@ai-gui/plugin-function

Function and calculus figures for AIGUI. The model writes y = f(x) and an interval; the curve, its tangents, the area under it and its Riemann rectangles are computed here.

Install

pnpm add @ai-gui/plugin-function

No plotting library, no canvas, no runtime dependency beyond @ai-gui/core. The output is an SVG string.

Usage

import { fn } from "@ai-gui/plugin-function"
import { buildSystemPrompt } from "@ai-gui/core"

<AIRenderer plugins={[fn()]} />

// The model has no prior for this block, so the spec is what makes it usable at all.
const system = buildSystemPrompt({ registry, plugins: [fn()], locale: "zh-CN" })

f(x) = x² 在 x = 1 处的切线斜率为 2，切线方程 y = 2x − 1。

```function
{
  "plot": [{ "id": "f", "expr": "x^2", "domain": [-1.5, 2.5], "label": "y = x²" }],
  "marks": [
    { "tangent": { "of": "f", "at": 1 } },
    { "point": { "on": "f", "at": 1, "label": "P(1, 1)" } }
  ],
  "caption": "f(x) = x² 在 P(1,1) 处的切线"
}
```

Why the protocol looks like this

An expression, never sampled points. A model that plots the curve itself has put its own arithmetic into the picture, and a wrong point looks exactly like a right one. A definition containing points, data, values or samples is refused outright.

The slope is measured, not stated. tangent takes the point; the derivative is computed by central difference. An answer that mis-differentiates in its prose still draws the right line — and the k = … label on the figure comes from the same measurement, so the picture cannot contradict itself.

Every reference must resolve. A mark naming a curve no plot defines is refused rather than skipped, so a figure never silently omits the thing the answer is pointing at.

Intervals may be written the way a question states them. [0, "2*pi"] and ["-pi/2", "pi/2"] are constant expressions, evaluated by the same parser. Forcing 6.283185 is unnatural and is one more place for the model to do arithmetic.

The expression grammar

x is the only variable. Multiplication is always explicit (2*x, never 2x), powers use ^, and functions need brackets. Available: sin cos tan asin acos atan sinh cosh tanh exp ln log log2 sqrt abs sign floor ceil round, plus pi and e.

There is no eval anywhere: this is a recursive-descent parser over a fixed grammar with a fixed function table, looked up with Object.hasOwn so an expression cannot reach Object.prototype. A sign binds looser than a power, so -x^2 is negative — parsed the other way it is a different curve, and one that looks perfectly reasonable on screen.

Marks

| | | | --- | --- | | tangent | {"of":"f","at":1} — slope measured here | | area | {"of":"f","from":0,"to":2}, or {"between":["f","g"],…} | | riemann | {"of":"f","from":0,"to":1,"n":8,"rule":"left"\|"right"\|"mid"} | | point | {"on":"f","at":1,"label":"P"} | | asymptote | {"x":0} or {"y":1} | | derivative | {"of":"f"} — the curve of f′, sampled the same way f is |

Not in this version, and the prompt spec tells the model to explain them in prose or use ```chart instead: implicit curves, polar and parametric curves, surfaces, the complex plane, and the scatter of a sequence or distribution.

Options

• width?, height? — figure size in CSS pixels, default 640 × 380.
• samples? — points per curve, default 480.
• maxCurves? — default 8. maxSourceBytes? — default 16 KiB.

Testing note

src/fixtures/ holds the twenty figures a model produced when given this plugin's prompt spec and twenty textbook questions. They are part of the test suite: a protocol change they stop parsing is one that breaks answers already being written.

See the root README for the full plugin list.