Modular Arithmetic
Istruzione
1,99 €
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.
Valutazioni e recensioni
L’app non ha ricevuto un numero sufficiente di valutazioni o recensioni per poter mostrare una panoramica.
Added dark and tinted icons for iOS 18.
Lo sviluppatore, Benjamin Burton, ha indicato che le procedure per la tutela della privacy dell’app potrebbero includere il trattamento dei dati descritto di seguito. Per scoprire di più, consulta l’informativa sulla privacy dello sviluppatore .
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Accessibilità
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Informazioni
- Dimensioni
- 2,2 MB
- Categoria
- Istruzione
- Compatibilità
Richiede iOS 12.0 o versioni successive.
- iPhone
Richiede iOS 12.0 o versioni successive. - iPad
Richiede iPadOS 12.0 o versioni successive. - iPod touch
Richiede iOS 12.0 o versioni successive. - Mac
Richiede macOS 10.15 o versioni successive. - Apple Vision
Richiede visionOS 1.0 o versioni successive.
- Lingue
- Inglese
- Età
4+
- 4+
- Fornitore
Benjamin Burton
- Benjamin Burton non si identifica come operatore commerciale per questa app. Se ti trovi all’interno dello Spazio economico europeo, i diritti dei consumatori non si applicano agli accordi tra te e il fornitore.
- Copyright
- © 2013–2024 Benjamin Burton
