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| It's a long-standing gotcha which amounts to `MatrixForm` being (arguably) badly designed. If one uses e.g. `InputForm` or `FullForm` then the formatting is applied and the wrapper disappears. The `MatrixForm` wrapper alas does not disappear. So... |
| If `Solve` could handle that system, `DSolve` would have used that result instead of giving what it did. You might have more success using `ParametricNDSolve` since that result can be instantiated with specific parameter values. |
| What I mean is that you provided no detail as to what you would like added. Community threads are often closed in such situations. I was suggesting that you add sufficient detail so that this one remains open. Also you might consider reaching out... |
| Might want to use `Together`. In[3]:= Together[f[x]] (* Out[3]= 1/4 (1 + x) (a[1] + 2 x a[1] - 2 x^3 a[1] - x^4 a[1] - a[1]^3 - 2 x a[1]^3 + 2 x^3 a[1]^3 + x^4 a[1]^3 + 7 a[2] + 4 x a[2] + 6 x^2 a[2] - x^4 a[2] + 3... |
| To summarize, the equation you posted had `elctrn[eV]==0` whereas, as Gianluca Gorni shows, you most likely intended it to be `elctrn[eV]==6.14 10^-9`. Which gives a solution very close to the one you had obtained by plugging in possible values. |
| Please provide a concrete example of a problem you wish to solve. For example, a pair of such algebras for which you want to check isomorphism. Also you might want to state what you have in mind for derivations. |
| There is this Demonstration. https://demonstrations.wolfram.com/LUDecomposition/ And this Wolfram U course. https://www.wolfram.com/broadcast/video.php?c=105&p=30&ob=title&o=ASC&v=3327 But maybe one can modify the row reduction step-my-step... |
| [Rule 110 is Turing complete](https://en.m.wikipedia.org/wiki/Rule_110). Does that answer your question? |
| There is no actual definition of `listPower` in that notebook. Is it intended to be an image? |
| I do not know whether the step-by-step should work on this. One reasonable way to see why the limit is as claimed is to expand `(x + E^x)^(1/x)` as a series of order 1 at the origin. |