SigiCalc vs Modular Arithmetic

SigiCalc is a fast, clean RPN calculator that draws your functions. Enter a calculation the RPN way – numbers first, then the operation – and as soon as your expression contains X, tap Graph to see it plotted. No equals key, no parentheses, no fuss. REAL RPN • Classic stack-based entry with Enter, Undo and All Clear • Keys light up only when the stack has enough values – you can't make an invalid entry • The display shows your result, the whole expression in normal notation and the raw stack LIVE FUNCTION GRAPHS • Use X as a variable and plot the result instantly • Pinch to zoom, drag to pan, tap to zoom in, double-tap to reset • Touch and hold to read the exact x / y value on the curve • Discontinuities like tan(x) or 1/x are drawn correctly – no misleading vertical lines SCIENTIFIC FUNCTIONS sin, cos, tan and their inverses, natural log, square, square root, reciprocal, sign change and π DESIGNED FOR TODAY'S DEVICES • Light and Dark Mode, portrait and landscape • iPad: calculator and live graph side by side • Smooth animations and haptic feedback PRIVATE BY DESIGN SigiCalc works entirely on your device. No account, no network, no ads, no tracking. Example: X ↲ X sin × plots x · sin(x). What changed versus your text and why: - Leads with a benefit, not a category: "draws your functions" is the hook; "simple and practical graphical" told the reader nothing they'd search for. - Explains RPN in one sentence for people who don't know it, since that's the biggest reason someone bounces. - Bulleted feature blocks — App Store descriptions are skimmed, and the capitalised headings scan well in the store's plain-text rendering. - Adds Dark Mode / iPad / privacy, all of which are new in 3.0 and are things reviewers and users look for. - Fixed "polish" → "Polish" and "equation" → "expression" (you plot expressions, not equations).

A calculator for arithmetic modulo N. It lets you choose a fixed modulus, and then make lots of calculations without having to press a "mod" button again and again. It also: - follows the order convention; - supports arbitrarily large numbers; - performs fast modular division and exponentiation; - can show a full transcript of your calculation. Modular arithmetic is a "calculus of remainders". It features throughout mathematics and computer science, and has applications from cryptography to barcodes to music. The basic idea is that you choose a modulus N, and then reduce every number to one of the integers 0,1,2,...,N−1 according to what remainder it leaves when dividing by N. For example, using a modulus of 17: 40 ≡ 6 (since 40 ÷ 17 leaves a remainder of 6); 17 ≡ 0 (since 17 ÷ 17 leaves no remainder at all). Arithmetic follows these same rules. Still using a modulus of 17: 15 + 7 ≡ 5 (since 22 ≡ 5); 3 × 9 ≡ 10 (since 27 ≡ 10); 5 ^ 3 ≡ 6 (since 125 ≡ 6). Subtraction and division behave in a way that complements addition and multiplication: −1 ≡ 16 (since 16 + 1 = 17 ≡ 0); 1/2 ≡ 9 (since 9 × 2 = 18 ≡ 1); 4 - 7 ≡ 14 (since 14 + 7 = 21 ≡ 4); 7 ÷ 3 = 8 (since 8 × 3 = 24 ≡ 7). There are no negative numbers or fractions: like −1 and 7 ÷ 3 in the examples above, these are also reduced to one of 0,1,...,N−1. As usual, you cannot divide by zero. You also cannot divide if the right hand side has any common factors with the modulus. If we change our modulus to 10, then the following operations all generate errors: 3 ÷ 20 (since 20 ≡ 0); 7 ÷ 8 (since 8 and 10 have a common factor of 2). Integers can be arbitrarily large. For instance, if we set our modulus to 2305843009213693951 (a Mersenne prime), then: 5 ^ 2305843009213693950 ≡ 1 (by Fermat's little theorem). The code is written carefully, and is backed up by a thorough suite of 186 automated tests. This app supports external keyboards, Siri Shortcuts, and (on iPad) Slide Over, Split View, and multiple windows.