The modular-arithmetic tag has no wiki summary.
11
votes
2answers
380 views
Factorizing polynomials over fields other than $\mathbb{C}$
I'd like to take a polynomial in $\mathbb{Z}_5[x]$ of the form $ax^2+bx+c$ and factor it into irreducible polynomials.
For example:
Input...
x^2+4
Output...
...
9
votes
5answers
343 views
Incrementing a number where each digit has a different base
Let's say I have a list, for instance {10,5,3}, indicating the bases for each digit of my 3-digit number. Using this basis, if I wanted to increment {8,4,1} a couple of times, here's what I would get:
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9
votes
1answer
168 views
Modular arithmetic - efficiently calculating the remainders of factorials
When working on this question regarding the divisibility of the sum of factorials, I decided to write some code to test "small values" of the problem using the following code.
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7
votes
2answers
327 views
Solving/Reducing equations in $\mathbb{Z}/p\mathbb{Z}$
I was trying to find all the numbers $n$ for which $2^n=n\mod 10^k$ using Mathematica.
My first try:
Reduce[2^n == n, n, Modulus -> 100]
However, I receive ...
6
votes
1answer
98 views
Implementing Remainder Tree
I want to implement Remainder Tree based on this. With the answers on SE I've come up with:
...
6
votes
1answer
306 views
How to Simplify equations over a Ring with Mathematica?
For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
5
votes
1answer
273 views
Montgomery Modular Exponentiation
I'm trying to write a Montgomery exponentiation based on this which can compete with Mathematica PowerMod. We know that PowerMod ...
4
votes
2answers
145 views
Inverse of a polynomial in a polynomial ring
Let $N$ be a prime, and $q$ be a positive integer. Given a polynomial $f(x)$ in $R = \mathbb Z[x]/(x^N-1)$, I want to find another polynomial $f_q(x)$ in $R_q = \mathbb Z_q[x]/(x^N-1)$, such that
...
3
votes
0answers
194 views
Parallel PowerMod
Is there anyway to parallelize the PowerMod function?
Here is my Left-To-Right modular exponentation:
...
2
votes
2answers
250 views
decompose a number (less than 255) in a sum of powers of 2
Is there a built in function that would take a number and decompose it into a sum of powers of 2? The numbers will be non negative less than 256.
For what it's worth I'm trying to understand a paper ...
1
vote
1answer
264 views
Matrix Multiplication Modulo 2
I would like to perform matrix multiplication modulo 2. Hence, instead of the usual:
A.B
I did:
...
1
vote
1answer
348 views
Linear Solve with Modular Arithmetic
I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ...
1
vote
0answers
154 views
Faster GCD Implementation
Is there any chance to write a faster GCD than the built-in one in Mathematica?
@Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...
0
votes
1answer
57 views
How can I seperate specific elements from the list? [duplicate]
Possible Duplicate:
Question about MapThread and Dynamic
I write a function name as inputFieldsList and it returns both ...
0
votes
0answers
12 views
1+1+1+1+1+1+1+1+1+1+1+1 x 0+1 = 12 or 1? [migrated]
Does the expression 1+1+1+1+1+1+1+1+1+1+1+1 x 0+1 equal 1 or 12 ?
I thought it would be 12 ...
