Everything you need to get the most out of the solver — from your first problem to advanced LaTeX input, subject-specific tips, and API integration for engineers.
This is the feature that sets Zeretis apart from most math tools. You don't need to know special syntax to use the solver. Just type your problem the way you'd say it out loud, the way you'd write it in a text message, or the way you'd ask a teacher.
The big idea: Zeretis understands plain English, standard math notation, and LaTeX — all interchangeably. You can mix them freely in the same session. The solver figures out what you mean.
When you type a problem, Zeretis parses your input to identify the mathematical intent — whether you're asking to solve, differentiate, integrate, factor, simplify, or something else. It then checks for standard mathematical objects (variables, functions, operators, constants) and constructs the symbolic expression it will compute.
The solver shows you how it interpreted your input before displaying the solution. If it parsed your problem differently from what you intended, you can rephrase and it will re-interpret. This makes natural language input forgiving — you don't have to get the wording exactly right.
Tip: For complex or ambiguous problems, being slightly more explicit helps. Instead of "solve this" try "solve for x" or "find the integral of" — the solver will parse more reliably when the operation is stated clearly.
Zeretis accepts three input styles, all interchangeable. Use whichever is most natural for you in the moment.
Describe the problem the way you'd say it aloud. The solver understands common mathematical vocabulary and phrasing.
| You type | What it computes |
|---|---|
| derivative of x cubed | d/dx(x³) = 3x² |
| solve x squared equals 16 | x = ±4 |
| integral of e to the x | ∫eˣ dx = eˣ + C |
| factor x squared plus 5x plus 6 | (x+2)(x+3) |
| simplify (x squared minus 4) over (x minus 2) | x + 2 |
Use conventional math shorthand — the kind you'd type in a calculator or write in a text message. Zeretis understands the standard conventions.
| You type | Interpreted as |
|---|---|
| x^2 - 5x + 6 = 0 | x² − 5x + 6 = 0 |
| d/dx(sin(x)) | Derivative of sin(x) |
| int(x^2, x, 0, 1) | ∫₀¹ x² dx |
| sqrt(x^2 + y^2) | √(x² + y²) |
| [[1,2],[3,4]] | 2×2 matrix |
If you're already comfortable with LaTeX, paste it directly — the solver accepts standard LaTeX math expressions.
| LaTeX input | Interpreted as |
|---|---|
| \frac{d}{dx} x^3 | Derivative of x³ |
| \int_0^1 x^2 \, dx | ∫₀¹ x² dx |
| \lim_{x \to 0} \frac{\sin x}{x} | Limit as x→0 of (sin x)/x |
| \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} | 2×2 matrix |
You can mix all three styles. Type a problem in English, get the result, then type the next one in standard notation. The solver doesn't care — it interprets each input independently.
Zeretis covers the full range of symbolic mathematics from secondary school through to undergraduate level. Here's what to expect from each area and how to phrase inputs effectively.
Solving equations, factoring expressions, expanding brackets, simplifying rational expressions, and working with inequalities. The solver handles single-variable and multi-variable problems.
Derivatives (including partial derivatives, higher-order, implicit), indefinite and definite integrals, limits, and series. All results are exact symbolic expressions.
Matrix arithmetic, determinants, inverses, eigenvalues and eigenvectors, row reduction, and solving linear systems. All results are exact — no floating-point accumulation.
First and second order ODEs, with or without initial conditions. The solver uses integrating factors, characteristic equations, and variation of parameters. If a closed-form solution exists, you'll get it exactly — if not, the solver tells you.
The solver parses intent from your wording. "x² − 5x + 6" on its own is ambiguous — do you want it factored, simplified, or solved equal to zero? Adding the operation ("factor x²...") removes the ambiguity and gives you a more reliable result.
For multi-variable expressions, say which variable you're solving for: "solve 2x + y = 5 for x" rather than just "solve 2x + y = 5". This is especially important for systems of equations and implicit differentiation.
When typing in standard or LaTeX notation, use parentheses to make grouping explicit: 1/(x+1) rather than 1/x+1 (which would be parsed as (1/x)+1). The natural language parser is more forgiving, but explicit parentheses always help with complex expressions.
For problems with initial conditions or bounds, state them clearly: "solve y' = 2y with y(0) = 3" or "integrate x² from 0 to 1". The solver handles these as part of the problem, not as separate information.
The solver shows how it interpreted your input. If the interpretation doesn't match what you meant, the result will also be wrong — rephrase the input rather than trying to adjust the output. This is almost always the cause of unexpected results.
Zeretis is designed to work in live classroom settings. Here are the patterns that work best for teaching contexts.
The output layout is designed to be readable on a projector — high contrast, clean step numbering, and no extraneous interface elements that distract from the math. Increase your browser font size (Ctrl/Cmd +) if needed for visibility at the back of the room.
Rather than entering a problem and immediately scrolling to the answer, try revealing one step at a time — ask students to predict what happens next at each stage. The step labels tell you exactly which rule was applied, so you can ask "why did we use the chain rule here?" and have a specific reference point.
Use natural language input to generate worked examples rapidly: "differentiate sin(2x)", then "differentiate sin(3x)", then "differentiate sin(ax)" — each one takes seconds to enter and gives you a fully worked result you can use as a worksheet example or display.
When a student shows you their working, enter their answer into the solver and compare it to the full worked solution. If their method was right but they made an arithmetic slip, the steps will show you exactly where. If the approach itself was wrong, you'll see it immediately from the first step.
Zeretis is particularly useful for engineering work where you need exact symbolic results you can use in further derivations — not numerical approximations.
Results are returned in exact form — fractions, surds, and constants like π and e are preserved. This means you can use them directly in further symbolic manipulation. For example, if you solve for a transfer function symbolically, you can substitute specific values later without rerunning the full derivation.
Enter your own derivation step by step, then compare each intermediate result to what the solver gives. This is useful when you suspect an algebraic slip somewhere but can't find it — the solver will show you exactly where the divergence starts.
State initial conditions clearly: "solve y'' + 4y = 0 with y(0) = 1 and y'(0) = 0". The solver applies them after finding the general solution, giving you the particular solution directly rather than leaving arbitrary constants.
Enter matrices using square bracket notation: [[1,2,3],[4,5,6],[7,8,9]] for a 3×3 matrix. You can also use plain English: "the matrix with rows 1 2 3, 4 5 6, 7 8 9".
The Zeretis REST API gives programmatic access to the full solver engine. Send an expression, receive an exact symbolic result plus step-by-step JSON. See the Enterprise & API page for full pricing and endpoint documentation.
const res = await fetch('https://api.zeretis.com/v1/solve', { method: 'POST', headers: { 'Authorization': 'Bearer YOUR_KEY' }, body: JSON.stringify({ expression: 'solve(x^2 - 5x + 6 = 0, x)' }) }); // Returns: { result: "x = 2, x = 3", steps: [...], latex: "..." }
Natural language input works in the API too — pass any of the same English-language expressions you'd type in the browser and the solver interprets them identically.
See the Enterprise & API page → for full endpoint documentation, authentication details, and pricing.