Documentation

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.

01 — Core feature

Natural language input — just type normally.

This is the feature that sets Zeretis apart. You don't need special syntax. Type your problem the way you'd say it out loud, write it in a text message, or ask a teacher.

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The big idea: Zeretis understands plain English, standard math notation, and LaTeX — all interchangeably. Mix them freely. The solver figures out what you mean.

Examples

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

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

How it works

Zeretis parses your input to identify the mathematical intent — whether you're asking to solve, differentiate, integrate, factor, or simplify. It shows how it interpreted your input before displaying the solution. If it parsed differently from what you intended, rephrase and it will re-interpret.

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Tip: For complex problems, being slightly more explicit helps. Instead of "solve this" try "solve for x" — the solver parses more reliably when the operation is stated clearly.


02 — Input

Input formats — three ways to write problems.

Zeretis accepts three input styles, all interchangeable.

1. Plain English

Describe the problem the way you'd say it aloud.

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

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

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 freely. The solver interprets each input independently.


03 — Coverage

Subject coverage

Zeretis covers symbolic mathematics from secondary school through undergraduate level.

Algebra

Solving equations, factoring, expanding, simplifying rational expressions, and inequalities.

Examples

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

Calculus

Derivatives, integrals, limits, and series. All exact symbolic expressions.

Examples

derivative of x^3 * sin(x)3x²sin(x) + x³cos(x)
integrate x^2 * e^x dxx²eˣ − 2xeˣ + 2eˣ + C
limit of sin(x)/x as x approaches 01
Taylor series of e^x around x=0, 4 terms1 + x + x²/2 + x³/6 + ...

Linear algebra

Matrix arithmetic, determinants, inverses, eigenvalues, row reduction. All exact.

Examples

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
inverse of [[1,2],[3,5]][[-5, 2],[3, -1]]

Differential equations

First and second order ODEs with or without initial conditions. Exact closed-form solutions when they exist.

Examples

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

04 — Tips

Pro tips — getting better results.

Be explicit about the operation

"x² − 5x + 6" on its own is ambiguous. Adding the operation ("factor x²…") removes ambiguity and gives more reliable results.

Specify the variable when solving

For multi-variable expressions, say which variable: "solve 2x + y = 5 for x". Especially important for systems and implicit differentiation.

Use parentheses for grouping

Use 1/(x+1) rather than 1/x+1 (which parses as (1/x)+1).

State initial conditions clearly

"solve y' = 2y with y(0) = 3" or "integrate x² from 0 to 1".

If a result looks wrong, check the parsing

The solver shows how it interpreted your input. Rephrase the input rather than trying to adjust the output.


05 — Controls

Keyboard shortcuts

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

06 — Teaching

Tips for teachers

Projecting solutions

The output layout is designed to be readable on a projector — high contrast, clean step numbering. Increase browser font size (Ctrl/Cmd +) for visibility at the back of the room.

Using step-by-step output for discussion

Rather than scrolling to the answer immediately, reveal one step at a time and ask students to predict what happens next. Step labels tell you exactly which rule was applied.

Generating problem variations quickly

"differentiate sin(2x)", then "differentiate sin(3x)", then "differentiate sin(ax)" — each takes seconds and gives a fully worked result.

Verifying student working

Enter a student's answer and compare it to the full worked solution. If their approach was wrong, you'll see it from the first step.


07 — Engineering

Tips for engineers

Keeping results symbolic

Results are returned in exact form — fractions, surds, and constants like π and e are preserved. Use them directly in further symbolic manipulation.

Checking your working

Enter your own derivation step by step and compare each intermediate result. The solver shows exactly where 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.

Matrix input format

Enter matrices using square bracket notation: [[1,2,3],[4,5,6],[7,8,9]] for a 3×3.


08 — API

API reference

The Zeretis REST API gives programmatic access to the full solver engine. See the Enterprise & API page for full pricing and 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 works in the API too — pass the same English-language expressions you'd type in the browser.

Full API documentation →

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.