Zeretis
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How to use the Zeretis math solver.

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.

🌟 Natural language input — just type normally.

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.

Examples of natural language input

Youwhat is the derivative of x squared plus 3x minus 7
Solverf'(x) = 2x + 3 — power rule applied to each term, sum rule used

Yousolve x squared minus 5x plus 6 equals zero
Solverx = 2, x = 3 — factored as (x−2)(x−3) = 0

Youintegral of sin x from 0 to pi
Solver2 — antiderivative −cos(x) evaluated at both limits

Youfind the eigenvalues of the matrix 2 1 / 1 2
Solverλ = 1, λ = 3 — characteristic polynomial derived and solved

Youwhat is the limit of (x squared minus 4) over (x minus 2) as x approaches 2
Solver4 — factored and simplified before evaluating limit

How natural language parsing works

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.

Input formats — three ways to write problems.

Zeretis accepts three input styles, all interchangeable. Use whichever is most natural for you in the moment.

1. Plain English (recommended for most users)

Describe the problem the way you'd say it aloud. The solver understands common mathematical vocabulary and phrasing.

You typeWhat it computes
derivative of x cubedd/dx(x³) = 3x²
solve x squared equals 16x = ±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

2. Standard notation

Use conventional math shorthand — the kind you'd type in a calculator or write in a text message. Zeretis understands the standard conventions.

You typeInterpreted as
x^2 - 5x + 6 = 0x² − 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

3. LaTeX

If you're already comfortable with LaTeX, paste it directly — the solver accepts standard LaTeX math expressions.

LaTeX inputInterpreted as
\frac{d}{dx} x^3Derivative 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.

Subject coverage

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.

Algebra

Solving equations, factoring expressions, expanding brackets, simplifying rational expressions, and working with inequalities. The solver handles single-variable and multi-variable problems.

Example inputs and outputs

solve 2x + 5 = 13 x = 4
factor x^3 - 8 (x − 2)(x² + 2x + 4)
solve the system 2x + y = 5, x - y = 1 x = 2, y = 1
simplify (x^2 - 9) / (x + 3) x − 3

Calculus

Derivatives (including partial derivatives, higher-order, implicit), indefinite and definite integrals, limits, and series. All results are exact symbolic expressions.

Example inputs and outputs

derivative of x^3 * sin(x) 3x²sin(x) + x³cos(x)
integrate x^2 * e^x dx x²eˣ − 2xeˣ + 2eˣ + C
limit of sin(x)/x as x approaches 0 1
Taylor series of e^x around x=0, 4 terms 1 + x + x²/2 + x³/6 + ...

Linear algebra

Matrix arithmetic, determinants, inverses, eigenvalues and eigenvectors, row reduction, and solving linear systems. All results are exact — no floating-point accumulation.

Example inputs and outputs

determinant of [[1,2],[3,4]] −2
eigenvalues of [[2,1],[1,2]] λ = 1, λ = 3
row reduce [[1,2,3],[4,5,6],[7,8,9]] RREF with pivot positions shown
inverse of [[1,2],[3,5]] [[-5, 2],[3, -1]]

Differential equations

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.

Example inputs and outputs

solve y' + 2y = 4, y(0) = 1 y = 2 − e^(−2x)
solve y'' - y = 0 y = C₁eˣ + C₂e^(−x)
solve y'' + 4y = 0, y(0)=1, y'(0)=0 y = cos(2x)

Pro tips — getting better results.

Be explicit about the operation

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.

Specify the variable when solving

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.

Use parentheses for grouping

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.

State units or conditions when relevant

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.

If a result looks wrong, check the parsing

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.

Keyboard shortcuts

EnterSubmit the current expression
Shift + EnterNew line in multi-line input
↑ / ↓Navigate input history
Ctrl + LClear the current session
Ctrl + CCopy the last result
Ctrl + /Toggle LaTeX rendering
EscClear the input field
TabAutocomplete expression

Tips for teachers

Zeretis is designed to work in live classroom settings. Here are the patterns that work best for teaching contexts.

Projecting solutions

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.

Using the step-by-step output for discussion

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.

Generating problem variations quickly

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.

Verifying student working

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.

Tips for engineers

Zeretis is particularly useful for engineering work where you need exact symbolic results you can use in further derivations — not numerical approximations.

Keeping results symbolic for downstream use

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.

Checking your working against the solver

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.

ODE initial value problems

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.

Matrix input format

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".

API reference

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.

Quick example

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.

Ready to solve something?

The solver is free to start. Type any math problem in plain English and get an exact step-by-step solution.

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