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-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Mo naco" 1 9 0 0 255 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Monaco" 1 9 255 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 17 "Curve From Points" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee n redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name c hangecoords has been redefined\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 258 55 "Find the circle through the points (1,2), (3,4), (5,7):" }} {EXCHG {PARA 0 "" 0 "" {TEXT 256 9 "Solution:" }{TEXT 259 59 "\nWe wan t to fit a polynomial x^2 + y^2+ a x + b y + c = 0;" }{TEXT 257 1 "\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "v := vector([x^2 +y^2, x, y, 1 \+ ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%'vectorG6#7&,&*$)%\"xG \"\"#\"\"\"F.*$)%\"yGF-F.F.F,F1F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "v1 := vector([1^2 + 2^2, 1, 2, 1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v1G-%'vectorG6#7&\"\"&\"\"\"\"\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "v2 := vector([3^2 + 4^2, 3,4,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v2G-%'vectorG6#7&\"#D\"\"$\"\"%\" \"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "v3 := vector([5^2+7 ^2,5,7,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#v3G-%'vectorG6#7&\"# u\"\"&\"\"(\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A :=st ackmatrix(v,v1,v2,v3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'mat rixG6#7&7&,&*$)%\"xG\"\"#\"\"\"F/*$)%\"yGF.F/F/F-F2F/7&\"\"&F/F.F/7&\" #D\"\"$\"\"%F/7&\"#uF4\"\"(F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eqn := det(A) = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,, *$)%\"xG\"\"#\"\"\"F**&F*F+)%\"yGF*F+F+*&\"#QF+F)F+F+*&\"#eF+F.F+!\"\" \"#oF+\"\"!" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Graphical Displa y" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "gr := implicitplot(eqn, x=-40..40,y=-40..40, grid=[20,20]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display(gr, scaling=constrained,thickness=3);" }} {PARA 13 "" 1 "" {GLPLOT2D 212 192 192 {PLOTDATA 2 "6&-%'CURVESG6W7$7$ $!3)4@%ot%*y:B!#;$\"3aP&G?<=]o&!#<7$$!3;Tf)*fL'pN#F*$\"3u,Uot%*y:jF-7$ 7$$!3_Tf)*fL'pN#F*F17$$!3gD^[C*3GQ#F*$\"3AYLp\")R)f)pF-7$7$$!3_qli\\#R $>DF*$\"3Wnt%*y:j_5F*F77$F=7$$!3u*y:j_5na#F*$\"3-Y*y:j_NG\"F*7$7$$!3ql $)f!*pCpDF*$\"3q9j_5Uot9F*FC7$FI7$$!32MJK3'fk`#F*$\"3yP_;XVN%p\"F*7$7$ $!3vF8!He'o1DF*$\"3%>E0@%ot%*=F*FO7$FU7$$!3me._oIj]CF*$\"3i49%pV!eH?F* 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