Questions tagged [modular-arithmetic]

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1answer
85 views

Simplify Mod to subtraction when possible

FullSimplify[Mod[t,10], t>101 && t<109] It's a long shot, but can I get Mathematica to return t-100 or something ...
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2answers
1k views

Modular arithmetic in Mathematica? [closed]

I want to implement something like 1 + 1 = 0; i.e., simple modular arithmetic in Mathematica. This seems like it should be a really easy built-in option, but I can'...
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1answer
74 views

What is the correct idiom for mapping a 0 value in a modulo n expression back to n?

What is the correct idiom for mapping the $0$ value in a modulo $n$ expression back to $n$. For example if I want to be sure that any integer value maps back to the index for a character in the ...
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1answer
3k views

How to solve Mod equation with mathematica [closed]

i'm pretty noob with mathematica but i need to solve an equation: $$c\equiv m^2\pmod n$$ I tried something like ...
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1answer
301 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 ...
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1answer
111 views

Solving a modular equation with a large modulus [duplicate]

I am having trouble solving this equation: $17^n\equiv 1 \mod 640826899755722841329632946651705039010285107743541637238400825304943424424715705661705191669759$ for the smallest integer $n > 0$ I ...
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1answer
81 views

Converting an expression to modular arithmetic automatically

I have the expression $\frac{1}{15} \left(-(-1)^n-5\times 2^{n+2}+3\times 2^{2 n+1}+15\right)$ which I want to calculate mod m for a very large n. My current method is to ask for this exression in ...
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0answers
49 views

How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
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0answers
68 views

Last digits via PowerMod [closed]

Do you have an idea why this produces different results? PowerMod[2003, 2002^2001, 1000] 241 ...
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0answers
154 views

Solving an equation for rational modulus 1

I want to solve an system of equations of the form $$\prod_{i=1}^n x_i^{M_{i,k}}=1 \qquad k=1,\ldots,n$$ with complex $x_i$ with constraint $|x_i|=1$ and $M_{i,k}$ integers. This is basically a ...
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0answers
665 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
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1answer
240 views

Solving for $d$ in $x= E^d \bmod(n)$

With regards to Public Key Cryptography, I have been tasked with the problem of attacking some information given in an assignment and discovered a private key used to digitally sign a message. Known: ...
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1answer
42 views

Looping on ranges (Modular iterations)

Is it possible to make the following code modular, so that it works up till depth n, and returns an array of all possible combinations for used{}? ...
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1answer
50 views

Get missing cyclic numbers via modulus?

Consider a list of numbers: list = {1,2,3,4,5}; Taking a random set of three of these numbers: ...
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1answer
58 views

Putting some calculations together to form an algorithm

Considering these below where n is an odd number, k is also an odd number less than n: <...
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1answer
90 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 ...
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0answers
49 views

Finding a solution to a modular problem efficiently

I want to find a naïve hash function of the form Mod[a x + b, 2^p] which would produce a value less or equal to v for all ...
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0answers
100 views

Variables defined modulo $\pi$ and avoiding singularities; phase plotting for a map

I have the following $2$-dimensional implicitly defined map ...
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0answers
53 views

Function to add two matrices mod 2 [duplicate]

I have: lightstep[m_, gg_] := Which[gg == {1, 1}, m = Mod[m + m, 2]] Then I entered: A = {{1, 1, 0}, {1, 0, 0}, {0, 0, 0}} ...
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3answers
117 views

Create table of elements which belongs to specific sets

I would like to produce elements (preferably by Table or For-If commands) that they belong to specific sets. For example I want to write positive integers from 1 to 100 such that they are $2 \pmod 3$, ...
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1answer
72 views

Want code for a modular operation

Given numbers a1 and a2 and a positive integer k, such that ...

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