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1

One classic way to depict the effect of a plane linear transformation is to see what it does to a stylized drawing of a cat's face. First, a utility to transform points and a function to reflect across the vertical axis: pointQ[p_] := VectorQ[p, NumberQ] && Length[p] == 2 image[T_, object_] := object /. pt_?pointQ :> T[pt] reflect[p_?PointQ] ...


1

Something like this? g = FiniteGroupData[{"DihedralGroup", 4}, "CayleyGraph"]; g1 = SetProperty[g, VertexLabels -> "Name"]; l = PropertyValue[{g1, #}, VertexCoordinates] & /@ VertexList[g1]; m = {{2, 1}, {-1, 2}}; Framed@Row[{g1, SetProperty[g1, VertexCoordinates -> (m.# & /@ l)]}]


10

Generally - arbitrary-angle layout: Rotate[ ... /. x_Framed -> Rotate[x, -angle], angle] Now you can do it like this: Rotate[ToExpression@ToBoxes@TreeForm[a + b^2 + c^3 + d] /. x_Framed -> Rotate[x, -Pi/2], Pi/2] Or like this: P.S. ========================= Manipulate code for the record Manipulate[Show[Rasterize@ ...


1

I don't know if this is by any means what you're looking for, but you can use VertexCoordinateRules to determine the coordinates at which vertices should be placed: TreeForm[a + b^2 + c^3 + d, VertexCoordinateRules -> {{1, 4}, {2, 8}, {3, 8}, {4, 10}, {4, 6}, {3, 0}, {4, 3}, {4, -2}, {2, 0}}]


4

As b.gatessucks comments you can use inset. You can also use PlotLegends and customize, e.g. tab = nlm["ParameterTable"] plt = Show[ Plot[nlm[t], {t, 0, 5}, PlotRange -> Full, PlotLegends -> Placed[LineLegend[{Blue}, {Normal@nlm[t]}, LegendMarkerSize -> {50, 3}, LegendFunction -> (Column[{#, tab}, Frame -> True] ...


3

In the upcoming version (10?) there are useful BooleanRegion functions: {a, b} = {Disk[{-1/3, 0}, 1], Disk[{1/3, 0}, 1]}; RegionPlot@BooleanRegion[Xor, {a, b}] {a, b} = {Disk[{0, 0}, 2], Disk[{2, 0}, 2]}; RegionPlot[RegionDifference[a, b], Epilog -> {EdgeForm@Black, FaceForm@None, a, b}] Furthermore, regions can be more easily highlighted: {a, ...



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