# Questions tagged [modular-arithmetic]

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### Sparse matrix multiplication mod p

Let A and B be sparse matrices with integer coefficients between 0 and ...
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33 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 ...
0answers
366 views

### Parallel PowerMod

Is there anyway to parallelize the PowerMod function? Here is my Left-To-Right modular exponentation: ...
0answers
69 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 ...
0answers
73 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 ...
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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 ...
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627 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 ...
0answers
49 views

### How do I getting the integer value of a b?

In this equation, it is known that ( a * (b + c)) mod D = x ( e * (f + c)) mod G = x How can I get the values of a and b, if c, e, f, x, D, and G already known?
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77 views

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

I have the following $2$-dimensional implicitly defined map ...