28 lines
1.2 KiB
Markdown
28 lines
1.2 KiB
Markdown
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# mcalc
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mcalc is a calculator for modular arithmetic.
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## Quirks
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### Why can't exponents be expressions? Why do they have to be integers?
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This is easiest to explain with an example: what should `2^(3+4)` evaluate to
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modulo 7? In my opinion, it should be 2, since `2^7 = 2 (mod 7)`. However,
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because all the operators in the calculator are implemented as modular
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operators, it will first evaluate `(3+4)` as 0, leading to `2^0 = 1 (mod 7)`. I
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saw three options:
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1. Leave this behavior in, even if it's not what I think most people would expect.
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2. Complicate the code by handling exponent expressions non-modularly.
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3. Simply don't let exponents be expressions.
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I chose 3.
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### Why can't I compute square roots for a composite modulus?
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It is certainly possible to compute modular square roots with a composite
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modulus, and I would like to add the capability at some point, but as
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implemented, the calculator only supports a prime modulus.
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### Why is the `ord()` function so slow when the modulus is large?
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Partly because computing [multiplicative
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order](https://en.wikipedia.org/wiki/Multiplicative_order) is a hard problem,
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and partly because I'm too lazy at the moment to implement a slightly more
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efficient algorithm.
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