;\n" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eval(A);\n" } {MPLTEXT 1 0 29 "s:=subs(z=1,Determinant(A)):\n" }{MPLTEXT 1 0 24 "p : = a -> subs(x=a,s):\n" }{MPLTEXT 1 0 16 "degree(p(x),x):\n" }{MPLTEXT 1 0 6 "p(x);\n" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "X:=fsolve(p(x),x, complex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "for i from 1 to degree(p(x),x) do;\n" }{MPLTEXT 1 0 3 "i;\n" }{MPLTEXT 1 0 35 "v:=fsolve(f(X[i],y)=0,y,complex); \n" } {MPLTEXT 1 0 34 "w:=fsolve(g(X[i],y)=0,y,complex);\n" }{MPLTEXT 1 0 26 "for j from 1 to deg_f do \n" }{MPLTEXT 1 0 25 "for k from 1 to deg _g do\n" }{MPLTEXT 1 0 50 "if abs(v[j]-w[k]) < 0.0001 then Y[i] := v[j ] fi;\n" }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 4 "od;\n" }{MPLTEXT 1 0 1 "\n" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "for i from 1 to degree(p(x),x) do;\n" } {MPLTEXT 1 0 27 "print( [X[i] , Y[i] ] );\n" }{MPLTEXT 1 0 39 "abs(f (X[i],Y[i] ))+abs(g(X[i],Y[i] ));\n" }{MPLTEXT 1 0 3 "od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }