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QUESTION
I want to create two plots, one that has gaussian primes depicted in complex plane and another one that shows the number of (gaussian) prime factors of that complex number. I can calculate both the primality (the first scenario) and the factors (the second one), but can't find the correct format for the visualization.
In the first case I want to merely draw a tick for every prime in a complex plane of given dimensions, like pictured in this Wolfram Mathworld page. I have already defined a function with the following signature: is_gaussian_prime(c : complex) -> bool. What I'm missing is a suitable data structure for storing the information of the primacy of all the complex numbers from real_min to real_max and imag_min to imag_max and a way to visualize that data structure. I have looked into seaborn.relplot() as documented here, but cannot quite grasp, what kind of shape I want the data to be in.
The reason I want to use relplot() is because that allows drawing different sizes of ticks for different amount of prime factors in the second scenario. Meaning that I want to draw the second plot in such a way that the size of the tickers represent the number of prime factors of that particular gaussian number. To be more precise, in the second plot I want to draw gaussian primes with a distinct color and gaussian composites as black with bigger ticker size for composites that have more factors. For this case I have a function of the following signature already defined: number_of_gaussian_factors(c : complex) -> int.
ANSWER
Answered 2022-Mar-28 at 20:46You could generate a list of gaussian primes, and then call sns.scatterplot on the real and imaginary parts:
QUESTION
I am a computer science student, I am studying the Algorithms course independently.
During the course I saw this question:
Show an efficient randomized algorithm to factor Carmichael numbers (that is, we want a polynomial time algorithm, that given any Carmichael number C, with probability at least 3/4 finds a nontrivial factor of C). Hint: use the Rabin-Miller test.
my solution:
my idea is use Rabin-Miller test: i will check if C is prime i will use Rabin-Miller Primality tests steps:
- Find n-1=c^k*m
- choose a: 1 < a < n-1
- compute b_0 = a^m(mod n), b_i = b_(i-1)^2 (mod n)
- if b_0 = -/+1 this is prime, i will return nothing. if b_i = -1 this is prime, will return nothing. else if = 1 this is not prime i will return the factor of C.
algorithm:
...ANSWER
Answered 2022-Mar-17 at 13:40If Miller–Rabin fails on a Carmichael number n, then as a byproduct you get some x ≢ ±1 mod n such that x² ≡ 1 mod n. Both gcd(x + 1, n) and gcd(x − 1, n) are proper divisors of n.
The proof: x ≢ 1 mod n is equivalent to x − 1 ≢ 0 mod n, which is equivalent to x − 1 not being divisible by n. Therefore gcd(x − 1, n) ≠ n. Likewise, x ≢ −1 mod n implies that gcd(x + 1, n) ≠ n.
On the other hand, x² ≡ 1 mod n is equivalent to (x + 1) (x − 1) being divisible by n, hence gcd((x + 1) (x − 1), n) = n. We cannot have gcd(x + 1, n) = 1, or else gcd(x − 1, n) = n (since gcd(a b, c) = gcd(a, c) for all b such that gcd(b, c) = 1). Likewise, gcd(x − 1, n) ≠ 1.
QUESTION
I would like to implement a custom branching rule initially (for a few nodes in the top of the tree), and then use Scip's implementation of vanilla full strong branching rule (or some other rule like pseudocost). Is this possible to do using/by extending PySCIPOpt?
...ANSWER
Answered 2022-Feb-28 at 14:25I believe you can achieve this effect. SCIP has several branching rules and executes them one by one according to their priorities until one of them produces a result.
The default rule "relpscost" has a priority of 10000, so you should create a custom rule with a higher priority.
If you do not want to use your own rule at a node (deeper in the tree), you can
decide in the branchexeclp(allowedcons) callback of your rule to return a dict
QUESTION
I've implemented a 6k+-1 primality test function both in a C extension and pure Python code but seems pure Python code is much faster! is there something wrong with my C code or something else?
I also compiled a similar test in pure C with the is_prime function, and its execution time was the same as the C extension (almost 2sec)
primemodule.c
ANSWER
Answered 2022-Feb-21 at 14:28I think your C implementation is buggy regarding integer overflows and signedness and ends up in a bigger loop than the Python version.
Changing the parameter type to unsigned int (and i too, since otherwise that's a compiler warning):
QUESTION
I'm trying to caluclate complexity of below method in Big O notation
...ANSWER
Answered 2022-Feb-20 at 17:46The loop for (let i = 0; i < n.length; i++) is executed n times. The function m.filter((x) => x === n[i]).length checks every element in m, so executes m-times. So we have an execution time of O(n*m).
Considering
QUESTION
I have a lua file that is a database of all my raids in World of Warcraft game. It is generated by an addon in the game and has the information of which player received which loot for which price. Like this:
...ANSWER
Answered 2022-Jan-24 at 17:19CSV and TSV is basically the same thing you just have a different delimiter.
Writing .xls or xlsx is a bit more complicated.
If you want to use xlsx you open a web brower and enter "lua xlsx" into any websearch. You'll find https://github.com/jmcnamara/xlsxwriter.lua for example.
QUESTION
I'm trying to solve a simple optimization problem:
...ANSWER
Answered 2022-Jan-06 at 16:00The constraints
QUESTION
I've written primality test program in python but I'm certain of big issues. One being that program execution becomes very slow if the number to test is extremely big, I've used a generator. And it could be that the program utilizes a huge memory space. Is there any way the program can be optimized?
...ANSWER
Answered 2022-Jan-01 at 13:49As indicated in the comments, the fastest way to find all primes below a certain number is the Sieve Of Eratosthenes method. Checked on my machine, this algorithm is about 1000 times faster than the above one.
A nice comparison between different methods can be found here: analysis-different-methods-find-prime-number-python
Just in case the external link will change in the future, I'm putting here the code:
QUESTION
I'm totally new to this stuff. Never even heard of json/api/etc three days ago. Basically, I'm using the google sheets formula "=ImportJSON("https://universalis.app/api/Primal/7024")" to import data. However, there's almost 4000 cells worth of data in there and I only want about 10-20 cells worth of that. How can I narrow down what data it sends? These are the only cells I want info from D2-D12. I assume I can adjust the formula after if I want, say, D2-D22 instead. Thank you.
...ANSWER
Answered 2021-Dec-17 at 05:22If your ImportJSON is from this, how about the following modified formula?
QUESTION
I'm a beginner. I am suppossed to write a simple primal factorization programm and what i came up with has a weird behavior. Inputs are suppossede to be in the range of 64 bits integer(long long).
It works just fine until i input values of certain length i.e. 13. (picture attached), in which case it just shut's down without an error, which i assume indicated that the programm sees the number as 0, because it should give an error otherwise.
Now, i think problem may be in pointers or in scanf function, so i'd much appreciate if somebody points me in the way of where my mistake is. I programm in VS on Windows 10, using standard command prompt as terminal.
...ANSWER
Answered 2021-Oct-28 at 16:07In this function:
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