Recursion Equation – Mathematica Stack Exchange

The output from Mathematica is just a copy of the input. What am I doing wrong?

RSolve(r1((n + 1)*t) == 1/2 (r1(n*t) + 
r4(n*t) + (r1(n*t) - r4(n*t)) Cosh(
  2 (-1 + n)* t) + (-r2(n*t) + r3(n*t)) Sinh(2 t - 2 n *t)),r2((n + 1)*t) == 1/2 (r2(n*t) + r3(n*t) + (r2(n*t) - r3(n*t)) Cosh(
   2 (-1 + n) *t) + (-r1(n*t) + r4(n*t)) Sinh(2 t - 2 n* t)), r3((n + 1)*t) == 1/2 (r2(n*t) + 
 r3(n*t) + (-r2(n*t) + r3(n*t)) Cosh(
   2 (-1 + n)* t) + (r1(n*t) - r4(n*t)) Sinh(2 t - 2 n *t)), r4((n + 1)*t) == 1/2 (r1(n*t) + r4(n*t) + (-r1(n*t) + r4(n*t)) Cosh(2 (-1 + n) *t) + (r2(n*t) - r3(n*t)) Sinh(2 t - 2 n *t)), r1(0) == 1, r2(0) == r3(0) == r4(0) == 0}, {r1(n), r2(n), r3(n), r4(n)}, n )

Numerical Integration – Can I numerically solve this equation in Mathematica?

I have these few equations:

$ partial_ mu partial ^ mu z ^ i + G ^ {i bar {p}} ( partial_j G_ {k bar {p}}) partial_ mu z ^ j partial ^ mu z ^ k + G ^ {i bar {j}} ( partial _ { bar {j}} G_ {k bar {l}}) partial mu z ^ k partial ^ mu z ^ { bar {l}} = 0
$

and

$ partial_ mu partial ^ mu z ^ { bar {i}} + G ^ {p bar {i}} ( partial _ { bar {j}} G _ { bar {k} p }) partial_ mu z ^ { bar {j}} partial ^ mu z ^ { bar {k}} + G ^ { bar {i} j} ( partial_j G_ {k bar {l }}) partial_ mu z ^ k partial ^ mu z ^ { bar {l}} = 0
$

They are the equation of motion of z (scalar field) and its complex conjugate on complex coordinates. $ mu = $ 0,1,2,3 (Lorentz index) and $ i, j, … = 1,2, …, $ to any values

Can I solve these equations in Mathematica to get $ z ^ i $ and the matrix $ G_ {ij} $ also numerical?

Front End – The Mathematica 12.0 interface looks blurry and pixelated for Windows 10

For some reason, the Mathematica for Mathematica 12.0 interface on Windows 10 looks extremely pixelated and blurry.

I saw some posts in this forum for a similar issue, but they all came from a few years ago, and it was discovered that there was a problem where Mathematica was not known for high DPI values ​​- but that was before 5 years!

Is this a known problem and is there a workaround / solution?

Why does Mathematica deliver this output?

I calculate the limit

$$ lim_ {n to infty} a ^ {1 / n} $$

Use the code:

Assuming(Element(a,Reals)&& a>0, Limit(a^(1/n),n->Infinity) )

The expected value is 1. But if I give the input

Assuming(Element(a,Reals)&& a<0, Limit(a^(1/n),n->Infinity) )

This again results in the output 1. I do not know why. Any suggestion or clarification of this problem would be appreciated.

Plotting – Can Mathematica create zoombare plots with embedded text of different sizes?

I'm trying to figure out how to do something with MMa that's pretty easy for Matlab. I Some data points that each map a numeric parameter to a point in 2D space. I have to draw the parameter values ​​to the point in 2D. The following code does so much, even if it is a bit awkward. The & # 39; data & # 39; are simulated with random numbers.

data = RandomReal[1, {200, 2}];
b = Table[{Text[i, data[[i]]]}, {i, 1, Length[data]}];
ListPlot[{0, 0}, PlotStyle -> PointSize[.004], PlotRange -> {{0, 1}, {0, 1}}, Epilog -> b]

So, first of all, there is the ability to ONLY draw when I'm in this & # 39; epilogue & # 39; b without having to falsify this {0,0} data point. I can only get ListPlot to test a plot as an epilogue, and only epilogs are plotted after some data.

Second, is there a way to create a chart that I can zoom into, changing the font size to be legible? If you run the above code, the plot is too clear to read, but if I could zoom in and resize it, it would be readable wherever I look.

Differential Equations – Mathematica 12: Avoid crashes when using NDSolve in a large domain

I have a bunch of linked PDEs that I want to solve numerically with Mathematica (11.3 or 12.0).
The problem is that I have to solve in a large area to make sure there are no edge effects.
Mathematica seems to have problems with such calculations (probably due to my RAM only). Therefore, I decided to split the problem into small time intervals and export only parts of the solution and start with the last solution as a new initial condition.
Now Mathematica crashes in this calculation, z. After 30 passes of the loop. Why so? Is there a way to avoid that?

Here is the code:

$HistoryLength = 0; (* save *)
(*PDEs*)
pde11 := 
  D(pp(t, x), t) == 
   1.*Laplacian(pp(t, x), {x}) + 
    pp(t, x)*(1 - c11*pp(t, x) - z(t, x)/(1 + pp(t, x)^2));
pde21 := D(z(t, x), t) == 
   1.*Laplacian(z(t, x), {x}) + 
    z(t, x)*(eps*pp(t, x)/(1 + pp(t, x)^2) - m);
(*Initial conditions*)
lo = 7498;
hi = 7502;
domlen = 15000;
ic11(x_) := Which(x > lo && x < hi, 6, True, 0);
ic21(x_) := Which(x < hi && x > lo, 0.5, True, 1/c11);
eps = 1.4434; m = 0.3; c11 = 0.1732;
tfin = 30;
For(i = 0, i <= IntegerPart(6000/30), i++,
 Print(i);
 sol1d = NDSolve({pde11, pde21, z(0, x) == ic11(x), 
    pp(0, x) == ic21(x)}, {pp, z}, {t, 0, tfin}, {x, 0, domlen}, 
   MaxStepSize -> 0.1);
 resultsForExport = {};
 For(j = 0, j < tfin, j = j + 0.1,
  resultsForExport = 
    Append(resultsForExport, Evaluate(z(j, 7500)) /. sol1d);
  );
 resultsForExport = Flatten(resultsForExport);
 Export("largedomain" <> ToString(i) <> ".dat", resultsForExport);
 ic11(x_) := sol1d((1, 2, 2))(tfin, x);
 ic21(x_) := sol1d((1, 1, 2))(tfin, x);
 )

I suspect my expedition is not too elegant – I'm sorry.
I have done this several times now (takes a long time) and it keeps crashing $ i = 20 $ and $ i = 30 $,

All thoughts / help / workarounds / comments are appreciated.

Sum of n sums, permutations of indices, how to write them in Mathematica?

I was wondering how to write a function $ F (r, q, n, f) $ in Mathematica, defined as follows:

$$ F (r, q, n, f): = sum_ {i_0 = 1} ^ qf (i_0) biggl ( sum_ {i_1 = i_0 + 1} ^ {q + 1} f (i_1) biggl ( sum_ {i_2 = i_1 + 1} ^ {q + 2} f (i_2) Bigl ( ldots ( sum_ {i_n = i_ {n-1} +1} ^ {q + n} f (i_n) ) ldots Bigl) biggl) Biggl) $$
it.
$$ sum_ {i_0 = 1} ^ 2 f (i_0) Biggl ( sum_ {i_1 = i_0 + 1} ^ {3} f (i_1) biggl ( sum_ {i_2 = i_1 + 1} ^ {4 } f (i_2) biggl) biggl) = f (1) f (2) f (3) + f (1) f (2) f (4) + f (1) f (3) f (4) + + f (2) f (3) f (4) $$

Is there already an operator that can be used this way?

When trying to write this function on Mathematica, I realized that the "recursion" is variable and I do not know how to program in this case.

Thank you very much

$ $

$ $

another example

$$ sum_ {i_0 = 1} ^ 1 f (i_0) Biggl ( sum_ {i_1 = i_0 + 1} ^ {2} f (i_1) biggl ( sum_ {i_2 = i_1 + 1} ^ {3 } f (i_2) ( sum_ {i_3 = i_2 + 1} ^ {4} f (i_2)) biggl) biggl) = f (1) f (2) f (3) f (4) $$

System – Mathematica 12 blurred with High DPI 4k screen

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What is the difference between Mathematica and WolframAlpha Notebook Edition?

I have a license for Mathematica through my college. Today I downloaded and installed a trial version of WolframAlpha Notebook Edition. According to this support page, the notebook should look like this:

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On my computer (an iMac), new notebooks look like this:

Enter image description here

As far as I know, a user can use WolframAlpha Notebook Edition to enter and execute regular Mathematica commands. Apart from the fact that I have WolfraAlpha Notebook Edition on top of my notebook, I can not tell the difference between Mathematica and WolfraAlpha Notebook Edition.

Maybe it's easier for students to download and buy WolframAlpha Notebook Edition. Why use WolframAlpha Notebook Edition? I have read this blog post and still do not know why to use it.

Input – What is the correct method for percent multiplication in Mathematica?

I am very new to Mathematica and would like to calculate percentage multiplications. See picture below. in the In[3], I pressed space after this 50% and then pressed 80%, Mathematica automatically added the multiplication sign. in the In[4]I pressed manually *, the multiplication sign. Both do not seem to work. Where is the problem? Many thanks.

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