ExaktAI Workspace

AI mathematics is here to stay. The Workspace is a computational environment where you can validate and follow it. Mathematics is the language: write in the SymPy, Maple or Mathematica dialect, and compute with the Computer Algebra System (CAS) engine you choose. Every document opened in the Workspace has its dialect and its engine set, and you can change them independently of each other.

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The Workspace

It includes SymPy, NumPy, SciPy and Matplotlib, and drives your own Maple or Mathematica, or the Wolfram Engine, which you can install free for personal use. Plots are interactive by default, drawn with Plotly: you can zoom and pan them, or read a value off the curve, whichever CAS engine computed them. You can also open mathematics you have: a Maple worksheet, a Mathematica notebook, a Jupyter notebook for SymPy, a Python script.

Dialect you write	SymPy	Maple	Mathematica
	Engine that computes
SymPy	runs as written	translated	translated
Maple	translated	runs as written	translated
Mathematica	translated	translated	runs as written

Translation between dialects has limits: not every command exists in all three systems. It is a growing capability.

A CAS environment whose dialect is SymPy

A computer algebra environment for SymPy and the rest of the Python scientific stack.

The dialect of the document is SymPy's own, read as mathematics: no imports and no declaring symbols, a free name declares itself, x^2 is a power, 3/2 stays exact, == makes an equation rather than a true/false verdict. Edit a line above and run it again, carry a result forward by its equation label, read output as typeset mathematics, or the same mathematics inline in a text region, and organise the whole with sections, subsections and hyperlinks. In Presentation mode, Export as LaTeX writes the document out as a paper.

The SymPy 101 tutorial that ships with the ExaktAI Workspace, twice: on the left its thirteen sections collapsed, from exact arithmetic to a differential equation; on the right section twelve open, deriving a projectile's range with solve and trigsimp and plotting the trajectory, both chips reading sympy to sympy with the CAS badge lit — The SymPy 101 that ships with the Workspace on the left, one of its sections run on the right. The chip **(sympy → sympy)** indicates the dialect and engine. The **CAS** badge is lit: `x^2` is a power, `3/2` exact, `==` an equation, every result numbered and reusable by its number.

The Workspace includes an AI assistant beside the document, its own help pages, CAS 101 tutorials for each of the dialects, and a page for every command of whichever dialect you write in. F1 on a command you typed opens its help page; hovering a typeset function in the output shows how it is written in the dialect, and links to its page. And the Digital Library of Mathematical Functions opens in a window of its own, where an identity on one of its pages is taken into the document, written directly in the document's dialect, ready to use.

NumPy, SciPy and Matplotlib are bundled beside SymPy and run as themselves: their numbers are machine floats, and a region that computes with them stays a program. The mathematics is SymPy's; the arrays and the Matplotlib figures are Python's.

Open what you already have

Four formats, decoded natively.

A notebook of your own opens as it was written: its SymPy, NumPy and SciPy code keeps Python's own semantics, and the stack that runs it is included in the Workspace. What is new is around it, the document now being one of your collection, with the engines, the labels and the assistant beside it.

Or the same notebook is imported as a CAS document, which converts rather than opens: the bookkeeping goes, the notation becomes the dialect's, and the author's comments become the document's text. Regions that really are programs, computing with NumPy or SciPy on machine numbers, stay programs. The converted document must give the same answers as the original before it ships.

The chip at the top right says which reading a document is in: the CAS badge lit for the dialect's notation, dimmed for literal Python. Clicking it rewrites the whole document into the other reading, in either direction.

The same Jupyter notebook for SymPy open twice in the ExaktAI Workspace: on the left as written, with symbols declared by hand and A**2 in Python notation; on the right imported as a CAS document, where the declarations are gone, the matrices are typeset, and A squared and A times b are written as mathematics — One notebook, twice. Opened as written on the left, *imported as a CAS document* on the right, where the bookkeeping goes and the notation becomes the dialect's: the same computation, with less programming in the way.

A Maple worksheet (.mw) and a Mathematica notebook (.nb) are read directly, with no Maple and no Wolfram on the computer, with the computing engine set to SymPy. And if you do have Maple or Mathematica, a right click on any line offers to run this one using a different CAS engine.

Two ExaktAI Workspace documents side by side: on the left a Maple-notation document whose chip reads maple to sympy, computing on the bundled SymPy; on the right a Mathematica-notation document with the right-click menu open on a Limit line, offering Execute in SymPy, Execute in Maple with a check mark and the hint option-as-written, and Execute in Mathematica, that line's result badged Maple — A Maple document and a Mathematica document, both computing on the bundled SymPy, on a computer with neither installed: the chips read **maple → sympy** and **mathematica → sympy**. The menu on the right is the other half of that freedom, one line sent to another engine and its answer badged with whichever engine gave it.

If you already own Maple or Mathematica

Your engine, your dialect, and a workspace around them.

Within the ExaktAI Workspace, the Maple dialect on the Maple engine is Maple sent to Maple; the Mathematica dialect on the Wolfram engine is Wolfram Language sent to Wolfram. The Workspace just drives the copy installed on your machine.

Your document outlives your licence

A colleague with no Maple or Mathematica reads your document as you wrote it. Where its constructs all translate, the bundled SymPy re-runs it in your dialect. For a Mathematica document, you can install the Wolfram Engine, free for personal use, and run it on Wolfram's own kernel.

Equation labels that compute

All results carry an equation label that can be used to reference them: use it thirty lines later, change the earlier line, and the derivation recomputes. Maple has had this for years; here every dialect does, SymPy included.

Two ExaktAI Workspace documents side by side: on the left a Maple worksheet on Lagrangians in rotating frames, chip reading maple to maple, with vector results carrying equation labels that later lines reference; on the right a Mathematica notebook on classical mechanics, chip reading mathematica to mathematica, ending in a three-dimensional trajectory plotted by the Wolfram engine — Your own engines, driven from here: **maple → maple** on the left, **mathematica → mathematica** on the right, each document in its own dialect on the copy installed on this machine.

All your work in progress, kept

Keep a dozen investigations going at once, and have only the ones you need in front of you.

Real work is a dozen half-finished investigations: the one you are on, the three you will come back to, the one from last month whose result you now need. The Workspace keeps them as a collection, outputs and context included. Close it and open it again: every document is where you left it, the unsaved ones included, at the line you were editing. Search across the text and the inputs of everything open, filter, bookmark, and put only what you need on the tab bar without discarding the rest.

Two ExaktAI Workspace windows: on the left a Maple document on the retarded and Lienard-Wiechert potentials with the screen split and the workspace panel open, listing five documents as cards with their dialect, whether each is Edited or Saved, and when it was last touched, above a search box and filters by time, engine and state; on the right the SymPy 101 tutorial — An afternoon's collection, on the left. Every open document is a card carrying its dialect, its state and when it was last touched, over a search that reads the text and the inputs of all of them.

Where validated AI mathematics lands

The Workspace is also the reading room for ExaktAI Validation.

When ExaktAI validates an AI's solution with SymPy, the result arrives here: an editable document holding the AI's reasoning as narrative and every computation as executable input, already run and already validated. Audit it, change a line, re-run it, extend it. Validating with Maple or Mathematica produces the corresponding native document instead.

On the left ExaktAI Validation, an ADMM problem answered by Codex and validated with SymPy in five and a half minutes; on the right the ExaktAI Workspace document that arrived from it, each step of the reasoning a paragraph of text followed by an executable input carrying its own computed result, down to the optimum at minus three and three — Where a validated run lands. ExaktAI Validation checked Codex's ADMM solution step by step with SymPy; the document that arrived from it holds every step as an executable input, so changing a line re-runs the derivation.

What it needs, and what it does not do

SymPy, NumPy, SciPy and Matplotlib are bundled and run locally. Maple and Mathematica execution needs those products installed and licensed on your machine. Ordinary document and CAS work is local; no hosted AI is required to use the Workspace.

Translation between dialects grows command by command and does not preserve every engine-specific construct. An imported document keeps its saved output without re-executing it, and a structure the reader does not know falls back to plain text rather than guessing. An exported document preserves its contents, but may produce different results when run in another system.

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The Workspace is the first of the two ExaktAI products to open. We can reach out when it is ready to try.

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