https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions from all groups sorted by active. https://community.wolfram.com/groups/-/m/t/3680280 Built this over few weekends, an MCP server that connects AI agents (Claude, Codex etc) directly to your local Mathematica. It lets the agent run Wolfram Language code, manipulate frontend notebooks, export plots, and query Wolfram Alpha(82 tools total). You don'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 **Would love for people in this community to give it a try. Your feedback would help me keep improving it.** [](https://www.youtube.com/watch?v=TjGSkvVyc1Y) --- *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.* --- ## Documentation * **[GitHub Repository](https://github.com/AbhiRawat4841/mathematica-mcp)**: All files and documentations * **[Technical Reference](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/docs/technical-reference.md)**: Architecture, tools, and configuration * **[Security Model](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/SECURITY.md)**: Threat model, permissions, and vulnerability reporting * **[Benchmarks](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/docs/benchmarks.md)**: Performance data and reproduction steps * **[Contributing](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/CONTRIBUTING.md)**: Development setup, testing, and PR process * **[Changelog](https://github.com/AbhiRawat4841/mathematica-mcp/blob/main/CHANGELOG.md)**: Version history * **[Examples](https://github.com/AbhiRawat4841/mathematica-mcp/tree/main/docs/examples)**: Polished agent session walkthroughs ## Why This Exists LLMs can write Mathematica code, but they can't run it, verify it, or interact with live notebooks. This MCP server bridges that gap: - **Live notebook control**: create, edit, evaluate, and screenshot Mathematica notebooks directly from your AI agent - **Symbolic + numeric + visual in one MCP**: ~82 tools covering algebra, calculus, plotting, data import/export, Wolfram Alpha, and interactive UIs - **Agent-optimized**: compact response shaping, session state tools, and computation journaling designed for how LLM agents actually work - **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 - **Local and private**: core execution runs on your machine — optional tools like `wolfram_alpha` and repository search contact Wolfram's cloud services when invoked > Ask your agent for a derivation, a 3D plot, a notebook edit, or a verification step, and it can actually do it. --- ## Who This Is For ![enter image description here][2] --- ## What You Can Ask For **"Integrate x^2 sin(x) from 0 to pi, then verify the result."** ```text execute_code("Integrate[x^2 Sin[x], {x, 0, Pi}]") => -4 + Pi^2 verify_derivation(steps=["Integrate[...", "-4 + Pi^2"]) => All steps valid ``` **"Plot the sombrero function in a new notebook."** ```text create_notebook(title="Sombrero") execute_code("Plot3D[Sinc[Sqrt[x^2+y^2]], {x,-4,4}, {y,-4,4}]", style="notebook") => [3D surface plot rendered in live notebook] ``` **"Interactive: slider for Sin[n x]"** ```text execute_code("Manipulate[Plot[Sin[n x],{x,0,2Pi}],{n,1,10}]", style="interactive") => [Live slider UI in Mathematica frontend] ``` 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. --- ## How It Compares ![enter image description here][3] \*Core computation runs locally. Optional tools (`wolfram_alpha`, repository search) contact Wolfram cloud services when invoked. --- ## Quick Start From install to first working notebook plot in under 2 minutes. ### Prerequisites 1- **Mathematica 14.0+** with `wolframscript` in your PATH - [Download Mathematica](https://www.wolfram.com/mathematica/) - macOS: Add to `~/.zshrc`: `export PATH="/Applications/Mathematica.app/Contents/MacOS:$PATH"` 2- **uv package manager** curl -LsSf https://astral.sh/uv/install.sh | sh ### One-Command Setup ```bash # For Claude Desktop uvx mathematica-mcp-full setup claude-desktop # For Cursor uvx mathematica-mcp-full setup cursor # For VS Code (requires GitHub Copilot Chat extension) uvx mathematica-mcp-full setup vscode # For OpenAI Codex CLI uvx mathematica-mcp-full setup codex # For Google Gemini CLI uvx mathematica-mcp-full setup gemini # For Claude Code CLI uvx mathematica-mcp-full setup claude-code # Optional: select a tool profile (default is "full") uvx mathematica-mcp-full setup claude-desktop --profile notebook ``` Then restart Mathematica and your editor. Done! ####VS Code: Alternative setup via Command Palette > **Prerequisite:** [GitHub Copilot Chat](https://marketplace.visualstudio.com/items?itemName=GitHub.copilot-chat) extension must be installed - MCP support is built into Copilot. 1. Press `Cmd+Shift+P` (Mac) / `Ctrl+Shift+P` (Windows) 2. Type "MCP" -> Select **"MCP: Add Server"** 3. Choose **"Command (stdio)"**: *not "pip"* 4. Enter command: `uvx` 5. Enter args: `mathematica-mcp-full` 6. Name it: `mathematica` 7. Choose scope: Workspace or User ####Alternative: Interactive Installer ```bash bash <(curl -sSL https://raw.githubusercontent.com/AbhiRawat4841/mathematica-mcp/main/install.sh) ``` ### Verify Installation ```bash uvx mathematica-mcp-full doctor ``` > **Tip:** If you encounter errors after updating, clear the cache: > ```bash > uv cache clean mathematica-mcp-full && uvx mathematica-mcp-full setup <client> > ``` --- ## Execution Styles Control where results appear with natural language or the `style` parameter: ![enter image description here][4] If you don't include a keyword, the default depends on your [tool profile](#tool-profiles). --- ## Tool Profiles Choose how many tools to expose: ![enter image description here][5] Pass `--profile` during setup or set `MATHEMATICA_PROFILE` env var. --- ## Built for Agent Workflows The server is designed for how LLM agents actually work: long conversations with context limits, intermittent failures, and token budgets: ![enter image description here][6] 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. ### Routing Intelligence (opt-in) For power users, the server can learn from transport outcomes and adapt: ```bash # Observe mode: collect stats, no behavior change export MATHEMATICA_ROUTING_MEMORY=observe # Advise mode: + routing hints + enables adaptive routing export MATHEMATICA_ROUTING_MEMORY=advise export MATHEMATICA_ROUTING_ACTION=compute_cli_skip # optional: skip failing transport ``` 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. > **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. --- ## Manual Installation For full details, troubleshooting, and advanced configuration, see the **[Installation Guide](docs/installation.md)**. ####Quick manual setup 1. **Clone & Install**: git clone https://github.com/AbhiRawat4841/mathematica-mcp.git cd mathematica-mcp uv sync 2. **Install Mathematica Addon**: wolframscript -file addon/install.wl *Restart Mathematica after this step.* 3. **Configure your editor**: add the MCP server to your client'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. --- ## License MIT License [1]: https://github.com/AbhiRawat4841/mathematica-mcp [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table1.jpg&userId=20103 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table2.jpg&userId=20103 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table3.jpg&userId=20103 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table4.jpg&userId=20103 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Table5.jpg&userId=20103 Abhishek Singh Rawat 2026-04-10T00:05:40Z https://community.wolfram.com/groups/-/m/t/3684105 This work explores a computational model that conceptualizes numbers as physical states embodied in neural activity. Using Wolfram Language, we define functions estimating the neural population involved in representing each number from 1 to 100, along with their associated mass and energy based on neuro physiological parameters. The model demonstrates a scalable relationship where larger numbers correspond to increased neural mass and energy, reflecting a physical embodiment of mathematical quantities. Such a model offers a new perspective on the intersection of computation, physics, and neuroscience and can be extended for simulations or further theoretical exploration. Please read the PDF below to get a more detailed explanation and detailed math. Ricky Cespedes 2026-04-13T03:04:40Z https://community.wolfram.com/groups/-/m/t/3673962 ![View of the Moon from Artemis II][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ArtemisIIFlyBy_final.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/54c0ec26-f350-4965-a1bc-bd7b5e34dbf5 Jeffrey Bryant 2026-04-03T19:51:12Z https://community.wolfram.com/groups/-/m/t/3683663 The definition of a conchoid surface is: rc[u, v] = r[u, v] + k (r[u, v] - P)/Norm[r[u, v] - P] and rc[u, v] = r[u, v] - k (r[u, v] - P)/Norm[r[u, v] - P] , P is the pole, k distance and r[u, v] the base surface. In this notebook we will obtain the conchoid surface of the Plücker conoid: {0, 0, Sin[2 u]} + v {Cos[u], Sin[u], 0} with the distance k = 3 and as pole P = {0, 0, 0}. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/4d2d3c71-d5d7-4b73-afb6-1c19f1dcfedf Alejandro Latorre Chirot 2026-04-12T20:21:29Z https://community.wolfram.com/groups/-/m/t/3683654 This notebook presents a set of planes on a straight line. The straight line is known as the axis of the sheaf, and the sheaf is sometimes called a pencil: (n1 X + p1) + u (n2 X + p2) == 0 Where the parameter u. can take any value. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/9bee8e2f-0be8-46f4-8f1c-36768760ee39 Alejandro Latorre Chirot 2026-04-12T17:53:05Z https://community.wolfram.com/groups/-/m/t/3678548 Please join us in a study group devoted to differential equations that begins **Monday, April 13**. This study group will meet daily, Monday to Friday, over the next two weeks. We will share the excellent lesson videos from the Wolfram U course "Introduction to Differential Equations." The study group sessions will include time for exercises, discussion and Q&A. This study group will help you achieve the course completion **certificate** for the "Introduction to Differential Equations" course after you complete the course quizzes. >[**REGISTER HERE**][1] ![enter image description here][2] [1]: https://www.bigmarker.com/series/intro-to-differential-equations/series_details [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image-2026-03-20T22-14-17Z.png&userId=20103 Luke Titus 2026-04-08T20:24:18Z https://community.wolfram.com/groups/-/m/t/3682277 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/5a00b496-c1d9-43a1-a9fe-5e6beeb08cec Rory Foulger 2026-04-12T00:57:27Z https://community.wolfram.com/groups/-/m/t/3682367 ![enter image description here][1] For options A, B, C, and D, how to draw visual diagrams for all valid path scenarios that meet the conditions? For each distinct case, draw a detailed diagram, and use these visual illustrations to help understand and solve the problem. (*Find all valid non-negative integer solutions*)sol = FindInstance[{x + y + z + w == 4, x - y == -2, w == z, x >= 0, y >= 0, z >= 0, w >= 0}, {x, y, z, w}, Integers, 10] (*Calculate number of paths for each solution*) paths = 4!/(x! y! z! w!) /. sol (*Total number of valid paths*) total = Total[paths] (*Check if option A is correct*) Print["Is option A correct? ", total == 12] The above is the computational method I used to verify whether Option A is correct. Now I want to visualize all valid paths for each option using grid diagrams, count the number of paths and calculate the probabilities to determine the correctness of each option. How can I draw such diagrams? [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-04-11_092228.png&userId=3593842 Bill Blair 2026-04-11T01:43:23Z https://community.wolfram.com/groups/-/m/t/3682670 The definition of a conchoid surface is: rc[u, v] = r[u, v] + k (r[u, v] - P)/Norm[r[u, v] - P] and rc[u, v] = r[u, v] - k (r[u, v] - P)/Norm[r[u, v] - P], P is the pole, k distance and r[u, v] the base surface. In this notebook we will obtain the conchoid surface of the paraboloid: {u Cos[v], u Sin[v], u^2} with the distance k = 1.5 and as pole P = {0, 0, 1}. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/82298e0e-efcc-4213-bc6c-98eaeb66a35a Alejandro Latorre Chirot 2026-04-11T20:20:28Z https://community.wolfram.com/groups/-/m/t/3682264 Obtain the Monge point for the next tetrahedron: {9/2, 3/2, 0}, {2, 7/2, 0}, {7/2, 3, 0} y {5/2, 5/2, 2} , then trace the crcumscribed sphere. The Monge point of a tetrahedron is the point of concurrence of the anti-mediator planes that pass through the midpoint of each edge and is perpendicular to the opposite edge. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/59a0ba6c-fe24-43bc-91b8-ec05fc38bf44 Alejandro Latorre Chirot 2026-04-11T19:36:53Z https://community.wolfram.com/groups/-/m/t/3682254 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/e2f3db49-8fcb-4dda-832a-1319ce202f12 Myrto Terpsiadou 2026-04-11T13:27:03Z https://community.wolfram.com/groups/-/m/t/3682521 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ecb910fc-6c9c-4b3e-b082-4c29b8155e5a Housam Binous 2026-04-11T08:39:24Z https://community.wolfram.com/groups/-/m/t/3682083 The definition of a conchoid surface is: rc[u, v] = r[u, v] + k (r[u, v] - P)/Norm[r[u, v] - P] and rc[u, v] = r[u, v] - k (r[u, v] - P)/Norm[r[u, v] - P] , P is the pole, k distance and r[u, v] the base surface. In this notebook we will obtain the conchoid surface of the hyperbolic paraboloid: {u, v, u v + 1} with the distance k = 1.5 and as pole P = {0, 0, 1}. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/13fc44d3-d44e-424b-a396-b9696a589d0d Alejandro Latorre Chirot 2026-04-10T20:34:27Z https://community.wolfram.com/groups/-/m/t/3682155 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/c71dc2ab-aaae-483f-8ad8-c1df5123fa14 Housam Binous 2026-04-10T17:43:39Z https://community.wolfram.com/groups/-/m/t/3681468 ![Atomic-scale stick-slip through a point defect][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Atomic-scalestick-slipthroughapointdefect.png&userId=20103 [2]: https://www.wolframcloud.com/obj/34d3352e-a7a1-41b4-be41-b4ebe4ca62dd Enrico Gnecco 2026-04-10T17:00:36Z https://community.wolfram.com/groups/-/m/t/3681925 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/64303660-b4e4-4803-a2d0-5adaa34c994e Housam Binous 2026-04-10T12:15:35Z https://community.wolfram.com/groups/-/m/t/3673980 Suppose, we have the following code (i.e., `f[r]` and `g[r]` can be any function, where `f[r+c]<V[r]<g[r+d]` or `g[r+d]<V[r]<f[r+c]` and `c`, `d` are small constants; e.g., between $-10$ and $10$.) V[r_]:=V[r]=r!+1 f[r]:=f[r]= g[r_]:=g[r]= LengthS[r_] := LengthS[r] = {f[r],g[r]} LengthS1[r_, x_] := LengthS1[r, x] = LengthS[r][[x]] LengthS2[j_, y_] := LengthS2[j, y] = LengthS[j][[y]] We approximate the constants, in the code below, using this equation: > If $F:\mathbb{N}\to\mathbb{R}$ and $G:\mathbb{N}\to\mathbb{R}$ are > arbitrary functions, we want to calculate this equation with > Mathematica: > > $$\small{\begin{equation} c=\inf\left\{|1-\mathbf{c_1}|:\forall(\varepsilon>0)\exists(\mathbf{c_1}>0)\forall(r\in\mathbb{N})\exists(v\in\mathbb{N})\left(\left|\frac{F(r)}{G(v)}-\mathbf{c_1}\right|<\varepsilon\right)\right\} \tag{1}\label{eq:1} \end{equation}}$$ cV1[r_, 1, 2] := cV1[r, 1, 2] = N[Min[Table[ RealAbs[1 - V[r]/LengthS1[v, x]], {v, 1, 30000}]]] cV1[r_, 2, 1 ] := cV1[r, 2, 1] = N[Min[Table[ RealAbs[1 - LengthS1[r, x]]/V[v], {v, 1, 30000}]]] cV2[r_, 1, 2] := cV2[r, 1, 2] = N[Min[Table[ RealAbs[1 - V[r]/LengthS2[v, y]], {v, 1, 30000}]]] cV2[r_, 2, 1] := cV2[r, 2, 1] = N[Min[Table[ RealAbs[1 - LengthS2[r, y]/V[v]], {v, 1, 30000}]]] c[r_, 1, 2] := c[r, 1, 2] = N[Min[Table[ RealAbs[1 - LengthS1[r, x]/LengthS2[v, y]], {v, 1, 30000}]]] c[r_, 2, 1] := c[r, 2, 1] = N[Min[Table[ RealAbs[1 - LengthS2[r, y]/LengthS1[v, x]], {v, 1, 30000}]]] In case the outputs are incorrect, use Equation \eqref{eq:1} to solve the exact value. In addition, w.r.t. the inequality `f[r+c]<V[r]<g[r+d]`, we adjust `r+c` and `r+d` into `r+c1` and `r+d1`, using `P1` (i.e., `c1==c+1||c1==c||c1==c-1` and `d1==d+1||d1==d||d1==d-1`). If this makes no sense, then analyze the code. P1 = 3 (*P1 can be any constant positive integer*) Min11[r_, x_] := Min11[r, x] = Max[r1 /. FindInstance[LengthS1[r1, x] <= V[r] < LengthS1[r1 + 1, x], {r1}, PositiveIntegers]] Min12[r_, x_] := Min12[r, x] = ArgMin[{RealAbs[LengthS1[r2, x] - V[r]], r - P1 <= r2 <= r + P1}, r2, PositiveIntegers] Min21[r_, y_] := Min21[r, y] = Max[r3 /. FindInstance[LengthS2[r3, y] <= V[r] < LengthS2[r3 + 1, y], {r3}, PositiveIntegers]] Min22[r_, y_] := Min22[r, y] = ArgMin[{RealAbs[LengthS1[r4, y] - V[r]], r - P1 <= r4 <= r + P1}, r4, PositiveIntegers] rMin1[r_, x_] := rMin1[r, x] = Min12[r, x] + Sign[Floor[RealAbs[2 r - Min11[r, x] - Min12[r, x]]/2]] rMin2[r_, y_] := rMin2[r, y] = Min22[r, y] + Sign[Floor[RealAbs[2 r - Min21[r, y] - Min22[r, y]]/2]] Putting it together, here is what I want: For any `LengthS1[r,x]=f[r+c1]` and `LengthS2[r,y]==g[r+d1]` such that for any function `f` and `g`, where `f[r+c1]<V[r]<g[r+d1]` or `g[r+d1]<V[r]<f[r+c1]`, consider four out of sixteen cases. (I figured out the other cases, so I will not include them): 1. Case 11: LengthS1[rMin1[r, x], x] > V[r] && V[r] > LengthS2[rMin2[r, y], y] && RealAbs[LengthS1[rMin1[r, x], x] - V[r]] > RealAbs[LengthS2[rMin2[r, y], y] - V[r]] and extra criteria including `cV1`, `cV2`, and `c` (see Equation \ref{eq:1}). 2. Case 12: LengthS1[rMin1[r, y], y] > V[r] && V[r] > LengthS2[rMin2[r, x], x] && RealAbs[LengthS1[rMin1[r, y], y] - V[r]] > RealAbs[LengthS2[rMin2[r, x], x] - V[r]] and extra criteria including `cV1`, `cV2` and `c` (see Equation \ref{eq:1}) 3. Case 15: LengthS2[rMin2[r, y], y] > V[r] && V[r] > LengthS1[rMin1[r, x], x] && RealAbs[LengthS2[rMin2[r, y], y] - V[r]] > RealAbs[LengthS1[rMin1[r, x], x] - V[r]] and extra criteria including `cV1`, `cV2` and `c` (see Equation \ref{eq:1}) 4. Case 16: LengthS2[rMin2[r, x], x] > V[r] && V[r] > LengthS1[rMin1[r, y], y] && RealAbs[LengthS2[rMin1[r, x], x] - V[r]] > RealAbs[LengthS1[rMin2[r, y], y] - V[r]] and extra criteria including `cV1`, `cV2` and `c` (see Equation \ref{eq:1}). In the code below (I assume) there should be five sign functions involved with `cV1`, `cV2`, and `c` in Equation \eqref{eq:1} that are multiplied by `c[r,x,y]` (in `Q11`), `c[r,y,x]` (in `Q12`), `c[r,y,x]` (in `Q15`), and `c[r,x,y]` (in `Q16`). **Note:** In my research paper, I want the sign functions in (`Q11` and `Q12`) *and* (`Q15` and `Q16`) to be the same, except that the `x` and `y` are swapped. (See the code, for an example of such functions.) **Question:** How do I change the five sign functions (in each criteria) to match any example that satisfies the former criteria? (Keep reading for specific examples.) ---------- Here is what I got: Q11[r_, x_, y_] := Q11[r, x, y] = Sign[cV2[r, y, x] - cV1[r, y, x]] Sign[cV1[r, y, x] - cV2[r, x, y]] Sign[cV2[r, x, y] - cV1[r, x, y]] Sign[c[r, x, y] - c[r, y, x]] Sign[cV2[r, x, y] - cV2[r, y, x]] c[r, x, y] >= c[r, y, x] && c[r, y, x] >= cV2[r, y, x] && LengthS1[rMin1[r, x], x] > V[r] && V[r] > LengthS2[rMin2[r, y], y] && RealAbs[LengthS1[rMin1[r, x], x] - V[r]] > RealAbs[LengthS2[rMin2[r, y], y] - V[r]] Q12[r_, x_, y_] := Q12[r, x, y] = Sign[cV2[r, x, y] - cV1[r, x, y]] Sign[cV1[r, x, y] - cV2[r, y, x]] Sign[cV2[r, y, x] - cV1[r, y, x]] Sign[c[r, y, x] - c[r, x, y]] Sign[cV2[r, y, x] - cV2[r, x, y]] c[r, y, x] >= c[r, x, y] && c[r, x, y] >= cV2[r, x, y] && LengthS1[rMin1[r, y], y] > V[r] && V[r] > LengthS2[rMin2[r, x], x] && RealAbs[LengthS1[rMin1[r, y], y] -V[r]] > RealAbs[LengthS2[rMin2[r, x], x] - V[r]] Q15[r_, x_, y_] := Q15[r, x, y] = Sign[cV2[r, x, y] - cV1[r, x, y]] Sign[cV1[r, x, y] - cV2[r, y, x]] Sign[cV1[r, y, x] - cV2[r, y, x]] Sign[c[r, y, x] - c[r, x, y]] Sign[cV1[r, x, y] - cV1[r, y, x]] c[r, y, x] >= c[r, x, y] && c[r, x, y] >= cV1[r, y, x] && LengthS2[rMin2[r, y], y] > V[r] && V[r] > LengthS1[rMin1[r, x], x] && RealAbs[LengthS2[rMin2[r, y], y] - V[r]] > RealAbs[LengthS1[rMin1[r, x], x] - V[r]] Q16[r_, x_, y_] := Q16[r, x, y] = Sign[cV2[r, y, x] - cV1[r, y, x]] Sign[cV2[r, y, x] - cV1[r, x, y]] Sign[cV1[r, x, y] - cV2[r, x, y]] Sign[c[r, x, y] - c[r, y, x]] Sign[cV1[r, x, y] - cV1[r, y, x]] c[r,x, y] >= c[r, y, x] && c[r, y, x] >= cV1[r, x, y] && LengthS2[rMin2[r, x], x] > V[r] && V[r] > LengthS1[rMin1[r, y], y] && RealAbs[LengthS2[rMin2[r, x], x] - V[r]] > RealAbs[LengthS1[rMin1[r, y], y] - V[r]] **Examples:** Here are the cases I worked with (they should satisfy the known criteria in the post). Note that `r` can be any natural number (e.g., `r==10`). I have not gotten the output I wanted for all the specific cases. 1. `LengthS[r_]:=LengthS[r]={11r!/8+1, 2r!/3+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={True,False,False,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,True,False,False}`) 2. `LengthS[r_]:=LengthS[r]={2r!/3+1, 11r!/8+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={False,False,True,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,False,False,True}`) 3. `LengthS[r_]:=LengthS[r]={4r!/3+1, 7r!/8+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={True,False,False,False}` and `{Q11[r,2,1],Q12[r,2,1],Q13[r,2,1],Q14[r,2,1]}=={False,True,False,False}`) 4. `LengthS[r_]:=LengthS[r]={7r!/8+1, 4r!/3+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={False,False,True,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,False,False,True}`) 5. `LengthS[r_]:=LengthS[r]={11r!/8+1, 33r!/50+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={True,False,False,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,True,False,False}`) 6. `LengthS[r_]:=LengthS[r]={33r!/50+1, 11r!/8+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={False,False,True,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,False,False,True}`) 7. `LengthS[r_]:=LengthS[r]={7r!/9+1, 11r!/8+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={True,False,False,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,True,False,False}`) 8. `LengthS[r_]:=LengthS[r]={11r!/8+1, 7r!/9+1}` (it should return `{Q11[r,1,2],Q12[r,1,2],Q15[r,1,2],Q16[r,1,2]}=={False,False,True,False}` and `{Q11[r,2,1],Q12[r,2,1],Q15[r,2,1],Q16[r,2,1]}=={False,False,False,True}`) Bharath Krishnan 2026-04-03T22:22:57Z https://community.wolfram.com/groups/-/m/t/3682128 A parabola is rotated 30 degrees with respect to the line x = 1 and its new parametric equations are requested. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/aa3a9e67-2b63-4c3f-bdf6-893f98032c15 Alejandro Latorre Chirot 2026-04-10T14:41:34Z https://community.wolfram.com/groups/-/m/t/3677702 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ae38869b-b54e-46c4-b3ea-ccd182dc1316 Tigran Nersissian 2026-04-08T01:43:51Z https://community.wolfram.com/groups/-/m/t/3634024 The architecture dresses in luxury with Viviani's curved windows, here are the 6 ways to get it... &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/2e033a24-d5a9-4412-9683-d1e04d46a345 Alejandro Latorre Chirot 2026-02-03T15:25:25Z