Showing posts with label visualisering. Show all posts
Showing posts with label visualisering. Show all posts

Friday, December 26, 2008

Nuttet 3d visualisering af elliptisk kurve, med mulighed for selv at skrue på parametre

Meget meget nuttet tredimensionel demonstration af elliptiske kurver. Anvend i Mathematica følgende kode:
(eller se det online i linket under koden)

Manipulate[{F, G} = { x^3 - a y^2 + b x y^2 + c x^2 y, A x + B};
Plot3D[{F, G}, {x, -8, 10}, {y, -30, 30}, PlotRange -> All,
PlotStyle -> {LightBlue, Green},
MeshFunctions -> Function @@@ {{{x, y, z}, (F - G)}}, Mesh -> {{0}},
MeshStyle -> Directive[{Red, Thick}],
Epilog -> {Inset[
Graphics[
Text[Style[
Column[{"intersection curve",
Row[{a y^2, " = ", x^3 + b x y^2 + c x^2 y - A x - B}]},
Center], {12, 12}, Black]], ImageSize -> 240], {Center,
Top}], Inset[
Graphics[
Text[Style[
Column[{"surface", Row[{Style["z", Italic], " = ", F}]}], {12,
12}, Black]], ImageSize -> 200], {0.3, .1}],
Inset[Graphics[
Text[Style[
Column[{"plane", Row[{Style["z", Italic], " = ", G}]}], {12,
12}, Black]], ImageSize -> 150], {0.85, .1}]}, Axes -> None,
PlotPoints -> 45, Boxed -> False, ImageSize -> {375, 375},
SphericalRegion -> True, ViewAngle -> \[Pi]/6],
Style["parameters of the plane", Bold],
Style[Row[{"z = A x + B"}], Bold],
{{A, 11, "A (rotation)"}, -10, 25, 0.5, Appearance -> "Labeled",
ImageSize -> Tiny},
{{B, 12, "B (translation)"}, -20, 50, .01, Appearance -> "Labeled",
ImageSize -> Tiny},
Style["\nparameters of the surface", Bold],
Style["z = \!\(\*SuperscriptBox[\"x\", \"2\"]\)-a \
\!\(\*SuperscriptBox[\"y\", \"2\"]\)+b x \!\(\*SuperscriptBox[\"y\", \
\"2\"]\) + c \!\(\*SuperscriptBox[\"x\", \"2\"]\) y", Bold],
{{a, -1, "a"}, -2, 2, 0.01, Appearance -> "Labeled",
ImageSize -> Tiny},
{{b, 0, "b"}, -2, 2, 0.05, Appearance -> "Labeled",
ImageSize -> Tiny},
{{c, 0, "c"}, -5, 5, 0.2, Appearance -> "Labeled", ImageSize -> Tiny},
Delimiter, TrackedSymbols -> Manipulate, ControlPlacement -> Left,
SynchronousUpdating -> False]

http://demonstrations.wolfram.com/RealEllipticCurves/