Sign, variation and convexity tables in the French tkz-tab style, plus value tables (tableaux de valeurs). Supports auto-computed signs and values from Typst functions.

Basic sign + variation	Full f’/f’’ analysis	Rational function / pole
Auto-signs with fn	Direct signs (no factors)	Value table (fun-table)

Usage

#import "@preview/functable:0.1.0": sign-table, fun-table

Basic sign + variation table

#sign-table(
  factors: (
    (expr: $x - 1$, zeros: ((value: $1$, approx: 1),), signs: ("-", "+")),
    (expr: $x + 2$, zeros: ((value: $-2$, approx: -2),), signs: ("-", "+")),
  ),
  summary-label: $f'(x)$,
  variation: true,
  variation-label: $f(x)$,
  start-value: $-oo$,
  end-value: $+oo$,
  variation-values: (
    (at: -2, label: $5$),
    (at:  1, label: $-4$),
  ),
)

Auto-computed signs with fn

Provide a Typst function for each factor instead of (or in addition to) signs. The sign in each interval is inferred by evaluating the function at a test point:

#sign-table(
  factors: (
    (
      expr: $x + 1$,
      zeros: ((value: $-1$, approx: -1),),
      fn: x => x + 1,   // signs inferred automatically
    ),
    (
      expr: $x - 1$,
      zeros: ((value: $1$, approx: 1),),
      fn: x => x - 1,
    ),
  ),
  summary-label: $f'(x)$,
  variation: true,
  variation-label: $f(x)$,
)

signs always takes precedence over fn if both are provided. Return none from fn to mark an interval as HD (hors-domaine), e.g. fn: x => if x <= 0 { none } else { 1 / (2 * calc.sqrt(x)) }.

Direct signs — no factor rows

When the factorisation is not the point, give the signs of the function directly with the top-level signs/zeros parameters (mutually exclusive with factors). Zeros can be plain numbers — shorthand for (value: $n$, approx: n) — mixed with dictionaries:

#sign-table(
  signs: ("+", "-", "+"),
  zeros: (-1, (value: $2$, approx: 2, pole: true)),
  summary-label: $f(x)$,
)

The same mechanism gives a variation table alone (no sign row): leave summary-label at none, set variation: true, and the signs only steer the arrows:

#sign-table(
  signs: ("-", "+"),
  zeros: (2,),
  variation: true,
  variation-label: $f(x)$,
  start-value: $+oo$,
  end-value: $+oo$,
  variation-values: ((at: 2, label: $-3$),),
)

second-signs does the same for the f’’ block / convexity row, sharing the top-level zeros.

Full analysis table (f’ + variation + f’’ + convexity)

#sign-table(
  factors: (
    (expr: $3x^2 - 3$, zeros: (
      (value: $-1$, approx: -1),
      (value: $1$,  approx:  1),
    ), signs: ("+", "-", "+")),
  ),
  summary-label: $f'(x)$,
  variation: true,
  variation-label: $f(x)$,
  start-value: $+oo$,
  end-value: $+oo$,
  variation-values: (
    (at: -1, label: $2$),
    (at:  1, label: $-2$),
  ),
  second-factors: (
    (expr: $6x$, zeros: ((value: $0$, approx: 0),), signs: ("-", "+")),
  ),
  second-summary-label: $f''(x)$,
  convexity: true,
  convexity-label: $f(x)$,
)

Rational function with pole (valeur interdite)

Mark a zero as pole: true to draw a double bar (‖) and break the variation arrows:

#sign-table(
  factors: (
    (expr: $x + 1$, zeros: ((value: $-1$, approx: -1),), signs: ("-", "+")),
    (
      expr: $x - 2$,
      zeros: ((value: $2$, approx: 2, pole: true),),
      signs: ("-", "+"),
    ),
  ),
  summary-label: $f(x)$,
  variation: true,
  variation-label: $f(x)$,
)

Value table (explicit)

#fun-table(
  x-values: ($0$, $1$, $2$, $3$),
  rows: (
    (label: $f(x)$, values: ($1$, $3$, $5$, $7$)),
  ),
)

Value table with auto-computed values

Provide numeric x-values and a fn closure — values are computed automatically:

#fun-table(
  x-values: (-3, -2, -1, 0, 1, 2, 3),
  rows: (
    (label: $f(x) = x^2 - 1$, fn: x => x * x - 1),
  ),
)

For irrational x values or custom display, use dictionary entries:

#fun-table(
  x-values: (
    (display: $-pi\/2$, value: -calc.pi / 2),
    (display: $0$,      value: 0.0),
    (display: $pi\/2$,  value: calc.pi / 2),
  ),
  rows: (
    (label: $sin(x)$, fn: x => calc.sin(x), format: x => $#str(calc.round(x, digits: 4))$),
  ),
)

sign-table reference

Factor dictionary keys

Exactly one of signs or fn is required; every other key is optional.

Zero dictionary keys

Each entry in a zeros array is either a plain number — shorthand for (value: $n$, approx: n) — or a dictionary. value and approx are required; the rest are optional:

HD intervals

Set signs: (..., "HD", ...) for intervals where the expression does not exist, or return none from fn. The interval renders as a hatched band (controlled by hd-style).

Use mark: "hd" on a zero to continue the hatch through a boundary point (e.g. a cusp or vertical tangent where f’ is undefined but f continues), as opposed to mark: "bar" which draws the asymptote double-bar.

fun-table reference

Row dictionary keys

Changelog

[0.1.0] - 2026-07-14

Added

• sign-table: sign/variation/convexity tables in the tkz-tab style
• fun-table: simple function value tables (tableaux de valeurs)
• fn parameter on factors for auto-sign inference by numeric evaluation
• fn parameter on fun-table rows for auto-computed values from numeric x-values
• HD (hors-domaine) hatching with "hatch", "fill", and "blank" styles
• Pole / valeur interdite rendering with double bars (‖) and broken arrows
• Dual f’/f’’ block with convexity row (∪/∩)
• Variation arrows with auto-positioned function value labels
• Automatic zero merging across factors
• mark: "hd" for domain-boundary points without asymptote implication
• Top-level signs/zeros/second-signs for direct sign tables and standalone variation tables without factor rows
• Number shorthand in zeros arrays: zeros: (-2, 1) ≡ (value: $n$, approx: n) per entry
• Convexity display modes: "symbol" (∪/∩), "text" (“convexe”/“concave”), "both"