TraditionalForm, FullForm, TeXForm — one expression
Open the In/Out menu. Each entry is a representation, requested by name.
source
<notatio-out value="\frac{\sin(x)}{x^2+1}" label="Out" />Wolfram Language
The Wolfram Language is the reason most of this repository is spelled the way it is. Not a dependency — a naming authority, a design precedent, and an oracle we check our answers against.
Three separate debts, and they are worth separating.
The debt of names
Almost every head here is a Wolfram symbol. Binomial, Subsets, Permutations, IntegerPartitions, HurwitzZeta, PolyLog, StirlingS1, Manipulate, ContourPlot, TeXForm. When a thing we want already has a name in a kernel somebody can go and check, we take that name rather than invent one.
The rule this repository actually follows:
A head or a component that represents a symbol is named for that symbol. One that represents no symbol gets a descriptive name, and we say so out loud.
The second half is doing real work. <notatio-knob> is not a Wolfram symbol — Wolfram has Manipulator, but that is a slider with chrome, not a number you drag inside a sentence — so it is named for what it is. Reversion and GradeInvolution have no symbol either. Saying which is which, in the source, is how the rule survives contact with the parts that are genuinely ours.
The corollary is that names get checked against a kernel rather than remembered. wolframscript is on the machine for exactly that, and it has caught symbols we were sure existed and symbols we were sure did not.
The debt of design
Two ideas are lifted wholesale.
*Form symbols. A single expression can be shown many ways, and each way is a named representation you can ask for rather than a mode the renderer happens to be in. StandardForm, TraditionalForm, FullForm, TeXForm ship on <notatio-out>; the pictorial ones live in <notatio-figure> and the plots. The playground overview tracks the whole table.
Manipulate. A parameterised expression with a control per parameter, where the control spec is part of the expression rather than part of the UI: {a, 0, 5}, { {a, 2}, 0, 5, 0.5}, {k, {2, 3, 5, 7}}. We parse Wolfram's own tuple syntax, and the Manipulate page is that idea more or less intact — including the play button, which is Manipulate's own looping animation.
Wolfram's control tuples, parsed as written
source
<notatio-manipulate params="{ {A, 1}, 0, 2}; { {w, 2}, 0.5, 6}">
<notatio-plot value="_A * Sin(_w * x)" domain="-6.283,6.283" plot-range="-2,2" />
</notatio-manipulate>The debt of verification
This is the one that has actually changed the code.
@enumeratio/wolfram compiles MathJSON to Wolfram Language, which makes a kernel an oracle: take a reference entry, transpile it, evaluate it in a real kernel, compare. The last full sweep agreed on the large majority of entries and left a few dozen disagreements — each one classified and committed as golden data rather than waved away, because a disagreement with a kernel is either our bug, their quirk, or a genuine difference of convention, and those need different fixes.
MathJSON out as Wolfram
The transpiler, in the page. This is the same path the oracle sweep runs through.
source
<notatio-out value='["Binomial","n","k"]' format="mathjson" form="wolfram" label="Out" />Some of what the sweep found is worth keeping in public: N[HurwitzZeta[-n, a]] comes back wrong for negative integer n unless you go through FunctionExpand first. An oracle is a source of truth you argue with, not one you defer to.
Where we do not follow
Head[…] brackets. Wolfram's square brackets for application are unambiguous and we still did not take them, because the surface syntax here is Epsil and Epsil uses parentheses. The :wolfram pragma reads Wolfram syntax when you want it; the default stays one language.
The all-in-one kernel. Wolfram's coherence comes from everything living in one system with one evaluator. Ours has to come from a seam — a set of libraries declaring heads on a shared engine — and that is a real cost. Two libraries that both want Basis have to agree to share it, which is why @enumeratio/algebra exists at all.
Dynamic everywhere. Wolfram's reactivity is ambient: any displayed thing can be Dynamic and the front end keeps it live. Ours is scoped on purpose, to the inside of one wrapper, because an ambient version in a documentation site is a page that never stops recomputing.