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توضیحات

Rust Number Theory

ویژگی	مقدار
سیستم عامل	-
نام فایل	flagrs-0.1.4
نام	flagrs
نسخه کتابخانه	0.1.4
نگهدارنده	[]
ایمیل نگهدارنده	[]
نویسنده	Frank S. Hestvik
ایمیل نویسنده	-
آدرس صفحه اصلی	https://gitlab.com/franksh/flagrs/
آدرس اینترنتی	https://pypi.org/project/flagrs/
مجوز	BSD-3-Clause

# flagrs This is an experimental project parallel to my [PyNTL](https://gitlab.com/franksh/pyntl) project where I attempt to reimplement parts from my `flagmining` library as CPython extension code in Rust. Is designed to be fast. Uses the `rug` library as a lightweight wrapper around GMP. Due to some lacking functionality in `rust-cpython==0.6.0` it depends on my own fork of said project, so you probably won't be able to compile it. # ZZ : â„¤ ## Normal Integer Operations ### `x+y -> n`, `x-y -> n`, `x*y -> n` Normal addition, subtraction, and multiplication. ### `x//y -> q`, `x%y -> r`, `divmod(x,y) -> (q,r)` Integers act Euclidean. ### `x**e`, `pow(x,e)` Normal exponentiation. `e` must be a natural number (i.e. non-negative integer). ### `bool(x)`, `x.__bool__() -> bool` Numbers are true if they're non-zero. ### `n.sqrt() -> (w,r)` Floored integer square root with remainder. `w*w + r == n`. ### `n.root(d) -> (w,r)` Floored integer `d`th root with remainder. `w**d + r == n`. ### `-x` Negation. ### `abs(x)` Absolute value. ### `x.sign() -> s` The sign (also called signum) of `x` (-1, 0, or 1). ## Bitwise Operations ### `x|y`, `x&y`, `x^y` Bitwise OR, AND, and XOR. ### `~x` Bitwise negation, acting as if the integer had infinite width. Equivalent to `-x-1`. ### `x<<i`, `x>>i` Bit shifts (can be negative). ### `n.nbits() -> c` Number of bits needed to represent the absolute value of `n`. A synonym for `n.bit_length()` or `len(n)`. ### `n.weight() -> c` Number of bits set in the absolute value of `n`. ### `n.truncate(bits, [signed=False])` Truncate `n` to the given number of bits. Negative numbers are treated as if they're in two's-complement form for the given bit width. If `signed` is `True` the resulting bits will be re-interpreted as a signed value and so the result might be negative. ### `n.next_bit() -> b` Next power-of-two bigger than `n`. ### `list(n) -> [bool...]`. Integers also function implicitly as a list of bits, from least significant to most significant. ``` python-console >>> list(ZZ(256+16+1)) [True, False, False, False, True, False, False, False, True] ``` ### `n[i] -> bool` Checks bit `i` (0-indexed). ### `n[i:j] -> v` Returns a number with the bits set in the slice. Morally equivalent to `(n>>i) % (1<<j-i)` but supports full slice syntax, including negative numbers. TODO: `rust-cpython` doesn't have PySlice objects! ## Representation ### `str(x) -> str`, `x.__repr__()` Number in base-10 as a text string. ### `x.nbytes() -> l` Number of bytes needed to represent the number. For positive numbers this is equivalent to `(x.nbits() + 7)//8`. Negative numbers might require an extra bit (see `x.bytes()`). ### `x.bytes([order='big']) -> bytes` Interprets the number as base-256 and returns the digits as a bytestring. Negative numbers are treated as if they're in two's complement representation of the minimum bit width that will successfully represent them, so `-128` gives `b'\x80'` and `-129` gives `b'\xff\x7f'`. ### `x.digits(base) -> [d...]` Yields a list of digits in base `base`. The base can be negative, but must have a magnitude of 2 or more. ## Modular Arithmetic ### `n.inv_mod(m) -> r` Returns $1/n \pmod m$. ### `pow(x,e,m)` Exponentiation under a modulus. `e` can be negative if `gcd(x,m) == 1`. ### `a.kronecker(n) -> k` Kronecker symbol $$(\frac{a}{n})$$. For primes it corresponds to the Legendre symbol. ### `m.M -> <ZMod type>` Access to the modular numbers using the given number as modulus. See below for `ZMod`. ``` python-console >>> F = ZZ(13).M >>> F(3) * 5 (2) ``` ## Factors ### `n.gcd(m...) -> g` Returns the GCD of `n` with all arguments. ### `n.egcd(m) -> (g,x,y)` Extended GCD yielding BeÌzout coefficients. `x*n + m*y == g`. ### `n.lcm(m...) -> m` Returns the LCM of `n` with all arguments. ### `n.is_prime([reps=25]) -> bool` Trivial divisors, then Baille-PSW, then $(reps-24)$ rounds of Miller-Rabin. ### `n.next_prime() -> p` Returns the next prime larger than `n`. ### `n.make_odd() -> (q,e)` Returns the odd part and exponent of 2 in `n`. `2**e * q == n` ### `n.small_factors([upto=0x100000]) -> (q,[(p,e)...])` Factors out all primes smaller than `upto`. Returns the remaining factor `q` and a list of primes and their multiplicity. ### `x.factor_pollard(upto)` ... ### `x.factor_fermat(s, e)` ... # ZMod : â„¤_n Represents the residue ring (or field) of integers under a given modulus. The normal arithmetic works as expected. In cases where a field is required for the operation to be well-defined, the code will simply assume the user knows what they're doing and operate under the assumption that it is (i.e. that the modulus is prime). ### `x/y -> z` Normal division works as expected: ``` python-console >>> F = ZMod(17) >>> F(5)/2 (11) >>> F(11)*2 (5) ``` ### `x**e -> y` Exponentiation also works as expected: ``` python-console >>> ZMod(17179)(2)**0xdeadcafe (14537) ``` ### `p.EC(a,b) -> <EC type>` Access to the additive group of an Elliptic Curve using this modulus. # EC : Ellipic Curves

نحوه نصب

نصب پکیج whl flagrs-0.1.4:

pip install flagrs-0.1.4.whl

نصب پکیج tar.gz flagrs-0.1.4:

pip install flagrs-0.1.4.tar.gz