Math input

How an expression written on a math keyboard becomes a Julia value, and how a Julia value becomes typeset mathematics again.

GiacSlate offers two distinct entry points, which are easy to confuse:

giac"…" — the live literal

A giac"…" literal is ordinary Xcas source, evaluated by giac_eval:

factor(giac"x^6 - 1")
desolve(giac"y'' + 4*y = 0 and y(0) = 1 and y'(0) = 0", giac"y(t)")

What makes it special is the editor extension using GiacSlate installs: inside a code cell, such a literal renders as a typeset MathLive field. Click into it, edit the mathematics, press <kbd>Enter</kbd> — the literal's source is rewritten and the cell recomputes. The file stays perfectly ordinary Julia: outside Slate, giac"x^2+1" evaluates exactly the same.

<kbd>⌘</kbd>/<kbd>Ctrl</kbd>+<kbd>M</kbd> inserts a fresh field; the ∫ button in the cell toolbar does the same with the mouse.

An empty literal is missing, not an error:

giac""        # missing

That is deliberate: a blank math field should read as "not filled in yet" and flow through the grader as such, rather than breaking the cell.

Mathfield — the @bind control

When what you want is the reader's answer rather than an expression edited in place, bind a control:

@bind answer Mathfield(label = "your answer")

answer receives MathJSON — a String. To turn it into an expression:

expr = mathfield_to_giac(answer)   # a GiacExpr, or `missing` if the field is empty

Because the bound value is a plain String, SlateExtensionsBase's type-driven coerce/reconcile defaults apply as-is: the answer survives a re-run of the bind cell.

The front-end component (assets/mathfield.js) is fetched only on the first binding of a Mathfield, through required_assets.

Typesetting in prose

gmath and gdisplay render a Giac expression as LaTeX ready to be interpolated into a Markdown cell with {{ … }}:

# in a code cell
Hs = giac"1/(s^2 + 2*s + 5)"

The system has transfer function {{ gmath(Hs) }}, a second-order response. Its
unit-step response is

{{ gdisplay(yt) }}

gmath produces inline math ($…$), gdisplay a display block ($$…$$). Because the Markdown cell reads the variable, it re-typesets whenever that variable changes.

The bridge, in both directions

The two conversion functions are exported, and exposed to the front-end as the giac_tex and giac_src handlers:

GIAC source  ──[ giac_src_to_tex ]──▶  LaTeX          (display)
MathJSON     ──[ mathjson_to_giac_src ]──▶  GIAC source  (write-back)

• giac_src_to_tex evaluates, then renders to LaTeX. GIAC is lenient — it returns undef on malformed input instead of throwing — so undef is treated as an error here: an unreadable field must show as broken, not as the literal word undef.
• mathjson_to_giac_src returns source text and evaluates nothing. Empty input, a null, and the ["Error", …] payload MathLive emits for an invalid field all give "" — a half-typed formula must not break the cell being edited.
• mathfield_to_giac is the variant that does evaluate, returning a GiacExpr.

What the MathJSON walk translates

MathJSON heads are converted into Xcas source: arithmetic (Add, Subtract, Multiply, Divide, Power, Root, Sqrt), grouping (Delimiter, Sequence), List, Equal, Subscript, the usual constants (Pi, ExponentialE, ImaginaryUnit, GoldenRatio, the infinities), and a table of functions (trigonometric and hyperbolic, Exp, Ln, Log, Abs, Floor, Gamma, Factorial, …).

Two explicit refusals, rather than bogus symbols:

• string literals are not valid math input;
• decorated symbols (x̂, x̄, x⃗, ẋ, …) have no clean GIAC counterpart, so the conversion raises instead of inventing a hat(x) that would neither compute nor compare against anything. Use a plain name (xhat, xbar).

Likewise, a symbol still non-ASCII after canonicalisation is refused.

Greek letters and subscripts

A math keyboard emits Greek letters as Unicode glyphs, which GIAC treats as distinct from its ASCII identifiers. A single normaliser is shared by every ingress — the MathJSON bridge, the giac"…" macro, the display path, and the grader — folding:

This unifies encodings of one symbol; it never merges two distinct symbols.

Reference

giac"…"

gmath(e)

gdisplay(e)

Mathfield(; label = nothing, default = "")

mathfield_to_giac(mathjson) -> GiacExpr | missing

giac_src_to_tex(src) -> String

mathjson_to_giac_src(json) -> String