edulab is a collection of coding-agent skills that turn academic questions into interactive lesson web pages. It is used to solve and present educational problems, including solid-geometry exercises, through guided, self-contained lessons. The catalogue add-ons are the project's own education-focused skills and plugins.
Getting it into your agent
This one installs as part of its plugin. Adding the marketplace and installing the plugin brings it with everything else the plugin ships.
/plugin marketplace add wy51ai/edulab/plugin install edulabWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/wy51ai/edulab/edu-analytic-geometry)<a href="https://agentmods.dev/skills/wy51ai/edulab/edu-analytic-geometry"><img src="https://agentmods.dev/badge/skills/wy51ai/edulab/edu-analytic-geometry/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/wy51ai/edulab/edu-analytic-geometry"><img src="https://agentmods.dev/badge/skills/wy51ai/edulab/edu-analytic-geometry.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- Socket pass
- Snyk warn
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00450 | $0.03403 |
| Opus 5 | $0.00225 | $0.01702 |
| Sonnet 5 | $0.00090 | $0.00681 |
| Haiku 4.5 | $0.00045 | $0.00340 |
Grade A, and why
edu-analytic-geometry scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 10d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 154 lines — stays where its author put it; the contents beside it link to each section on GitHub.
解析几何解题 → 交互网页
这个技能产出什么
一个可直接用浏览器打开的单页 HTML（三栏）：
- 左栏：题面 + 动态控制台 —— 一个可变参数滑块（如直线倾斜角 θ / 动点参数 t）驱动实时 重算的几何量（交点坐标、斜率、数量积、弦长、面积…），以及"理论范围条"或"定值指示"。
- 中栏：分步解析（公式用 KaTeX），可一键收起把空间让给画板。
- 右栏：2D Canvas 动态几何画板（圆锥曲线 + 动直线/动点 + 向量 + 点标注 + 网格坐标轴）， 叠加画笔涂鸦工具栏。
形态与目标模板 /Users/wuyi/code/code2026/6/template/code_artifact.html 一致。
依赖（重要）
计算核心 lib/analytic_kernel.py 依赖 sympy。运行脚本前先确认有能 import sympy 的
解释器：python3 -c "import sympy"（本机用 /opt/homebrew/bin/python3.11，sympy 1.14）。
缺库时：若 import 报错（sympy 或后续任何库），先询问用户是否安装，同意后再装
（python3 -m pip install <库名>）或换一个已装该库的解释器；不要未经询问直接装。
下文 python3 均指这个能跑通依赖的解释器。
工作流程
第 1 步：得到 problem spec（三入口归一）
把题目整理成结构化 spec（曲线类型与参数、已知点/条件、所求类型与对象、语言）。
- 文字题：直接抽取。
- 图片：视觉读图抽取，并把识别到的题目回显给用户确认（题面/曲线/参数/所求/语言）再继续。
- 随机出题：选曲线 + 题型，随机参数 → kernel 求解，用
analytic_kernel.is_clean(...)判答案 是否规整，不规整就重抽。
输出语言跟随提示词语言：英文提示 → 英文网页，中文 → 中文。spec 记下
language。
第 2 步：用 kernel 精确计算（不要心算）
按 references/conventions.md 的解法配方，调用 lib/analytic_kernel.py 与 lib/conics.py：
conics.ellipse/hyperbola/parabola/circle(...)得曲线对象（精确 a,b,c、焦点、顶点、准线、 渐近线、eq_latex、以及给前端引擎的boarddict）。chord_setup(conic, through)联立含参直线x=my+c得 y 的二次方程 + 韦达量（精确）。- 目标量：
dot_product_expr/chord_len_sq_expr/triangle_area_expr/slope_product_central… - 取值范围：
range_over_m(expr, horizontal_valid=?)—— 含开闭端点判定（关键正确性点，见下）。 - 定值：
is_constant_in_m(expr)。
可命令行自检 kernel：
python3 lib/analytic_kernel.py # 旗舰题内置断言自检
⚠️ 端点开闭 = 正确性命门：过焦点的弦，水平线（x 轴，θ=0）与竖直线（θ=90）都是合法直线， 它们取到的端点要计入。例：椭圆 MA·MB 题，x 轴取到 −3、竖直线取到 7/4，故答案是闭区间
[-3, 7/4]（很多教辅误写成开的(-3, 7/4]）。range_over_m已据此判定，且这样答案与交互 工具一致——拖滑块到 0° 就读到 −3。抛物线焦点弦的"轴方向"是退化线（只交一点），其极限端点 不计入（horizontal_valid=False或限制 param 范围）。
第 3 步：组装数据并注入模板
📍 输出位置 & 唯一产物（最重要）：交付给用户的只有一个
.html，写到当前工作目录 （Path.cwd()）（除非用户显式指定路径）。cwd 里不要留任何别的文件——构建脚本（.py）、__pycache__、自检截图（.png）、临时文件都不是交付物，一律放/tmp或用完即删。 也绝不要写进技能自身目录（skills/edu-analytic-geometry/output/是技能内部样例）。
What ships with it
6 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 10d ago First seen · 154 lines · 450 tokens per session scan A 39f936412cb6
edu-analytic-geometry is a skill published in the GitHub repository wy51ai/edulab (1,158 stars, last pushed 29d ago), licensed Apache-2.0. It adds 450 tokens to every session and 3,403 once invoked, about $0.0022 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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