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Fix equation rendering#38

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FanwangM merged 3 commits intomainfrom
fix_rendering
Apr 23, 2026
Merged

Fix equation rendering#38
FanwangM merged 3 commits intomainfrom
fix_rendering

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Copilot AI review requested due to automatic review settings April 23, 2026 04:09
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Pull request overview

Updates README rendering so project metadata and mathematical formulas display correctly on GitHub.

Changes:

  • Updated the Python support badge (text, URL, and link target).
  • Switched formula blocks from fenced ```math blocks to $$ ... $$ LaTeX blocks.
  • Fixed minor indentation/formatting in the License section.

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Comment thread README.md
@@ -1,4 +1,4 @@
[![Python 3](http://img.shields.io/badge/python-3-blue.svg)](https://docs.python.org/3/)
[![This project supports Python 3.10+](https://img.shields.io/badge/Python-3.10+-blue.svg)](https://python.org/downloads)
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The Shields.io badge URL includes a literal "+" in the path ("3.10+"). Shields generally expects special characters to be URL-encoded; otherwise the badge can fail to render in some contexts. Consider encoding it as "%2B" ("3.10%2B") to make the badge URL robust.

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Comment thread README.md
Comment on lines 60 to 61
\text{per}(A) = \frac{1}{2^{N-1}} \cdot \sum_{\delta \in \left[\delta_1 = 1,~ \delta_2 \dots \delta_N=\pm1\right]}{
\left(\sum_{k=1}^N{\delta_k}\right){\prod_{j=1}^N{\sum_{i=1}^N{\delta_i a_{i,j}}}}}
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These equations are laid out across multiple lines in Markdown, but KaTeX/GitHub math rendering treats newlines inside $$ ... $$ as whitespace (not line breaks), so this will likely render as a single very long line and overflow on GitHub. Consider using an aligned/multline environment with explicit \\ line breaks to preserve the intended formatting.

Suggested change
\text{per}(A) = \frac{1}{2^{N-1}} \cdot \sum_{\delta \in \left[\delta_1 = 1,~ \delta_2 \dots \delta_N=\pm1\right]}{
\left(\sum_{k=1}^N{\delta_k}\right){\prod_{j=1}^N{\sum_{i=1}^N{\delta_i a_{i,j}}}}}
\begin{aligned}
\text{per}(A) &= \frac{1}{2^{N-1}} \cdot \sum_{\delta \in \left[\delta_1 = 1,~ \delta_2 \dots \delta_N=\pm1\right]}{ \\
&\quad \left(\sum_{k=1}^N{\delta_k}\right){\prod_{j=1}^N{\sum_{i=1}^N{\delta_i a_{i,j}}}}}
\end{aligned}

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Comment thread README.md
Comment on lines +68 to +70
$$
\text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} \\ \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N}\end{matrix}\right) = \frac{1}{(M - N + 1)!} \cdot \text{per}\left(\begin{matrix}a_{1,1} & \cdots & a_{1,N} & 1_{1,N+1} & \cdots & 1_{1,M} \\ \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \\ a_{M,1} & \cdots & a_{M,N} & 1_{M,N+1} & \cdots & 1_{M,M}\end{matrix}\right)
```
$$
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This matrix identity is extremely wide; with $$ ... $$ and no explicit line breaks it will likely overflow horizontally in GitHub’s renderer. Consider splitting it across multiple lines using aligned/multline (and \\) so it remains readable on narrow screens.

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Comment thread README.md
Comment on lines 97 to +107
@@ -103,7 +104,7 @@ This can be neatly fit into the original formula by extending the inner sums ove
}
}
}
```
$$
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This multi-line formula will render as a single line under KaTeX unless you add an aligned/multline environment and explicit \\ breaks. As-is, it’s likely to overflow horizontally and be hard to read on GitHub.

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Comment thread README.md Outdated

This code is distributed under the GNU General Public License version 3 (GPLv3).
See <http://www.gnu.org/licenses/> for more information. No newline at end of file
See <http://www.gnu.org/licenses/> for more information.
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The license link uses plain HTTP. It’s preferable to use HTTPS here to avoid unnecessary redirects and mixed-content warnings in some contexts.

Suggested change
See <http://www.gnu.org/licenses/> for more information.
See <https://www.gnu.org/licenses/> for more information.

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@FanwangM FanwangM merged commit d781399 into main Apr 23, 2026
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