Timeline for Keeping Phase Factors in Sqrt
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11, 2021 at 22:38 | vote | accept | El Rafu | ||
| Jan 7, 2021 at 0:14 | comment | added | J. M.'s missing motivation | Have you seen this? | |
| Jan 6, 2021 at 19:38 | answer | added | Dominic | timeline score: 7 | |
| Jan 6, 2021 at 18:00 | history | tweeted | twitter.com/StackMma/status/1346879205594849283 | ||
| Jan 6, 2021 at 17:15 | history | edited | El Rafu | CC BY-SA 4.0 | Added example |
| Jan 6, 2021 at 15:55 | comment | added | Daniel Lichtblau | For the sum I'd say do the pedestrian thing: convert to complex (Cartesian), add, convert back to polar. | |
| Jan 6, 2021 at 15:55 | comment | added | Dominic | Can you post a simple example f with simple g and h which would exhibit the problem you're having? | |
| Jan 6, 2021 at 15:50 | comment | added | El Rafu | @Dominic No I'm trying to ParametricPlot a complex function $f$ that goes something like $f(z)=\sqrt{g(z)^4+h(z)^4}$ with complicated functions $g$ and $h$, and I get a wrong result because Mathematica kills all phase factors inside the $\sqrt{\cdot}$ before it can evaluate the Sqrt. The problem is that the range of Sqrt is only the right half complex plane, and I would like it to be the whole complex plane. | |
| Jan 6, 2021 at 15:37 | comment | added | Dominic | Are you asking how to plot the real or imaginary components of the multivalued function f(z)=z^a for a complex? | |
| Jan 6, 2021 at 15:15 | history | edited | El Rafu | CC BY-SA 4.0 | [Edit removed during grace period] |
| Jan 6, 2021 at 15:08 | comment | added | El Rafu | @DanielLichtblau Any ideas on how one would define the sum? | |
| Jan 6, 2021 at 14:54 | comment | added | El Rafu | @BobHanlon I agree, however even if I would manage to prevent Mathematica from evaluating $e^{2\pi i}=1$, Sqrt would give 1 since the real part of Sqrt is never negative. | |
| Jan 6, 2021 at 14:50 | comment | added | Bob Hanlon | Sqrt is not the issue since g[Exp[Pi I/2]] evaluates to 1 before the Sqrt sees its input. | |
| Jan 6, 2021 at 14:47 | comment | added | El Rafu | Thanks, I think this could work if all functions are defined this way by hand. Unfortunately I also use built in functions such as EllipticTheta and DedekindEta, which themselves transform under modular transformation with phases. | |
| Jan 6, 2021 at 14:43 | history | edited | El Rafu | CC BY-SA 4.0 | added 2 characters in body |
| Jan 6, 2021 at 14:37 | comment | added | Daniel Lichtblau | This is just an unpolished idea, but maybe work in (r,theta) coordinates, with power((r,theta),n) defined as (r^n,n*theta). I'm also curious to see if there are good ways to handle this question. | |
| Jan 6, 2021 at 14:29 | history | asked | El Rafu | CC BY-SA 4.0 |