mathpix | Query the mathpix API to convert math images to LaTeX | Math library

I am not sure whether this is an iOS issue or whether this is an issue with Kivy or even with Python (e.g. https://bugs.python.org/issue37788), but I am experiencing some problems with threading.

I have built an iPad app using the Kivy framework that makes several calls to an API, and uses the threading module to asynchronously make requests. Below is the code that handles the API requests:

I want to write the following function to wolframalpha

which means this function is defined by a different expression for x<0, 0<=x<=1 and x>1 by the expression above.

i found this answer which Brought me closer to the answer but not yet.
f(x,y) = cos(1/x) for x<0 , how to continue for the two different parts?

by the way, using Mathpix I could generate LATEX representation for this equation from the photo which wolfram should understand, but apparently not when splitting the function for different expression per domain...

how can I write this function to wolframAlpha?

Mathpix can automatically convert scanned formulas into LaTeX math code.

Is there a similar tool that automatically converts scanned formulas or LaTeX math-mode equations (code) into python (numpy) code?

I want to remove a specific pattern which starts with either \( or with \\( and ends with /) or //). There may or may not be a space before and after the pattern i.e the pattern can be in the starting or on the end too.

But the real problem is that There is very useful data inside a child pattern which starts with \text { preserve this data } too and I want to preserve that thing.

For example:

I am currently implementing a newton-raphson root-finding method that guarantees convergence in a multidimensional setting (not homework!). Currently it finds the root for x, but not for y. I also observed a strange behaviour where f1 and f2 get equalised to the same number. For example, after 2000 iterations both are ≈ 560.0. I think f1 and f2 both need to approach 0. At least, this is how it works using the classical newton-raphson method.

Can anyone see what could cause this? I need a second pair of eyes.

paper: https://arxiv.org/pdf/1809.04495.pdf and addendum: https://arxiv.org/pdf/1809.04358.pdf (section D.2 -> includes the attached math)

Note: U, L are the upper and lower triangular matrices of the Jacobian (matrix of partial derivatives).

My current implementation looks like the following (Eigen is used, but it's pretty clear what it does). Currently something strange