<?xml version="1.0" encoding="UTF-8"?>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns="http://purl.org/rss/1.0/" xmlns:dc="http://purl.org/dc/elements/1.1/">
  <channel rdf:about="https://community.wolfram.com">
    <title>Community RSS Feed</title>
    <link>https://community.wolfram.com</link>
    <description>RSS Feed for Wolfram Community showing any discussions tagged with Wolfram Language sorted by active.</description>
    <items>
      <rdf:Seq>
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3781869" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3781258" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/2705871" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/1992710" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3781131" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3680280" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3780545" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3779095" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/2137370" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3779221" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3778637" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3778625" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3778307" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3776120" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3631132" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3775105" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3773927" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/2380163" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3143033" />
        <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3067055" />
      </rdf:Seq>
    </items>
  </channel>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3781869">
    <title>Hermite polynomial representation of chromatography elution curves</title>
    <link>https://community.wolfram.com/groups/-/m/t/3781869</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/1a5be53f-c16e-4093-a015-de3af3a06c42</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-16T20:35:06Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3781258">
    <title>Tooltips are not always shown in DateListPlot</title>
    <link>https://community.wolfram.com/groups/-/m/t/3781258</link>
    <description>Tooltips are very useful when analyzing time series, but DateListPlot does not show the Tooltips always.  I tried PlotHighlighting and other options.  When are the Tooltips shown and when are they not shown?&#xD;
&#xD;
Attached notebook shows actual data with Tooltips and without Tooltips.&#xD;
&#xD;
![enter image description here][2]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
  [1]: https://www.wolframcloud.com/obj/24f1d5c5-68d5-4a8b-aa1a-7d2dd137c2f9&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=DateListPlotTooltips.jpg&amp;amp;userId=357084</description>
    <dc:creator>Ricardo MARTINEZ-LAGUNES</dc:creator>
    <dc:date>2026-08-14T18:46:45Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/2705871">
    <title>Solve the integral Cos(x)/x at the interval (0,infinite)</title>
    <link>https://community.wolfram.com/groups/-/m/t/2705871</link>
    <description>Dear All,&#xD;
&#xD;
I am trying to find Integral[Cos[x]/x,{x,0,infinite}].&#xD;
Integrate can not give a result since the expression is divergent.&#xD;
However, NIntegrate gives a result that I do not trust.&#xD;
&#xD;
    Integrate[1/x Cos[x], {x, 0, \[Infinity]}]&#xD;
    NIntegrate[1/x Cos[x], {x, 0, \[Infinity]}]&#xD;
&#xD;
Does anyone know if this integral can be taken? And how can we trust the result?&#xD;
&#xD;
Best wishes,&#xD;
&#xD;
İsa&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/d711ecdc-9215-408a-b65a-5bf9cb0334ce</description>
    <dc:creator>Isa Comez</dc:creator>
    <dc:date>2022-11-18T14:30:23Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/1992710">
    <title>Solve this mixed partial differential equation</title>
    <link>https://community.wolfram.com/groups/-/m/t/1992710</link>
    <description>This is my QS:&#xD;
![enter image description here][1]&#xD;
This is my Code:&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Mixedpartialdifferentialequation.png&amp;amp;userId=1983492&#xD;
  [2]: https://www.wolframcloud.com/obj/470eec73-0424-4cbc-8ba9-c2613051e7c6</description>
    <dc:creator>Yuhai Xiang</dc:creator>
    <dc:date>2020-06-01T19:19:58Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3781131">
    <title>Wong&amp;#x2013;Zakai regularization for continuous quantum measurement with NDSolve</title>
    <link>https://community.wolfram.com/groups/-/m/t/3781131</link>
    <description>![enter image description here][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2718hero-image.png&amp;amp;userId=1539902&#xD;
  [2]: https://www.wolframcloud.com/obj/3913da62-9056-46cb-9074-0c6d6b98978e</description>
    <dc:creator>Mohammad Bahrami</dc:creator>
    <dc:date>2026-08-14T16:57:12Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3680280">
    <title>Mathematica MCP: give your AI agent full control of your Wolfram kernel and notebooks</title>
    <link>https://community.wolfram.com/groups/-/m/t/3680280</link>
    <description>Built this over few weekends, an MCP server that connects AI agents (Claude, Codex etc) directly to your local Mathematica.  &#xD;
It lets the agent run Wolfram Language code, manipulate frontend notebooks, export plots, and query Wolfram Alpha(82 tools total). You don&amp;#039;t even need to know every Mathematica command, as the agent can look up functions and documentation on its own. Watch it in action: https://youtu.be/TjGSkvVyc1Y  &#xD;
&#xD;
**Would love for people in this community to give it a try. Your feedback would help me keep improving it.**&#xD;
&#xD;
[![Mathematica MCP Demo](https://www.wolframcloud.com/obj/e5519d22-b65d-4006-95f4-04f9a4bc8fc0)](https://www.youtube.com/watch?v=TjGSkvVyc1Y)&#xD;
&#xD;
---&#xD;
&#xD;
*An AI agent solving math, generating plots, and controlling a live Mathematica notebook. Errors are returned directly to the agent, no copy-pasting notebook output back into chat.*&#xD;
&#xD;
---&#xD;
&#xD;
## Documentation&#xD;
&#xD;
*   **[GitHub Repository](https://github.com/AbhiRawat4841/mathematica-mcp)**: All files and documentations&#xD;
*   **[Technical Reference](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/docs/technical-reference.md)**: Architecture, tools, and configuration&#xD;
*   **[Security Model](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/SECURITY.md)**: Threat model, permissions, and vulnerability reporting&#xD;
*   **[Benchmarks](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/docs/benchmarks.md)**: Performance data and reproduction steps&#xD;
*   **[Contributing](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/CONTRIBUTING.md)**: Development setup, testing, and PR process&#xD;
*   **[Changelog](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/CHANGELOG.md)**: Version history&#xD;
*   **[Examples](https://github.com/AbhiRawat4841/mathematica-mcp/tree/main/docs/examples)**: Polished agent session walkthroughs&#xD;
&#xD;
&#xD;
&#xD;
&#xD;
&#xD;
## Why This Exists&#xD;
&#xD;
LLMs can write Mathematica code, but they can&amp;#039;t run it, verify it, or interact with live notebooks. This MCP server bridges that gap:&#xD;
&#xD;
- **Live notebook control**: create, edit, evaluate, and screenshot Mathematica notebooks directly from your AI agent&#xD;
- **Symbolic + numeric + visual in one MCP**: ~82 tools covering algebra, calculus, plotting, data import/export, Wolfram Alpha, and interactive UIs&#xD;
- **Agent-optimized**: compact response shaping, session state tools, and computation journaling designed for how LLM agents actually work&#xD;
- **Error-aware execution**: Mathematica errors and warnings are returned directly to the agent, so it can debug without you manually copying notebook output back into chat&#xD;
- **Local and private**: core execution runs on your machine &amp;#x2014; optional tools like `wolfram_alpha` and repository search contact Wolfram&amp;#039;s cloud services when invoked&#xD;
&#xD;
&amp;gt; Ask your agent for a derivation, a 3D plot, a notebook edit, or a verification step, and it can actually do it.&#xD;
&#xD;
---&#xD;
&#xD;
## Who This Is For&#xD;
&#xD;
![enter image description here][2]&#xD;
&#xD;
---&#xD;
&#xD;
## What You Can Ask For&#xD;
&#xD;
**&amp;#034;Integrate x^2 sin(x) from 0 to pi, then verify the result.&amp;#034;**&#xD;
&#xD;
```text&#xD;
execute_code(&amp;#034;Integrate[x^2 Sin[x], {x, 0, Pi}]&amp;#034;)  =&amp;gt;  -4 + Pi^2&#xD;
verify_derivation(steps=[&amp;#034;Integrate[...&amp;#034;, &amp;#034;-4 + Pi^2&amp;#034;])  =&amp;gt;  All steps valid&#xD;
```&#xD;
&#xD;
**&amp;#034;Plot the sombrero function in a new notebook.&amp;#034;**&#xD;
&#xD;
```text&#xD;
create_notebook(title=&amp;#034;Sombrero&amp;#034;)&#xD;
execute_code(&amp;#034;Plot3D[Sinc[Sqrt[x^2+y^2]], {x,-4,4}, {y,-4,4}]&amp;#034;, style=&amp;#034;notebook&amp;#034;)&#xD;
=&amp;gt; [3D surface plot rendered in live notebook]&#xD;
```&#xD;
&#xD;
**&amp;#034;Interactive: slider for Sin[n x]&amp;#034;**&#xD;
&#xD;
```text&#xD;
execute_code(&amp;#034;Manipulate[Plot[Sin[n x],{x,0,2Pi}],{n,1,10}]&amp;#034;, style=&amp;#034;interactive&amp;#034;)&#xD;
=&amp;gt; [Live slider UI in Mathematica frontend]&#xD;
```&#xD;
&#xD;
Beyond these: **data import/export** (hundreds of formats), **Wolfram Alpha queries**, **notebook reading/analysis**, **symbolic debugging**, and more. See the [Technical Reference](docs/technical-reference.md) for the full tool list.&#xD;
&#xD;
---&#xD;
&#xD;
## How It Compares&#xD;
&#xD;
![enter image description here][3]&#xD;
&#xD;
\*Core computation runs locally. Optional tools (`wolfram_alpha`, repository search) contact Wolfram cloud services when invoked.&#xD;
&#xD;
---&#xD;
&#xD;
## Quick Start&#xD;
&#xD;
From install to first working notebook plot in under 2 minutes.&#xD;
&#xD;
### Prerequisites&#xD;
&#xD;
1- **Mathematica 14.0+** with `wolframscript` in your PATH  &#xD;
   - [Download Mathematica](https://www.wolfram.com/mathematica/)  &#xD;
   - macOS: Add to `~/.zshrc`: `export PATH=&amp;#034;/Applications/Mathematica.app/Contents/MacOS:$PATH&amp;#034;`&#xD;
&#xD;
2- **uv package manager**&#xD;
&#xD;
        curl -LsSf https://astral.sh/uv/install.sh | sh&#xD;
&#xD;
&#xD;
### One-Command Setup&#xD;
&#xD;
```bash&#xD;
# For Claude Desktop&#xD;
uvx mathematica-mcp-full setup claude-desktop&#xD;
&#xD;
# For Cursor&#xD;
uvx mathematica-mcp-full setup cursor&#xD;
&#xD;
# For VS Code (requires GitHub Copilot Chat extension)&#xD;
uvx mathematica-mcp-full setup vscode&#xD;
&#xD;
# For OpenAI Codex CLI&#xD;
uvx mathematica-mcp-full setup codex&#xD;
&#xD;
# For Google Gemini CLI&#xD;
uvx mathematica-mcp-full setup gemini&#xD;
&#xD;
# For Claude Code CLI&#xD;
uvx mathematica-mcp-full setup claude-code&#xD;
&#xD;
# Optional: select a tool profile (default is &amp;#034;full&amp;#034;)&#xD;
uvx mathematica-mcp-full setup claude-desktop --profile notebook&#xD;
```&#xD;
&#xD;
Then restart Mathematica and your editor. Done!&#xD;
&#xD;
####VS Code: Alternative setup via Command Palette&#xD;
&#xD;
&amp;gt; **Prerequisite:** [GitHub Copilot Chat](https://marketplace.visualstudio.com/items?itemName=GitHub.copilot-chat) extension must be installed - MCP support is built into Copilot.&#xD;
&#xD;
1. Press `Cmd+Shift+P` (Mac) / `Ctrl+Shift+P` (Windows)&#xD;
2. Type &amp;#034;MCP&amp;#034; -&amp;gt; Select **&amp;#034;MCP: Add Server&amp;#034;**&#xD;
3. Choose **&amp;#034;Command (stdio)&amp;#034;**: *not &amp;#034;pip&amp;#034;*&#xD;
4. Enter command: `uvx`&#xD;
5. Enter args: `mathematica-mcp-full`&#xD;
6. Name it: `mathematica`&#xD;
7. Choose scope: Workspace or User&#xD;
&#xD;
&#xD;
&#xD;
####Alternative: Interactive Installer&#xD;
&#xD;
```bash&#xD;
bash &amp;lt;(curl -sSL https://raw.githubusercontent.com/AbhiRawat4841/mathematica-mcp/main/install.sh)&#xD;
```&#xD;
&#xD;
&#xD;
### Verify Installation&#xD;
&#xD;
```bash&#xD;
uvx mathematica-mcp-full doctor&#xD;
```&#xD;
&#xD;
&amp;gt; **Tip:** If you encounter errors after updating, clear the cache:&#xD;
&amp;gt; ```bash&#xD;
&amp;gt; uv cache clean mathematica-mcp-full &amp;amp;&amp;amp; uvx mathematica-mcp-full setup &amp;lt;client&amp;gt;&#xD;
&amp;gt; ```&#xD;
&#xD;
---&#xD;
&#xD;
## Execution Styles&#xD;
&#xD;
Control where results appear with natural language or the `style` parameter:&#xD;
&#xD;
![enter image description here][4]&#xD;
&#xD;
If you don&amp;#039;t include a keyword, the default depends on your [tool profile](#tool-profiles).&#xD;
&#xD;
---&#xD;
&#xD;
## Tool Profiles&#xD;
&#xD;
Choose how many tools to expose:&#xD;
&#xD;
![enter image description here][5]&#xD;
&#xD;
Pass `--profile` during setup or set `MATHEMATICA_PROFILE` env var.&#xD;
&#xD;
---&#xD;
&#xD;
## Built for Agent Workflows&#xD;
&#xD;
The server is designed for how LLM agents actually work: long conversations with context limits, intermittent failures, and token budgets:&#xD;
&#xD;
![enter image description here][6]&#xD;
&#xD;
Notebook execution is strict about the requested target: if notebook transport fails, the server returns a notebook error instead of silently rerunning the work through CLI fallback.&#xD;
&#xD;
### Routing Intelligence (opt-in)&#xD;
&#xD;
For power users, the server can learn from transport outcomes and adapt:&#xD;
&#xD;
```bash&#xD;
# Observe mode: collect stats, no behavior change&#xD;
export MATHEMATICA_ROUTING_MEMORY=observe&#xD;
&#xD;
# Advise mode: + routing hints + enables adaptive routing&#xD;
export MATHEMATICA_ROUTING_MEMORY=advise&#xD;
export MATHEMATICA_ROUTING_ACTION=compute_cli_skip  # optional: skip failing transport&#xD;
```&#xD;
&#xD;
The adaptive routing circuit-breaker automatically skips persistently failing compute CLI transport with half-open probe recovery. See the [Technical Reference](docs/technical-reference.md#intelligent-routing--observability) for details.&#xD;
&#xD;
&amp;gt; **Privacy:** Routing memory stores only aggregate counters; the in-memory journal stores short code/output previews (not persisted). Notebook extraction results are cached to `~/.cache/mathematica-mcp/notebooks/` with mtime-based invalidation; delete the directory to clear the cache.&#xD;
&#xD;
---&#xD;
&#xD;
## Manual Installation&#xD;
&#xD;
For full details, troubleshooting, and advanced configuration, see the **[Installation Guide](docs/installation.md)**.&#xD;
&#xD;
####Quick manual setup&#xD;
&#xD;
1.  **Clone &amp;amp; Install**:  &#xD;
&#xD;
        git clone https://github.com/AbhiRawat4841/mathematica-mcp.git&#xD;
        cd mathematica-mcp&#xD;
        uv sync&#xD;
&#xD;
&#xD;
2.  **Install Mathematica Addon**:  &#xD;
&#xD;
        wolframscript -file addon/install.wl&#xD;
    *Restart Mathematica after this step.*&#xD;
&#xD;
3.  **Configure your editor**: add the MCP server to your client&amp;#039;s config file. See the **[Installation Guide](docs/installation.md#step-4-configure-your-editor)** for Claude Desktop, Cursor, VS Code, and other client configs.&#xD;
&#xD;
&#xD;
&#xD;
&#xD;
---&#xD;
&#xD;
## License&#xD;
MIT License&#xD;
&#xD;
&#xD;
  [1]: https://github.com/AbhiRawat4841/mathematica-mcp&#xD;
  [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table1.jpg&amp;amp;userId=20103&#xD;
  [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table2.jpg&amp;amp;userId=20103&#xD;
  [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table3.jpg&amp;amp;userId=20103&#xD;
  [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table4.jpg&amp;amp;userId=20103&#xD;
  [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table5.jpg&amp;amp;userId=20103</description>
    <dc:creator>Abhishek Singh Rawat</dc:creator>
    <dc:date>2026-04-10T00:05:40Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3780545">
    <title>Analytical dynamics with Lagrange and Hamilton</title>
    <link>https://community.wolfram.com/groups/-/m/t/3780545</link>
    <description>![Analytical dynamics with Lagrange and Hamilton][1]&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][2]&#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3675hero.png&amp;amp;userId=20103&#xD;
  [2]: https://www.wolframcloud.com/obj/046a414f-f3af-4e0e-9d20-7a1e47c11739</description>
    <dc:creator>Akram Masoud</dc:creator>
    <dc:date>2026-08-13T23:11:11Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3779095">
    <title>Getting results from parallel computations</title>
    <link>https://community.wolfram.com/groups/-/m/t/3779095</link>
    <description>Parallel instances read a global but do not set a global?&#xD;
&#xD;
&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/16b31aaa-f36c-4e26-a8d6-272b95854c7f</description>
    <dc:creator>David Golber</dc:creator>
    <dc:date>2026-08-11T15:42:12Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/2137370">
    <title>Produce a ListPlot with Dataset</title>
    <link>https://community.wolfram.com/groups/-/m/t/2137370</link>
    <description>Suppose I have the following Dataset:&#xD;
![enter image description here][1]&#xD;
&#xD;
I want to use ListPlot to produce a plot of v (voltage) vs. t (time).&#xD;
Seems quite simple and straightforward, but I didn&amp;#039;t find an answer on the net.&#xD;
I was thinking about doing&#xD;
&#xD;
    ListPlot[Thread[{mydata[All, &amp;#034;t&amp;#034;], mydata[All, &amp;#034;v&amp;#034;]}]]&#xD;
&#xD;
but `mydata[All, &amp;#034;t&amp;#034;]` gives an error:&#xD;
&#xD;
    Failure[Dataset,Association[&amp;#034;MessageTemplate&amp;#034; :&amp;gt; MessageName[Dataset, &amp;#034;partnotapplicable&amp;#034;],&amp;#034;MessageParameters&amp;#034; -&amp;gt; Association[&amp;#034;Type&amp;#034; -&amp;gt; TypeSystem`Vector[TypeSystem`AnyType, 2], &amp;#034;Part&amp;#034; -&amp;gt; &amp;#034;t&amp;#034;,&amp;#034;Symbol&amp;#034; -&amp;gt; Part]]]&#xD;
&#xD;
&#xD;
I wouldn&amp;#039;t be surprised to learn that there is a short way to do that, without the use of `Thread`.&#xD;
&#xD;
  [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=9170csv.PNG&amp;amp;userId=1344988</description>
    <dc:creator>Ehud Behar</dc:creator>
    <dc:date>2020-12-14T10:06:23Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3779221">
    <title>Chromatographic peak reconstruction via stagewise plate model with linear adsorption</title>
    <link>https://community.wolfram.com/groups/-/m/t/3779221</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/647ded57-7011-451f-a59b-e75657fdc8d2</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-11T12:07:47Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3778637">
    <title>Is the &amp;#034;average&amp;#034; of the function $\mathcal{G}:\mathbb{R}\to\mathbb{R}$ non-zero and finite?</title>
    <link>https://community.wolfram.com/groups/-/m/t/3778637</link>
    <description>This is a restatement of [this post][1], since it is difficult to read and [this post][2] since the latter might later be closed. I don&amp;#039;t know where else to share.&#xD;
&#xD;
**Motivation:** Consider the function $\mathcal{G}:\mathbb{R}\to\mathbb{R}$,&#xD;
&#xD;
&amp;gt;  (**Example of** $\mathcal{G}$) Let $(q_t)_{t\in\mathbb{N}}$ be a [numbering][3] of the rational numbers and $k_t=2^{2^t}$, and define functions $s_t$ as follows:&#xD;
&amp;gt;&#xD;
&amp;gt; If $s_0=0$ everywhere and: &#xD;
$$\small{ s_{t+1}(x)=\begin{cases} q_{t/2} &amp;amp; x\in\bigcup_{j\in\{1,\cdots,t\}}(q_j-1/k_t,q_j+1/k_t), \, t \text{ is even}\\ k_t^2 &amp;amp; x \in\bigcup_{j\in\{1,\cdots,t\}}(q_j-1/k_t,q_j+1/k_t), \, t \text{ is odd}\\ s_t(x) &amp;amp; \text{otherwise} &#xD;
\end{cases}}$$ each $s_{t+1}$ agrees with $s_t$ at all real numbers except a set of measure $&amp;lt;1/2^t$ for big $t$, so one could consider $\mathcal{G}$ the pointwise limit of the functions $s_t$, which is defined everywhere except measure $0$ (in those bad points just define $\mathcal{G}=0$). &#xD;
&#xD;
Here is the partial code of the example using Mathematica:&#xD;
&#xD;
    Clear[&amp;#034;Global`*&amp;#034;]&#xD;
&#xD;
    enumerateRationals[n_Integer?Positive] := &#xD;
      Module[{posRationals, &#xD;
        fullList},(*Generate enough positive rationals using the Calkin-&#xD;
       Wilf step*)&#xD;
&#xD;
       posRationals = NestList[1/(2 Floor[#] - # + 1) &amp;amp;, 1, Ceiling[n/2]];&#xD;
       (*Interleave:0,q1,-q1,q2,-q2...*)&#xD;
&#xD;
       fullList = Riffle[posRationals, -posRationals];&#xD;
&#xD;
       Prepend[fullList, 0][[1 ;; n]]];&#xD;
&#xD;
    enumerateRationals[0] = {};&#xD;
&#xD;
    q[t_] := q[t] = enumerateRationals[t][[t]]&#xD;
    (*Takes the t-value in an enumeration*)&#xD;
&#xD;
    k[t_] := k[t] = 2^(2^t)&#xD;
&#xD;
    s[0, _] = 0;&#xD;
    s[t_Integer, x_] := &#xD;
     s[t, x] = &#xD;
      Piecewise[{{q[(t - 1)/2], &#xD;
         EvenQ[t - 1] &amp;amp;&amp;amp; &#xD;
          0 &amp;lt;= Min[Abs[x - enumerateRationals[t - 1]]] &amp;lt; 1/k[t - 1]}, {k[&#xD;
           t - 1]^2, &#xD;
         OddQ[t - 1] &amp;amp;&amp;amp; &#xD;
          0 &amp;lt;= Min[Abs[x - enumerateRationals[t - 1]]] &amp;lt; 1/k[t - 1]}}, &#xD;
       s[t - 1, x]]&#xD;
&#xD;
    FullSimplify[PiecewiseExpand[s[5, x]]]&#xD;
    (*Example of s[t,x]*)&#xD;
&#xD;
(I want to compute `s[t,x]` as `t-&amp;gt;Infinity` to get $\mathcal{G}(x)$ or `bigG[x]`.)&#xD;
&#xD;
In the usual sense, the mean of $\mathcal{G}$ w.r.t. the Lebesgue measure over a family of bounded and finite measure sets converging to $\mathrm{dom}(\mathcal{G})=\mathbb{R}$ is always undefined, since $\mathcal{G}$ satisfies two properties:&#xD;
&#xD;
1. The restriction of $\mathcal{G}$ to any interval has infinite area both above and below $y=0$.&#xD;
2. For all $a&amp;lt;b$ and $c&amp;lt;d$ real numbers, $\{x\in (a,b):\mathcal{G}(x) \in (c,d)\}$ is a set with positive Lebesgue measure.&#xD;
&#xD;
Furthermore, the mean w.r.t. the Hausdorff measure in its dimension of a family of bounded functions (with different bounded domains of finite measure) converging to $\mathcal{G}$ is defined but has different values depending on the family of bounded functions chosen. Hence, the former mean is non-unique.&#xD;
&#xD;
**Question:** In my concept paper (see the following summary and attatchments), assuming $\mathbf{R}$ is the origin and $E=1/2$, what is the *average* of the example of $\mathcal{G}$ using Mathematica? Is the &amp;#034;average value&amp;#034; non-zero and finite? If not, explain why?&#xD;
&#xD;
&amp;gt; Every reference in the next section refers to the Sections, Definitions, and pages of the concept paper.&#xD;
&#xD;
## Summary of The Concept Paper##&#xD;
&#xD;
My attempt to average of $\mathcal{G}(x)$ on $\small{(-\infty,+\infty)}$ is defined w.r.t. to four definitions:&#xD;
&#xD;
 - The [reference point][6] $\mathbf{R}\in\mathbb{R}^{2}$:&#xD;
&#xD;
&amp;gt; For every *chosen* reference point, there should be a unique, &amp;#034;satisfying&amp;#034; (i.e., see the section &amp;#034;**Modeling Question Summary**&amp;#034; at the bottom), and either:&#xD;
&amp;gt;&#xD;
&amp;gt; 1. a finite mean of $\mathcal{G}$&#xD;
&amp;gt; 2. if not a finite mean of $\mathcal{G}$, then an infinite mean&#xD;
&amp;gt; 3. if not a finite or infinite mean, then an undefined mean of $\mathcal{G}$.&#xD;
&#xD;
 - The &amp;#034;measure&amp;#034; (Definitions 20-22 (pg. 20-25) of a family of each bounded function’s graph, where $\{G_r^{\star}:r\in\mathbb{R}^{+}\}=\{\mathrm{graph}(f_r^{\star}):r\in\mathbb{R}^{+}\}$ and $\{f_r^{\star}:r\in\mathbb{R}^{+}\}$ is a family of bounded functions with different bounded domains of finite measure converging to $\mathcal{G}$):&#xD;
&#xD;
&amp;gt; The preliminary step to defining the &amp;#034;measure&amp;#034; of a family of each bounded function&amp;#039;s graph (Definition 20, pg. 20-22) is to partition each of their graphs into equal measure sets which take a sample point from each partition, pathways of line segments between sample points, lengths of line segments in each pathway, removed lengths which are outliers, remaining lengths which are converted into a probability distribution, the entropy of the distribution, and the maximum entropy w.r.t all pathways.&#xD;
&amp;gt;&#xD;
&amp;gt; -----------------&#xD;
&amp;gt;&#xD;
&amp;gt; &amp;#039;The &amp;#034;measure&amp;#034; (Definition 22, pg. 23-25) involves the supremum of the sample size (i.e., when applying the preliminary step to each bounded function&amp;#039;s graph in a chosen family) such that the entropy in the preliminary step is less than or equal to the entropy (i.e., when applying the preliminary step to each bounded function&amp;#039;s graph in a &amp;#034;non-equivalent&amp;#034; family [Definition 18-19, pg. 19-20]), then dividing the former by the following sample size (i.e., when applying the preliminary step to each bounded function&amp;#039;s graph in the &amp;#034;non-equivelant&amp;#034; family) and taking its &amp;#034;supremum&amp;#034; and &amp;#034;infimum&amp;#034; w.r.t. to all possible partitions and samples. (The &amp;#034;supremum&amp;#034; and &amp;#034;infimum&amp;#034; should be equal.) To better understand the definitions, consider the following examples (Section A.7.1-A.7.3, pg. 179-197).&#xD;
&#xD;
 - The expected rate of expansion:&#xD;
&#xD;
&amp;gt; The expected rate of expansion is an arbitrary fixed constant and is&#xD;
&amp;gt; written as the function $E:\mathcal{A}(A)\to\mathbb{R}$ (i.e.,&#xD;
&amp;gt; $\mathcal{A}(A):=\mathbb{R}^{+}$ is the chosen index set of a family of functions or&#xD;
&amp;gt; sets).&#xD;
&#xD;
 - The actual rate of expansion (Definition 23, pg. 25-26):&#xD;
&#xD;
&amp;gt; The actual rate of expansion of a family of each bounded function&amp;#039;s&#xD;
&amp;gt; graph is the &amp;#034;derivative&amp;#034; of a function of the &amp;#034;average&amp;#034; $2$-dimensional Euclidean&#xD;
&amp;gt; distance between every point in each bounded function&amp;#039;s graph and the&#xD;
&amp;gt; reference point $\mathbf{R}\in\mathbb{R}^{2}$&#xD;
&#xD;
-------&#xD;
&#xD;
### Modeling Question Summary: ###&#xD;
&#xD;
&amp;gt; Combining &amp;#034;the measure&amp;#034; and the actual rate of expansion, we get a general notion of the choice function in the modeling question (Section 3.1, pg. 27-30). The choice function should pick &amp;#034;equivelant&amp;#034; families (Definition 15-17, pg. 17-18) of bounded functions converging to $\mathcal{G}$ which satisfy all the criteria in the modeling question, such that:&#xD;
&amp;gt;&#xD;
 - the &amp;#034;measure&amp;#034; (Definition 20-22, pg. 20-25) of each chosen family of each bounded function&amp;#039;s graph increases at a rate linear or superlinear (Definition 22, pg. 23-25) to that of each &amp;#034;non-equivelant&amp;#034; family (Definition 18-19, pg. 19-20) of each bounded function&amp;#039;s graph (Section 3.1 criterion 2)&#xD;
 - the absolute difference between the $y$-coordinate of the reference point $\mathbf{R}\in\mathbb{R}^{2}$ and the mean of each chosen family of bounded functions converging to $\mathcal{G}$ is minimized (Definition 13 [pg. 13-14], Section 3.1 criterion 4)&#xD;
 - the absolute difference between the expected rate of expansion and the actual rate of expansion of each chosen family of each bounded function&amp;#039;s graph is minimized  (Definition 23 [pg. 25-26], Section 3.1 criterion 4), &#xD;
&amp;gt;&#xD;
so that it&amp;#039;s more likely the choice function, which answers the modeling question, chooses the desired families. Hence, we take the mean of the chosen &amp;#034;equivelant&amp;#034; (Definition 15-17, pg. 17-18) families as the new mean (i.e., the &amp;#034;equivelant&amp;#034; families should have the same mean). &#xD;
&#xD;
&#xD;
  [1]: https://community.wolfram.com/groups/-/m/t/3769559?p_p_auth=EIl3sQDy&#xD;
  [2]: https://scicomp.stackexchange.com/questions/45512/can-we-average-pathological-function-mathcalg-mathbbr-to-mathbbr-in-a&#xD;
  [3]: https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree&#xD;
  [4]: https://mathematica.stackexchange.com/a/319780/34171&#xD;
  [5]: https://www.researchgate.net/publication/410022187_Reformatted_Averaging_an_Explicit_Non-Lebesgue_Integrable_and_Unbounded_Function_That_Is_Defined_Without_The_Axiom_of_Choice&#xD;
  [6]: https://en.wikipedia.org/wiki/Frame_of_reference</description>
    <dc:creator>Bharath Krishnan</dc:creator>
    <dc:date>2026-08-11T00:50:32Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3778625">
    <title>Liquid chromatography: plate model with linear adsorption and temperature gradient</title>
    <link>https://community.wolfram.com/groups/-/m/t/3778625</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/e3780e27-7c98-4efc-9494-86f49cddb5ab</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-10T23:44:18Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3778307">
    <title>Liquid chromatography with linear adsorption equilibrium and plate model</title>
    <link>https://community.wolfram.com/groups/-/m/t/3778307</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/691e48da-b2e1-4830-81fa-a3e76d150693</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-10T15:42:23Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3776120">
    <title>Carta&amp;#039;s Analytic Chromatogram Solution for a Glucose-Sucrose-Fructose Separation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3776120</link>
    <description>&amp;amp;[Wolfram Notebook][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/67574a39-6fe3-4b96-a0e0-e2fcc394ee18</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-08T13:48:19Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3631132">
    <title>A testable quantum graph theory of spacetime: seeking collaboration for simulation</title>
    <link>https://community.wolfram.com/groups/-/m/t/3631132</link>
    <description>Hello everyone,&#xD;
&#xD;
I am developing a model of spacetime that shares some fundamental concepts with the Wolfram Physics Project but introduces a specific focus on testability and quantum noise signatures.&#xD;
In my theory, spacetime is represented as a finite directed quantum graph. The core idea is that the connectivity of the graph isn&amp;#039;t just an abstract representation but directly dictates the physical observables we see in quantum systems.&#xD;
&#xD;
Key features of the model:&#xD;
&#xD;
Discrete Topology: Nodes represent Planck-scale events, and directed edges represent causal relationships.&#xD;
&#xD;
Emergent Physics: I have derived that the Einstein field equations and Maxwell&amp;#039;s equations emerge as a low-energy limit of these graph dynamics.&#xD;
Experimental Predictions: Most importantly, the model predicts specific spectral signatures in the decoherence noise of current NISQ-era quantum processors and anomalies in high-energy particle scattering.&#xD;
&#xD;
Iam looking for collaborators who are interested in:&#xD;
&#xD;
Visualizing the graph dynamics using the Wolfram Language.&#xD;
&#xD;
Simulating the noise patterns to compare them with existing data from IBM or Google quantum hardware.&#xD;
&#xD;
I believe that by identifying the right &amp;#034;rewrite rules&amp;#034; for this directed graph, we can bridge the gap between discrete spacetime models and experimental verification.&#xD;
&#xD;
Looking forward to your feedback and potential collaboration!</description>
    <dc:creator>Sergej Materov</dc:creator>
    <dc:date>2026-01-30T11:52:49Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3775105">
    <title>Locating and Classifying Critical Points of a 2D Function via Particle Swarm Optimization</title>
    <link>https://community.wolfram.com/groups/-/m/t/3775105</link>
    <description>&amp;amp;[3][1]&#xD;
&#xD;
&#xD;
  [1]: https://www.wolframcloud.com/obj/8c0f3da8-ac8c-4ae3-80f3-6f03079a146c</description>
    <dc:creator>Housam Binous</dc:creator>
    <dc:date>2026-08-06T08:27:07Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3773927">
    <title>Mathematica help descriptions for Parallelize are needlessly complicated</title>
    <link>https://community.wolfram.com/groups/-/m/t/3773927</link>
    <description>Complaint: The examples in the Mathematica Help are needlessly complicated, and in fact hinder the process of informing the user.  Here&amp;#039;s an example:&#xD;
&#xD;
The first example of the use of Parallelize, in the definition of the Parallelize operation, is&#xD;
&#xD;
    (1)  Parallelize[Map[Composition[Framed,FactorInteger],{1,11,111,1111,11111,111111}]]&#xD;
&#xD;
This is more or less&#xD;
&#xD;
    (2) Parallelize[{FactorInteger[1], FactorInteger[11], FactorInteger[111], FactorInteger[1111], FactorInteger[11111], FactorInteger[111111]}]&#xD;
&#xD;
Which takes about 50% more characters, but only two operators (Parallelize and FactorInteger) instead of five (Parallelize, Map, Composition, Framed, FactorInteger).&#xD;
&#xD;
But, in fact, neither (1) or (2) tells the reader anything more about what Parallelize does, or how to use it, than&#xD;
&#xD;
    (3) Parallelize[{1^2, 2^2, 3^2, 4^2, 5^2, 6^2}]&#xD;
&#xD;
(3) has no operators other than the one which the example is there to explain.  And it has fewer characters than (1) or (2).&#xD;
&#xD;
Can anyone defend why (1) should be the example instead of (3).</description>
    <dc:creator>David Golber</dc:creator>
    <dc:date>2026-08-05T01:09:19Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/2380163">
    <title>About MxNet as Mathematica backend choice</title>
    <link>https://community.wolfram.com/groups/-/m/t/2380163</link>
    <description>I recently noticed that Mathematica uses MxNet as the backend for neural networks. It seems to have been integrated in 2015. The blog post listing the rationale is [here](https://www.oreilly.com/content/apache-mxnet-in-the-wolfram-language/).&#xD;
&#xD;
MxNet seems to have not gained the momentum to become popular, you can see the [trends](https://paperswithcode.com/trends) from &amp;#034;papers with code&amp;#034;. Lack of popularity means framework may be slow to develop.&#xD;
&#xD;
For instance, this [question](https://mathematica.stackexchange.com/questions/256323/neural-network-automatic-differentiation-autograd) about using neural networks to fit ODEs from&#xD;
Joshua Schrier. It requires underlying framework to support higher order gradients. There&amp;#039;s an [issue](https://github.com/apache/incubator-mxnet/issues/10002) to add support in MxNET but progress has stalled. Meanwhile PyTorch/TensorFlow/JAX support this feature.</description>
    <dc:creator>Yaroslav Bulatov</dc:creator>
    <dc:date>2021-10-06T00:49:07Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3143033">
    <title>Mathmatica pefromance and CPU usage in equation solving</title>
    <link>https://community.wolfram.com/groups/-/m/t/3143033</link>
    <description>I have a general question that may have been addressed previously, albeit not directly. I utilize Mathematica to solve a set of non-linear equations and achieve successful results. However, the computation time is considerably long despite the minimal CPU and memory usage. Additionally, the computer I am using is a high-performance PC, yet the execution speed of this code resembles that of my laptop. Am I overlooking something? Why isn&amp;#039;t Mathematica utilizing more resources? For instance, the CPU usage remains around 7% max.</description>
    <dc:creator>Nima Moini</dc:creator>
    <dc:date>2024-03-18T23:02:58Z</dc:date>
  </item>
  <item rdf:about="https://community.wolfram.com/groups/-/m/t/3067055">
    <title>Sharing Cloud Folders</title>
    <link>https://community.wolfram.com/groups/-/m/t/3067055</link>
    <description>Hi all, I&amp;#039;ve been using WL this year in physics. Each student has created a cloud folder called &amp;#034;Physics&amp;#034; to store their project notebooks. We just had a major project completed this week and we are about to go on Fall break. I had them all share their notebooks with me via email. I would rather have a shared folder in which they put their work. &#xD;
&#xD;
When you look at the properties of a folder in the cloud, you can see &amp;#034;permissions&amp;#034; which has a default setting of private. Is it possible to create a CloudObject that is a named folder, set Permissions to &amp;#034;Public&amp;#034; and then distribute the URL of that object to my students? If possible, is this the way people generally do this?</description>
    <dc:creator>John Martin</dc:creator>
    <dc:date>2023-11-17T20:24:51Z</dc:date>
  </item>
</rdf:RDF>

