# I've tried too many times to get ChatGPT translate equations (from scientific paper) to code with Wolfram. I'm desperate

I’m currently doing my master in physics. I need this for my thesis.

This is my very first post, I wouldn’t ask for help if I wasn’t hopeless (I’m not native in English). I apologize beborehand if I commit mistakes presenting this issue. The folowing is my prompt:
(paper DOI: 10.1049/iet-smt.2017.0221)

I have twelve equations related to the ion mobility spectrum.

I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?

{Equations:

1-. $I =  \begin{cases} \frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\ e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0  \end{cases}$


2-. $\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$

3-. $I =  \begin{cases} \sum_{i=1}^N \frac{2 \pi e n_i \mu_i L U}{\ln \left( r_2/r_1 \right)}, & m=0 \\ \sum_{i=1}^m e n_i \pi\left( r_2^2 - r_1^2 \right) u_0 + \sum_{i=m+1}^N \frac{2 \pi e n_i \mu_i L U}{\ln \left( r_2/r_1 \right)}, & m=1,2,3, \ldots, N  \end{cases}$


4-. $n_m = \frac{\sum_{i=m}^N n_i \mu_i - \sum_{i=m+1}^N n_i \mu_i}{\mu_m}$

5-. $\mu_m = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU_m}$

6-. $n_m =  \begin{cases}  \frac{\ln{r_2/r_1}}{2\pi e L}\frac{\Delta I /\Delta U \left|_{U_{m-1} \leq U \leq U_m} \right. - \Delta I /\Delta U \left|_{U_m \leq U \leq U_{m+1}} \right.}{\mu_m}, & m=1,2,3, \ldots, N-1 \\ \frac{\ln{r_2/r_1}}{2\pi e L}\frac{\Delta I /\Delta U \left|_{U_{m-1} \leq U \leq U_m} \right.}{\mu_m}, & m=N  \end{cases}$


7-. $n_m =  \begin{cases}  \frac{U_m}{e u_0 \pi\left(r_2^2-r_1^2\right)}\left(\left.\frac{\Delta I}{\Delta U}\right|_{U_{m-1} \leq U \leq U_m}-\left.\frac{\Delta I}{\Delta U}\right|_{U_m \leq U \leq U_{m+1}}\right)\!\!, & m=1,2,3, \ldots, N-1 \\ \left.\frac{U_m}{e u_0 \pi\left(r_2^2-r_1^2\right)} \frac{\Delta I}{\Delta U}\right|_{U_{m-1} \leq U \leq U_m}, & m=N  \end{cases}$


8-. $\mu_{\text {ave}} = \frac{\sum_{i=1}^N n_i \mu_i}{\sum_{i=1}^N n_i}$

9-. $\mu_\mathrm{ave} = \frac{u_0\left( r_2^2 - r_1^2 \right) \ln(r_2/r_1)}{2L} \frac{\Delta I /\left.\!\! \Delta U\right|_{U_0 \leq U \leq U_1}}{I_N}$

10-. $U_\mathrm{sat} = \frac{I_N}{\Delta I /\left.\!\! \Delta U\right|_{U_0 \leq U \leq U_1}}$

11-. $U_\mathrm{sat} = \frac{\sum_{i=1}^N I_i}{\sum_{i=1}^N I_i/U_{0i}}$

12-. $\mu_\mathrm{ave} = \frac{u_0\left( r_2^2 - r_1^2 \right) \ln(r_2/r_1)}{2LU_\mathrm{sat}}$

}

This equations are precisely for that, finding number densities $n_i$​ and mobilities $μ_i$ given data of Voltaje vs Current curves measured with a Gerdien condenser. I have my own data and I need the code to compute it.

Please obtain the context you need from this PDF doc_id: "9e8c573e-3a21-49e6-8276-7b6d5ffd30df"


It simple gets nowhere no matter how I present the issue. Thank you so much for your help!

Welcome to the forum.

First off it would help if we have a faithful reproduction of the prompt as entered. While you did provide the prompt in your post, when it appears to us in this Discourse forum it is not one continuous flow.

If instead you could do this when pasting the prompt it might help us.

Discourse uses Markdown and one of the Markdown delimiters is the triple backtick, AKA Fenced Code Blocks




It is a fence delimiter meaning you need two of them to act like a fence around what they contain, e.g.


I have twelve equations related to the ion mobility spectrum.
I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?
{Equations:
1-. $I = begin{cases} \frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\ e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0 \end{cases}$
2-. $\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$



So the above is what it would look like when using the Discourse editor and this is how it would appear to others in Discourse

I have twelve equations related to the ion mobility spectrum.
I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?
{Equations:
1-. $I = begin{cases} \frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\ e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0 \end{cases}$
2-. $\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$


The next thing about the triple backtick is that you can also describe the data in the fence, this makes use of https://highlightjs.org/ and can get rather detailed but for your use of the triple backtick just use plaintext, e.g.

plaintext
I have twelve equations related to the ion mobility spectrum.
I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?
{Equations:
1-. $I = begin{cases} \frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\ e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0 \end{cases}$
2-. $\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$



which will appear in Discourse as

I have twelve equations related to the ion mobility spectrum.
I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?
{Equations:
1-. $I = begin{cases} \frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\ e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0 \end{cases}$
2-. $\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$


Once we have a faithful reproduction of your prompt then we can work on your prompt.

Please obtain the context you need from this PDF doc_id: "9e8c573e-3a21-49e6-8276-7b6d5ffd30df"


I have never heard of a doc_id. I would have expected a DOI but that is not a DOI.
Any way, ChatGPT can not access anything external

Prompt
ChatGPT May 24 Version

PDF doc_id: "9e8c573e-3a21-49e6-8276-7b6d5ffd30df"


Completion

I apologize, but as an AI text-based model, I don't have direct access to files or the ability to retrieve specific documents. If you have any questions or need assistance with a topic, I'll be happy to help you to the best of my abilities using the information I have been trained on.


So that will not help ChatGPT.

Since I am not an expert in ion mobility I tried this to see if ChatGPT with the Wolfram plugin installed could fill in the gaps, it could not but it seems to be some progress.

Prompt
ChatGPT May 24 Version

$\mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU}$

Demonstrate this with Wolfram Alpha using data you created. If possible generate a graph that depicts the ion mobility spectrum.


Completion

The equation you've provided seems to be related to ion mobility, but it's not a standard form that I recognize. Ion mobility ($$\mu$$) is typically defined as the velocity of an ion under an electric field, and it's usually given by the equation $$\mu = \frac{v}{E}$$, where $$v$$ is the drift velocity and $$E$$ is the electric field.

The equation you've provided seems to involve the permeability of free space ($$u_0$$), some radii ($$r_1$$ and $$r_2$$), a logarithm of the ratio of these radii, and some length $$L$$ and voltage $$U$$. It's not clear what these variables represent in the context of ion mobility.

Could you provide more context or clarify the equation? This would help me generate meaningful data and a graph.
`

Screenshot to show that the Wolfram plugin was enabled.

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