signchart directive

The signchart directive generates visual sign charts (fortegnsskjema in Norwegian) for polynomial functions. Sign charts show where a function is positive (+), negative (-), or zero (0).

Basic Usage

Quadratic Function

Fig. 3 Sign chart for f(x) = x² - 4

Cubic Function

Fig. 4 Sign chart for g(x) = x³ - x

Without Factors

You can hide the factored form by setting factors: false:

Fig. 5 Sign chart without factors shown

Different Widths

Full Width

Fig. 6 Full width sign chart

Fixed Width

Fig. 7 Fixed width sign chart (600px)

Higher Degree Polynomials

Quartic Function

Fig. 8 Sign chart for f(x) = x⁴ - 5x² + 4

Quintic Function

Fig. 9 Sign chart for g(x) = x⁵ - 5x³ + 4x

Custom Domain

You can restrict the sign chart to a specific interval using xmin and xmax:

Fig. 10 Sign chart for A’(k) restricted to domain [0, 3]

This is useful when:

• The function has a restricted domain in the problem context

• You only want to show behavior in a specific interval

• The function represents a real-world quantity with physical constraints

Another example with a rational function derivative:

Fig. 11 Sign chart for A’(r) on [0, 10]

Features

Automatic Factorization

The directive automatically factors the polynomial and shows:

• All zeros (roots) of the function

• The sign of the function in each interval

• The factored form (when factors: true)

Caching

Sign charts are cached as SVG files to speed up rebuilds. To force regeneration:

```{signchart}
---
function: x**2 - 4, f(x)
nocache: true
---

### Accessibility

- Alt text defaults to "Fortegnsskjema" (Sign chart)
- Can be customized with the `alt` option
- SVG includes `role="img"` and `aria-label` for screen readers

## Options Reference

| Option | Type | Default | Description |
|--------|------|---------|-------------|
| `function` | string (required) | - | Polynomial expression and optional label |
| `factors` | boolean | `true` | Show factored form |
| `xmin` | number | auto | Minimum x-value for domain |
| `xmax` | number | auto | Maximum x-value for domain |
| `width` | string | auto | Width (e.g., "80%", "600px", "500") |
| `align` | string | `center` | Alignment: "left", "center", "right" |
| `alt` | string | "Fortegnsskjema" | Alt text for accessibility |
| `nocache` | flag | - | Force regeneration of chart |
| `class` | string | - | Additional CSS classes |
| `name` | string | - | Reference name for cross-referencing |

## Syntax

### YAML Front-matter Style

```markdown
```{signchart}
---
function: expression, label
factors: true
width: 80%
---
Caption text

### Simple Key-Value Style

```markdown
```{signchart}
function: expression, label
factors: true
width: 80%

Caption text

## Function Format

The `function` option accepts two formats:

1. **String with comma**: `"expression, label"`
   - Example: `"x**2 - 4, f(x)"`
   
2. **Tuple/list**: `("expression", "label")`
   - Example: `("x**2 - 4", "f(x)")`

The label is optional. If omitted, no function name is shown in the chart.

## Dependencies

This directive requires the `signchart` Python package to be installed:

```bash
pip install signchart

The package uses SymPy for symbolic mathematics and Matplotlib for rendering.