<notatio-vector-plot>

Split a field attribute into its two components. Handles an optional \{...\}, {...} or (...) wrapper and only splits on a comma at brace / paren depth zero, so \{\frac{y}{2}, -x\} survives intact. / export function splitField(raw: string): [string, string] | undefined { let s = raw.trim(); const unwrap: [string, string][] = [ ["\\{", "\\}"], ["\\left(", "\\right)"], ["{", "}"], ["(", ")"], ["[", "]"], ]; for (const [open, close] of unwrap) { if (s.startsWith(open) && s.endsWith(close)) { s = s.slice(open.length, s.length - close.length).trim(); break; } } let depth = 0; for (let i = 0; i < s.length; i++) { const c = s[i]; if (c === "{" || c === "(" || c === "[") depth++; else if (c === "}" || c === ")" || c === "]") depth--; else if (c === "," && depth === 0) { const u = s.slice(0, i).trim(); const v = s.slice(i + 1).trim(); if (u && v) return [u, v]; return undefined; } } return undefined; }

const log = debug("vectorplot");

/** <notatio-vector-plot u="-y" v="x" xrange="-2,2" yrange="-2,2"> -- a planar vector field (Wolfram's VectorPlot): u/v are the two components in notatio, or field="-y, x" gives both at once. Arrows sit on an n×n grid of cell centres, their length and colour scaling with |F|.

type="stream" switches to StreamPlot: streamlines traced from the same grid by fixed-step RK4 on the normalised field -- deterministic, so the same field always draws the same picture (no random seeding).

Stories in the playground·packages/notatio-lit/src/notatio-vector-plot.ts· in Vue: <VectorPlot>

Attributes

Attribute	Type	Default	Notes
u	string	""	The x component of the field, in notatio.
v	string	""	The y component of the field, in notatio.
field	string	""	Both components at once, comma-separated — "-y, x".
xvar	string	"x"	The variable on the x axis; defaults to the expression's first unknown.
yvar	string	"y"	The variable on the y axis; defaults to the next unknown after xvar.
xrange	string	"-2,2"	The x sampling range, as lo,hi.
yrange	string	"-2,2"	The y sampling range, as lo,hi.
n	number	0	Arrows (or streamline seeds) per side.
type	"vector" | "stream"	"vector"	vector for arrows, stream for RK4 streamlines.
steps	number	60	Streamline integration steps taken in each direction from a seed.
axes	string	"true"	"false" hides the axes.
x-label property xLabel	string	""	Axis label for x.
y-label property yLabel	string	""	Axis label for y.
label	string	""	Caption drawn above the figure.