How to auto scale plot

I have this large equation involving the variables x, y and I need to plot it with all its important features. How? Is there an auto fit/zoom feature?

25448251500000 - 535526010000 x + 5077310000 x^2 - 36775800 x^3 +    250890 x^4 - (6199 x^5)/5 + (17 x^6)/5 - x^7/250 + 920347020000 y -    16448410100 x y + 122367000 x^2 y - 607718 x^3 y + (15694 x^4 y)/   5 - (7099 x^5 y)/500 + (9 x^6 y)/250 - (x^7 y)/25000 +    15128205050 y^2 - 220083300 x y^2 + 1275939 x^2 y^2 - (   19598 x^3 y^2)/5 + (8699 x^4 y^2)/1000 - (11 x^5 y^2)/500 + (   x^6 y^2)/50000 + 152047500 y^3 - 1691358 x y^3 + 7640 x^2 y^3 - (   96 x^3 y^3)/5 + (13 x^4 y^3)/500 - (x^5 y^3)/25000 + 1032409 y^4 - (   40191 x y^4)/5 + (119 x^2 y^4)/5 - (11 x^3 y^4)/250 + (x^4 y^4)/   50000 + (24094 y^5)/5 - (12299 x y^5)/500 + (9 x^2 y^5)/250 - (   x^3 y^5)/25000 + (14699 y^6)/1000 - (23 x y^6)/500 + (x^2 y^6)/   50000 + (13 y^7)/500 - (x y^7)/25000 + y^8/50000 +    5089650300000 Sin[x] - 107105202000 x Sin[x] +    1015462000 x^2 Sin[x] - 7355160 x^3 Sin[x] + 50178 x^4 Sin[x] -    6199/25 x^5 Sin[x] + 17/25 x^6 Sin[x] - (x^7 Sin[x])/1250 +    133172901000 y Sin[x] - 2218630000 x y Sin[x] +    14318780 x^2 y Sin[x] - 47992 x^3 y Sin[x] + 6299/50 x^4 y Sin[x] -    9/25 x^5 y Sin[x] + (x^6 y Sin[x])/2500 + 1693912000 y^2 Sin[x] -    21830360 x y^2 Sin[x] + 112000 x^2 y^2 Sin[x] -    304 x^3 y^2 Sin[x] + 12/25 x^4 y^2 Sin[x] - (x^5 y^2 Sin[x])/1250 +    13470380 y^3 Sin[x] - 119968 x y^3 Sin[x] + 408 x^2 y^3 Sin[x] -    4/5 x^3 y^3 Sin[x] + (x^4 y^3 Sin[x])/2500 + 71778 y^4 Sin[x] -    10199/25 x y^4 Sin[x] + 17/25 x^2 y^4 Sin[x] - (x^3 y^4 Sin[x])/   1250 + 12299/50 y^5 Sin[x] - 21/25 x y^5 Sin[x] + (x^2 y^5 Sin[x])/   2500 + 12/25 y^6 Sin[x] - (x y^6 Sin[x])/1250 + (y^7 Sin[x])/2500 ==   0 

Why some regions in parametric plot are in different color?

I’m using ParametricPlot, I felt there is only one singularity in those equations. But in the plot, it is showing one more region and when i change the range of radius, I’m getting different graphs. Why that region is formed other than at (-1,0)?. I’m I missing anything in math or is it a problem with code?

x21[x1_, y1_] = -(1/((1 + x1)^2 + y1^2)) + x1^2/((1 + x1)^2 + y1^2) + y1^2/((1 + x1)^2 + y1^2);      y21[x1_, y1_] = (2*y1)/((1 + x1)^2 + y1^2);      ParametricPlot[{x21[x1, y1], y21[x1, y1]}, Element[{x1, y1}, Refine[ImplicitRegion[0.01 <= x1^2 + y1^2, {x1, y1}],          Element[{x1, y1}, Reals]]], ImageSize -> Medium] 

enter image description here

Box plot con Python

Estoy realizando unas representaciones mediante box plots, los datos que yo tengo son los siguientes:

id     Times 1      480 2      391 3      269 4      205 5      157 6      99 7      70 8      35 9      21 

Entonces lo que hago para representar el diagrama de caja y bigote es crear un alista en la que habría 480 unos, 391 doses, etc

Lista = [1,1,1,1,…..,2,2,2,2,……….]

Habría alguna forma de indicarle esto sin tener que crear la lista?

El código con el que pinto esto es:

traces.append(go.Box(y=lista_frecuencias, name="Box plot", marker ={"size":4})) 

Is it possible to fit such a large range plot in mathematica?

I am trying to solve the coupled differential equation numerically with Mathematica. But the range of values are large so mathematica cannot give correct plot. Here is the code:

a = 4.75388*10^26; b = 5.424*10^-3; d = 4.75388*10^20; {X, Y} = {x, y} /.  NDSolve[{x'[ z] == -((a/z) (x[z] - b*z^(3/2) E^(-z)) (BesselK[1, z]/BesselK[2, z])),  y'[z] == ((d/z) (x[z] - b *z^(3/2) E^(-z)) (BesselK[1, z]/ BesselK[2, z]) - (a *z/4) (BesselK[1, z]) y[z]),  x[0.1] == 1.552*10^-4, y[0.1] == 10^(-9)}, {x, y}, z] //  FullSimplify // First LogLogPlot[{X[z], Y[z]}, {z, 0.1, 100}, PlotRange -> All] 

Calculation using Integrate & Plot take too long time & some error

I want to plot this equation.

enter image description here

mu, Eb, gamma, Eg are constant parameters and x is independent parameter.

\[Mu] := 1; Eb := 0.040; \[CapitalGamma] := 1;(*Fitting parameter*) Eg := 2.354 Ebj := Eg - Eb/j^2 c := 1.4 (*fitting parameter*) A[x_?NumericQ] := \[Mu]^2/x (Sum[(2 Eb /j^3 Sech[(x - Ebj)/\[CapitalGamma]]), {j, 1, 10}] +  Integrate[Sech[(x - e)/\[CapitalGamma]] 1/(1 - c (e - Eg))(*1/(1-  E[-2 Pi Sqrt[Eb/(e-Eg)]])*) , {e, Eg, 2.355}])  Plot[A[x], {x, 2.0, 3.5}] 

There are two problem.

  1. Above the equation, I omit (1/(1-E[-2 Pi Sqrt[Eb/(e-Eg)]])) part because of NIntegrate : non-numerical values error. (maybe divergence issue)
  2. Although I omit some part, It takes too long time to Plot.

How remove that error and save calculation time?

Thank you

How to avoid copy and paste 3D plot options?

I noticed that when I use Plot3D, ContourPlot3D, etc., I usually pass the same many options like this

Plot3D[{x + y, x - y}, {x, -1, 1}, {y, -1, 1},  AspectRatio -> 1, ImageSize -> Large, AxesLabel -> Automatic,  PlotRange -> Full, LabelStyle -> {FontSize -> 18}, BoxRatios -> {1, 1, 1}] 

and

ContourPlot3D[x + y - z == 0, {x, -3, 3}, {y, -3, 3}, {z, -3, 3},  AspectRatio -> 1, ImageSize -> Large, AxesLabel -> Automatic,  PlotRange -> Full, LabelStyle -> {FontSize -> 18}, BoxRatios -> {1, 1, 1}] 

Is there a way to avoid copy and paste all the options?

How to speed up the production of this plot?

This is a followup question to this question. From this two answers I can build the function sol[r][[1]][t0] as follows:

ClearAll["Global`*"] Md = 10^(-9); P = 10; R = 10^4; α = 10^(-2); ϵ = 10^(-4); γ = 10^(-2); ke = 0.02*(1 + 0.6625); k0 = 5*10^20; σ = 5.67*10^-8; Rg = 8315; c = 3*10^8; G = 6.67/10^11; M = 2.8*10^30;  Ωk[r_] := Sqrt[(G*M)/r^3]; μ = Md/(3*Pi); κ = (27*ke)/(2*σ) Rg/μ; ic = {Co[0] == 1, β[0] ==      0, Σ[      0] == (μ^(3/5)*Ωk[          r]^(2/5)) (κ^(-1/5)*α^(-4/5)*Co[0]^(-1/5)),    h[0] == (κ*α*Σ[0]^2*        Co[0]/Ωk[r]^5)^(1/6),    T[0] == (1/2)*(Ωk[r]*h[0])^2*(μ/        Rg)*(1/(1 + β[0])),    Kkr[0] == (k0*(Σ[0]*h[0]))/T[0]^(7/2)};  eq = {Σ'[      t] == -Σ[        t] + κ^(-1/5) α^(-4/5) μ^(3/          5) Ωk[r]^(2/5)*Co[t]^(-1/5),    h'[t] == -h[        t] + (κ α Σ[t]^2 Ωk[           r]^(-5) Co[t])^(1/6),    T'[t] == -T[t] +       1/2 μ/Rg (Ωk[r]^2 h[t]^2)/(1 + β[t]),    Kkr'[t] == -Kkr[t] + k0 Σ[t]/h[t]*T[t]^(-7/2),    β'[      t] == -β[t] + μ/        Rg (4 σ)/(3 c) T[t]^3/Σ[t] h[t],    Co'[t] == -Co[t] + (1 + β[t])^4*(1 + Kkr[t]/ke)};    t0 = 20; sol =   ParametricNDSolveValue[{eq, ic}, {Σ, h,     T}, {t, 0, t0}, {r}] 

Now I need to perform the following integral for a plot:

int[r_?NumericQ, t_?NumericQ] := sol[r][[1]][t0] r^3 Cos[2 CapitalOmega]k[r] t] F1[t_?NumericQ] := NIntegrate[int[r, t], {r, 10^6, 10^8}] Plot[F1[t], {t, 0, 3*10^3}] 

In a whole night this code has not produced the plot. I tried with memoization for the function int:

 int[r_?NumericQ, t_?NumericQ] := int[r,t]=sol[r][[1]][t0] r^3 Cos[2 CapitalOmega]k[r] t] 

but nothing has changed. I tried with with ParallelTable, but Mathematica says it cannot communicate with the kernels (or something like that) and a simple Table[F1[t],{t,0,1000,100}] still has not produced an output.

How can I produce the desired plot?