ZetaCAS

macOS, iOS and Android. Full support.

Fully offline. No language model. Traditional mathematics. The same app on all three: type the question the way you would say it, and ZetaCAS returns the exact answer when there is one, the steps, the graph, and a short note when something is off.

See it work Where it goes further

Now on the Mac App Store. Version 1.0.12

The ZetaCAS start screen, version 1.0.12, with example questions and a list of topics from functions through complex numbers.

226commands and symbols
16topics, from calculus to logic
Offlineno network, no language model
Exactfirst, then honest digits
4languages for operation words
3platforms: macOS, iOS, Android

See it work.

Thirty seconds on the Mac, made from the real app: an integral with $10^{18}$ oscillations, the working behind an answer, a surface you can turn and zoom, a differential equation solved and drawn, and the complex roots too.

Where ZetaCAS goes further.

ZetaCAS answers in plain words, like WolframAlpha, but it runs on your own device and it keeps working on hard problems. As of October 2026, WolframAlpha cannot solve the first two of these, and on the third ZetaCAS is stricter and more correct, which matters for students. There are many more.

WolframAlpha cannot solve this today

Three exponentials inside a sine

integrate e^(x+sin(e^(e^(e^(x + 1/3))))) from -1 to 1

\begin{aligned}&\int_{-1}^{1} e^{\,x+\sin\left(e^{e^{e^{x+1/3}}}\right)}\,dx\\[6pt]&\approx 2.99633981197654\end{aligned}

No closed form exists, so ZetaCAS says so and gives the value to 15 digits. The integrand oscillates too fast for any grid, so it substitutes $t=e^{e^{e^{x+1/3}}}$ and moves each oscillating part onto a path in the complex plane where it decays.

It then checks the value against direct quadrature on part of the interval, which agrees to 12 digits, and at two precisions.

WolframAlpha cannot solve this today

A tangent of a tangent, exactly

integrate (sin(tan(tan(pi*x)))^2) from 0 to 1

\begin{aligned}&\int_{0}^{1} \sin^{2}\!\bigl(\tan(\tan(\pi x))\bigr)\,dx\\[6pt]&=\frac{1}{2}-\frac{1}{2\,e^{2\tanh 1}}\approx 0.39099216215153\end{aligned}

An exact answer, through the Cauchy distribution: over whole periods $\tan$ spreads its input like a Cauchy variable, and the tangent of a Cauchy variable is again Cauchy, so the integral is an average against one Cauchy law.

It is checked against a coarse numerical estimate.

Stricter, and more correct

Dividing by zero is not a solution

x^2/x=0

\frac{x^{2}}{x}=0 \quad\Longrightarrow\quad \text{no solution}

Cancelling the common factor leaves $x=0$ , but at $x=0$ the equation as written divides by zero ( $0/0$ ), so that point is kept out of the answer. Nothing else is left, so there is no solution.

It is the answer a teacher expects, and the one a student needs to see.

Numbers too big to print

Exact length, first digits, last digits

3^3^3^3

\begin{aligned}&3^{3^{3^{3}}} = 3^{7625597484987}\\[6pt]&\approx 1.25801429062749\times 10^{3638334640024}\end{aligned}

\begin{aligned}&2^{2^{100}}\\[6pt]&\approx 2.28536769422951\times 10^{381600854690147056244358827360}\end{aligned}

$3^{3^{3^{3}}}$ has 3,638,334,640,025 digits, more than the 1,000,000 the app writes out, so it stays the expression it is. Its length and its first digits come from its logarithm, worked out from its parts and checked at two precisions. Its last digits come from arithmetic modulo $10^{15}$ . All of these are exact, not estimates.

The answers shown are ZetaCAS's own, taken from the app. WolframAlpha is a trademark of Wolfram Alpha LLC. ZetaCAS is not affiliated with it. The comparison reflects what we found in October 2026.

Integration, many ways.

Twelve integral commands, and a search that tries the exact route first. When an exact answer exists you see it. When it does not, ZetaCAS says so and gives honest digits.

Antiderivatives, with the workingLinearity, table, partial fractions, substitution and integration by parts, shown step by step.
Definite integralsExact when an exact answer exists, honest digits when not. The exact search escalates before it settles for digits.
Oscillating integralsNo grid resolves them, so the phase is unfolded and the oscillation is moved into the complex plane.
Tangent layersExact, through the Cauchy distribution.
Infinite intervalsOscillating tails move into the complex plane, and improper integrals say when the plain area does not exist.
Cauchy principal valueAsk for it by name when a pole sits inside the range.
Double and triple integralsRanges in the order of dx dy. An inner range may use the outer variables.
Sinc productsExact, by Borwein's formula.
Numerical on demandSkip the exact search, ask for more decimals, or give a slow integral more time, up to a few minutes.
Arc length, area between curves, Riemann sumsLeft, right and midpoint sums.

What you can ask

226 commands and symbols, in 16 topics. Press ⌘K, or the Commands button on a phone, to search them. Each one comes with a worked example that arrives filled in, so it runs as it is.

Functions
Domain, range, roots, extrema, asymptotes, inflection, inverse and tangents, from one expression.
Calculus
Derivatives, integrals including improper ones, limits, series, Riemann sums, arc length and area.
Equations
Any degree, systems, inequalities, recurrences and differential equations. A trig equation returns the general solution, not two lucky roots.
Algebra and matrices
Factor, expand, simplify, partial fractions. Determinants, inverses, eigenvalues, row reduction, LU and QR.
Transforms
Laplace, Fourier series and transform, z-transform, Hilbert, convolution.
Chance and number
Eleven distributions, quantiles, regression, histograms. Primes, gcd, bases, continued fractions, gamma and zeta.
Discrete, geometry, complex
Counting, sets, and logic from truth tables to CNF. Polygons and triangles, in degrees or radians. Argand diagrams and every root.

The 16 topics

Calculus33
Integrals12
Algebra24
Linear algebra23
Numbers15
Statistics10
Probability14
Counting6
Sets9
Logic8
Geometry13
Graphs8
Trigonometry & complex17
Special functions14
Precision5
Symbols15

211 commands, plus 15 symbols such as $\pi,\ e,\ i,\ \infty$ .

It understands the sentence, including the typo.

Operation words work in English, Spanish, French and German. derivarive still means derivative.

\int_{0}^{\infty} e^{-x^{2}}\,dx = \frac{\sqrt{\pi}}{2}

Solving $x^{2}+1=0$ gives $x=\pm i$ , with a note that there is no real root.

Press ⌘K, or the command key on a phone, and 226 examples are there to try. A typo is matched to the operation. A language model is not involved.

The ZetaCAS command menu open on Calculus, listing differential equations, recurrences, Laplace and Fourier transforms.

An exact definite integral in ZetaCAS, with the closed form and fifteen digits beside it. — When a closed form exists, you see it, and the decimals beside it. This one is exact.

A polar plot of r equals sine of 4 theta, an eight-petalled rose. — Plots are part of the answer. Polar, implicit, parametric, slope fields and 3-D.

It shows the working, and it says when a number is only an estimate.

A differential equation comes back with the general solution, why the sines and cosines appear, and a few curves from the family. A probability question shades the band you asked for.

If the best answer is numerical, ZetaCAS writes the uncertainty instead of a long string of noise. You can ask for more decimals, or give a slow integral more time, up to a few minutes. A hung calculation cannot freeze the window: it runs on a clock.

The general solution of a differential equation, with several solution curves plotted.

Paper by day, ink by night. Same mathematics.

The app has its own light and dark page, separate from this website. Exact values stay next to the decimals: eigenvalues, a characteristic polynomial, the eigenvectors, the diagonalisation.

Roots that are not real are drawn on the complex plane. A polynomial’s real roots and its conjugate pairs, with the unit circle for scale.

ZetaCAS in its dark theme, showing eigenvalues of a 2 by 2 matrix, exact and decimal, with eigenvectors.

iOS and Android

Full support, not a cut-down page. A row of maths keys sits above the keyboard. Paper by day, ink by night.

ZetaCAS on a phone: the integral from -1 to 1 of e to the power x plus sin of e to the e to the e to the x plus one third, about 2.99633981197654 to 15 digits, with notes on why there is no closed form and how the value was computed. — An integral with no closed form: the value to 15 digits, and a note on how it was found.

ZetaCAS on a phone solving x squared plus 1 equals 0 in the complex numbers, with maths keys above the letter keyboard. — solve $x^{2}+1=0$ . The maths keys are part of the keyboard.

ZetaCAS on a phone in the dark theme, explaining why sines and cosines appear and plotting several solution curves. — Why the sines and cosines appear, and the curves of the family.

ZetaCAS on a phone showing the solutions x equals i and x equals minus i, and both roots on the complex plane. — $x=\pm i$ , drawn on the complex plane.

Thirty seconds on the iPhone.

The same engine in your pocket: the maths keys above the keyboard, the working, the graph, and no signal needed. Serious maths, on your device.

Fully offline. No language model.

A traditional computer-algebra engine. It runs with full support on macOS, iOS and Android. It does not call a language model, and it does not need a network to answer.

Report a problem opens your mail app with the question on screen already filled in. Nothing is sent until you send it. Read the terms and the privacy policy.

A normal distribution in ZetaCAS, mean 170 and sigma 10, with the probability between 160 and 185 shaded.

ZetaCAS 1.0.12

macOS, iOS and Android. Questions: mcebrian (at) ik.me