Questions tagged [modular-arithmetic]

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8 questions
138 views

Sparse matrix multiplication mod p

Let A and B be sparse matrices with integer coefficients between 0 and ...
27 views

FindEquationalProof to prove divisor theorem

I'm trying to implement proofs of concepts for Equational Proofs on some basic number theory theorems. One such example is: "let a and b be positive integers and let d = gcd (a, b). If t divides ...
366 views

Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
66 views

Finite fields package doesn't simplify

I'm trying to do arithmetic using the FiniteFields package. Supposing a is a generator of a Galois field (say GF(2^5)) I want to be able to simplify things like a^32 and (a^8)^-1. I don't care about ...
72 views

Sum of zeros in finite Galois field

In the following code: << FiniteFields` GF[{0}] + GF[{0}] == GF[{0}] GF[{0}] + GF[{0}] + GF[{0}] == GF[{0}] Why does the second line ...
151 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 ...
Variables defined modulo $\pi$ and avoiding singularities; phase plotting for a map
I have the following $2$-dimensional implicitly defined map ...