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Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

1 vote
Accepted

How to assign the roots of transcendental equation into an equation

Note that when you compute roots, you don't make any assignments to α[n]. That means that, if it just sees α[n] by itself, Mathematica doesn't know anything about which α[n] gets assigned to which val …
thorimur's user avatar
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2 votes
0 answers
43 views

Superfluous un-simplifiable condition returned by Reduce

No real "problem" here, just wondering why this is happening and how one might force Mathematica to simplify this. Consider: Reduce[(-1)^n == 1, n \[Element] Reals] (* Out: (C[1] \[Element] Integers …
thorimur's user avatar
  • 9,080
8 votes
Accepted

Determination of a Function

This is actually a tiny bit tricky as far as I'm aware, in that there's not a built-in syntax that "just does it"! Maybe someone's aware of a way Mathematica can easily solve for symbolic functions li …
thorimur's user avatar
  • 9,080
2 votes
Accepted

How to visualize a Lagrange problem with Mathematica?

It's typically useful in Mathematica to translate mathematical notation of the form $x_i$ into x[i]. If you do that with \[Sigma][i] (which looks much better in a Mathematica notebook!), we could defi …
thorimur's user avatar
  • 9,080
1 vote

Plotting equation with some unknown parameters

In this particular case, you can view the solution set in the $z,m_0$ plane (i.e. allowing $m_0$ to vary) with ContourPlot: z0 = 4.8; ContourPlot[ Tan[z] == Sqrt[(1/(2 m0)) (z0/z)^2 - 1], {z, -5, 5} …
thorimur's user avatar
  • 9,080
3 votes
Accepted

How to get Sum of array of integers?

A couple things: Mathematica generally doesn't require you to initialize arrays before constructing them or anything like that; you can just construct them! Array[A, 3] does not give any definitions …
thorimur's user avatar
  • 9,080
2 votes
0 answers
49 views

What sorts of expressions can be Solve'd for?

We can Solve for expressions that match _Symbol, as in Solve[x^2+1 == 0, x]—but we can also solve for more general expressions, such as x[1] (Solve[x[1]^2+1 == 0, x[1]]) and Subscripts (Solve[Subscrip …
thorimur's user avatar
  • 9,080
1 vote

Elimination of the variables

Ok, I'm not sure why, but after rationalizing your equations, performing the elimination in sequence seemed to work: y = [email protected]; x = [email protected]; n0 = 0; n1 = 1; gE0 = 1/g0 - Sqrt …
thorimur's user avatar
  • 9,080