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| It is subtle. If you write `y'` for the velocity, then In[35]:= D[y', y] Out[35]= 0 & because the internal form of `y'` is `Derivative[1][y]`, which does contain `y`. My advice is either to introduce the time variable throughout ... |
| You can always rescale the independent variable, for example this way: independentVariableChange = (a*t + b == x) dependentVariableChange = (g[t] == f[x]) dependentVariableChange /. Solve[independentVariableChange, x][[1]] % /.... |
| It looks like a bug. The correct value for the sum seems to be the absolute value of the formula given by Mathematica: s[n_] = Abs[Sum[(1 - k/(n + 2))^(1/n), {k, 1, n}]]; Table[Abs[s[n] - Sum[(1 - k/(n + 2))^(1/n), {k, 1, n}]], {n, 1, ... |
| No need for `InverseFunction`. Simply reverse the pairs of points to interpolate: Plot[x + Sin[x], {x, 0, 10}] ptsReversed = Table[N[{x + Sin[x], x}], {x, 0, 10, 1/10}]; ListPlot@ptsReversed inv = Interpolation[ptsReversed,... |
| You are not giving a value for `L`. |
| You may have a look at my old package [CurvesGraphics6][1] . Much of it has been gradually superseded by built-in functionality, but not everything yet. `PhasePlot` may help for your problem. [1]: https://www.dimi.uniud.it/gorni/Mma |
| I am baffled too. Last week I had two polyhedra with rational coordinates, whose `RegionIntersection` was floating-point. One would be led to think that geometric computing is done with floats. Now we see an example that goes in the opposite... |
| Floating point numbers are not very suitable for this calculation. I would do it with exact numbers: Reduce[0 |
| Here is a way: DynamicModule[{p1, pwr}, pwr[pt_List, k_Integer] := ReIm[({1, I} . pt)^k]; Manipulate[ Row[{Graphics[{Point[p1]}, PlotRange -> 2, Frame -> True], Graphics[{Point[pwr[p1, 2]]}, PlotRange -> 2, Frame... |
| You can make a replacement in the output using `RealAbs` instead of `Abs`, but then check that the result is correct: f = 1/(x (x - 1)); Integrate[f, x] /. Log[u_] :> Log[RealAbs[u]] FullSimplify[%, Element[x, Reals]] /. Abs ->... |