7
You could modify the formatting rules for the variables:
xy /: MakeBoxes[xy, StandardForm] := TagBox["xy", #&, SyntaxForm->"*"]
Δx /: MakeBoxes[Δx, StandardForm] := TagBox["Δx", #&, SyntaxForm->"*"]
Then:
Expand[(2x+Δx)^2]
Expand[(2xy+Δx)^2]
Solve[Δx+2 a x==(a+Δx)^2,x]
If you really want parentheses ...
6
We can query GeoProjectionData for the complete options for the default form of the specified projection:
GeoProjectionData["Orthographic"]
{"Orthographic", {"Centering" -> {0, 0},"GridOrigin" -> {0, 0},"ReferenceModel" -> 1}}
This suggests we can pass a "Centering" sub-option to achieve ...
5
xy /: MakeBoxes[xy, _] := RowBox[{"(", "xy", ")"}]
Δx /: MakeBoxes[Δx, _] := RowBox[{"(", "Δx", ")"}]
Expand[(2 x + Δx)^2]
Expand[(2 xy + Δx)^2]
Solve[Δx + 2 a x == (a + Δx)^2, x]
4
This can be done by the command
FindInstance[ Binomial[n - 1, 2] - 2 ((Binomial[m - 1, 2]) + (n - m) (m - 1) - 1) <= 0 &&
m >= 4 && n >= 3.41421*m, {m, n}, Reals]
(*{{m -> 537343., n -> 1.8346*10^6}}*)
4
Start from here:
σ = 1;
λ = 1/2;
ν = 1;
s1 = θ Cot[θ] + I ν θ;
eqn = σ + (λ s1);
ParametricPlot[{Re[eqn], Im[eqn]}, {θ, -3.5, 3.5}, AspectRatio -> 1]
2
Some bells and whistles.
Clear["Global`*"]
Since the "parameters ... are adjustable" use Manipulate.
Manipulate[
Module[{s1, θ, eqn},
s1 = θ*Cot[θ] + I*ν*θ;
eqn = σ + (λ*s1);
ParametricPlot[
{Re[eqn], Im[eqn]},
{θ, -Pi, Pi},
PlotRange -> {{-5, 3.5}, {-4.25, 4.25}},
AspectRatio -> 1]],
{{σ, 1}, 0, 2, 0.01, ...
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