[x ] I have read and followed all the instructions provided in the README.md.
[x ] I am on the latest version of both Open WebUI and Ollama.
I have included the browser console logs.
I have included the Docker container logs.
I have provided the exact steps to reproduce the bug in the "Steps to Reproduce" section below.
Expected Behavior:
A correct LaTeX rendering
Actual Behavior:
The LaTeX is rendered as plain text
Screenshots/Screen Recordings (if applicable):
Additional notes:
Text version of the chat:
## USER
$b_k - a_k = \frac{b_{k-1} - a_{k-1}}{2} = \frac{b_0 - a_0}{2^k}$
Can you explain to me the reason why this chain of equalities is true? (please use LaTeX for math formulas)
## ASSISTANT
Let's break down the derivation step-by-step and clarify why each equality holds:
**1. Initial Assumption (Implied):** We're working under a recursive definition or pattern for sequences $a_k$ and $b_k$. A crucial, though often implicit, assumption is that these sequences have a relationship where differences follow a specific pattern related to powers of 2.
**2. Recursive Relation (Central to the Proof):** The core logic lies in assuming a recursive formula resembling:
* \[ b_k - a_k = \frac{1}{2}(b_{k-1} - a_{k-1}) \]
This recursive definition means each term's difference is half the difference of the previous terms.
**3. Derivation using the Recursive Relation:**
* **From the recursive relation, we directly get:**
$b_k - a_k = \frac{1}{2}(b_{k-1} - a_{k-1})$
* **Applying this recursively k times:**
* Substitute $k-1$ with $k-2$, then $k-3$, and so on, until you reach the base case ($k=0$). Each time, you'll halve the difference:
* $b_k - a_k = \frac{1}{2} \cdot \frac{1}{2} \cdot ... \cdot \frac{1}{2} (b_1 - a_1) = \left(\frac{1}{2}\right)^k (b_1 - a_1)$
* **Connecting to the Initial Difference:** Since $b_0 - a_0$ is the initial difference, and we can express $(b_1 - a_1)$ in terms of $(b_0 - a_0)$ using the recursive relation, we ultimately arrive at:
* $b_k - a_k = \frac{b_0 - a_0}{2^k}$
**Key Points:**
* **Recursive Structure:** The proof hinges on repeatedly applying the given recursive definition for the differences.
* **Powers of 2:** The halving process in each recursive step directly leads to the $2^k$ factor in the final result.
Therefore, the chain of equalities is a consequence of the assumed recursive pattern and the repeated application of that pattern.
Originally created by @DanielusG on GitHub (Aug 27, 2024).
Original GitHub issue: https://github.com/open-webui/open-webui/issues/4941
# Bug Report
## Installation Method
Docker and updated with watchtower
## Environment
- **Open WebUI Version:** v0.3.15
- **Ollama (if applicable):** 0.3.6
- **Operating System:** Arch Linux (Garuda Linux)
- **Browser (if applicable):** Edge 127.0.2651.98
**Confirmation:**
- [x ] I have read and followed all the instructions provided in the README.md.
- [x ] I am on the latest version of both Open WebUI and Ollama.
- [ ] I have included the browser console logs.
- [ ] I have included the Docker container logs.
- [ ] I have provided the exact steps to reproduce the bug in the "Steps to Reproduce" section below.
## Expected Behavior:
A correct LaTeX rendering
## Actual Behavior:
The LaTeX is rendered as plain text
**Screenshots/Screen Recordings (if applicable):**
## Additional notes:
Text version of the chat:
```
## USER
$b_k - a_k = \frac{b_{k-1} - a_{k-1}}{2} = \frac{b_0 - a_0}{2^k}$
Can you explain to me the reason why this chain of equalities is true? (please use LaTeX for math formulas)
## ASSISTANT
Let's break down the derivation step-by-step and clarify why each equality holds:
**1. Initial Assumption (Implied):** We're working under a recursive definition or pattern for sequences $a_k$ and $b_k$. A crucial, though often implicit, assumption is that these sequences have a relationship where differences follow a specific pattern related to powers of 2.
**2. Recursive Relation (Central to the Proof):** The core logic lies in assuming a recursive formula resembling:
* \[ b_k - a_k = \frac{1}{2}(b_{k-1} - a_{k-1}) \]
This recursive definition means each term's difference is half the difference of the previous terms.
**3. Derivation using the Recursive Relation:**
* **From the recursive relation, we directly get:**
$b_k - a_k = \frac{1}{2}(b_{k-1} - a_{k-1})$
* **Applying this recursively k times:**
* Substitute $k-1$ with $k-2$, then $k-3$, and so on, until you reach the base case ($k=0$). Each time, you'll halve the difference:
* $b_k - a_k = \frac{1}{2} \cdot \frac{1}{2} \cdot ... \cdot \frac{1}{2} (b_1 - a_1) = \left(\frac{1}{2}\right)^k (b_1 - a_1)$
* **Connecting to the Initial Difference:** Since $b_0 - a_0$ is the initial difference, and we can express $(b_1 - a_1)$ in terms of $(b_0 - a_0)$ using the recursive relation, we ultimately arrive at:
* $b_k - a_k = \frac{b_0 - a_0}{2^k}$
**Key Points:**
* **Recursive Structure:** The proof hinges on repeatedly applying the given recursive definition for the differences.
* **Powers of 2:** The halving process in each recursive step directly leads to the $2^k$ factor in the final result.
Therefore, the chain of equalities is a consequence of the assumed recursive pattern and the repeated application of that pattern.
```
This has been addressed in dev, please check for duplicate issue before opening one. Thanks.
<!-- gh-comment-id:2312644910 -->
@tjbck commented on GitHub (Aug 27, 2024):
This has been addressed in dev, please check for duplicate issue before opening one. Thanks.
This has been addressed in dev, please check for duplicate issue before opening one. Thanks.
Sorry I searched only among the open issues and not also in the closed issues 😢
<!-- gh-comment-id:2312654158 -->
@DanielusG commented on GitHub (Aug 27, 2024):
> This has been addressed in dev, please check for duplicate issue before opening one. Thanks.
Sorry I searched only among the open issues and not also in the closed issues :cry:
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Originally created by @DanielusG on GitHub (Aug 27, 2024).
Original GitHub issue: https://github.com/open-webui/open-webui/issues/4941
Bug Report
Installation Method
Docker and updated with watchtower
Environment
Open WebUI Version: v0.3.15
Ollama (if applicable): 0.3.6
Operating System: Arch Linux (Garuda Linux)
Browser (if applicable): Edge 127.0.2651.98
Confirmation:
Expected Behavior:
A correct LaTeX rendering
Actual Behavior:
The LaTeX is rendered as plain text
Screenshots/Screen Recordings (if applicable):
Additional notes:
Text version of the chat:
@tjbck commented on GitHub (Aug 27, 2024):
This has been addressed in dev, please check for duplicate issue before opening one. Thanks.
@DanielusG commented on GitHub (Aug 27, 2024):
Sorry I searched only among the open issues and not also in the closed issues 😢