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{MPLTEXT 0 21 65 "Addition de deux points P et Q sur une courbe ellipt
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{PARA 0 "" 0 "" {MPLTEXT 0 21 41 "P+Q sur la courbe elliptique y^2=x^3
+ax+b" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 35 "Add2P := proc(a,b,P1,P2)           " }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 33 "  local lambda,x1,x2,x3,y1,y2,y3:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 37 "  if P1=infinity then RETURN(P2): fi;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "  if P2=infinity then RETURN(P1): f
i;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "  x1:=op(1,P1):y1:=op(2,P1):x
2:=op(1,P2):y2:=op(2,P2);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "  if x
1=x2 and y1=-y2 then RETURN(infinity): fi;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "  if x1<>x2 then lambda:=(y1-y2)/(x1-x2):" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 38 "   else lambda:=(3*x1^2+a)/(2*y1): fi;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "  x3:=-x1-x2+lambda^2:y3:=-(lambda*
(x3-x1)+y1):RETURN([x3,y3]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " end
:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 7 "Exemple" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 25 "Add2P(-4,1,[-1,2],[0,1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$\"\"#\"\"\"" }}}}{MARK "1 0 0" 65 }{VIEWOPTS 1 1 0 1 
1 1803 }