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Questions on the numerical functions of Mathematica, implementing numerical methods and numerical computing with Mathematica.

2
votes
1answer
In Mathematica, the Weierstrass $\wp$-function is expressed by WeierstrassP[u + I v, {g₂, g₃}] where g₂ and g₃ are the invariants and Mathematica can convert the two half-periods $\omega_1$ and $\ …
asked Jul 17 '15 by Benighted
18
votes
1answer
Mathematica doesn't seem to have built-in tools to deal with the Eisenstein series: $$\begin{align*} E_{2}(\tau)&= 1-24 \sum_{n=1}^{\infty} \frac{n e^{2 \pi i n \tau}}{1-e^{2 \pi i n \tau}}\\ E_{4}(\ …
asked Jul 29 '15 by Benighted
3
votes
2answers
Given the function $y=\sin x$ defined over the region $-\pi \leq x \leq \pi$, I need to implement a "do loop" such that I sweep over 100 or so points $-1 \leq y \leq 1$ and find precisely the two $x$ …
asked Jul 27 '15 by Benighted
1
vote
0answers
When plotting the Eisenstein Series (great information here Eisenstein Series in Mathematica?) you observe highly non-trivial branch cut behavior close to the real axis. This makes the numerics
asked May 15 '16 by Benighted
1
vote
0answers
I have a relatively complicated function of two variables F[x,y] whose zero locus contains a number of intersecting paths in the $x,y$-plane. A problem I've been struggling with for a great while now …
asked Jun 16 '16 by Benighted
1
vote
0answers
. Numerics is not my strong suit, but there seems to be two ways potentially of doing this: (I) First use a fit to find approximate closed form the the curve. (This isn't ideal for me because in my case …
asked Aug 6 '16 by Benighted
1
vote
0answers
I have the following code: f[x_, y_, p_] = ( p (E^( π/y) x + 2 x Cosh[(2 π x)/y] - 2 Sinh[(2 π x)/y]))/(y (E^(π/y) + 2 Cosh[(2 π x)/y])); y1 = 1/11; t1 = I*y1; p1 = 1; xf = NArgMax[{Abs[f …
asked Aug 10 '15 by Benighted