# 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 ...
38 views

### Why gives Modulo of complex numbers different answers for rationals and reals

When running Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 0.5}] Table[1.*Mod[(1 + I)^(1 + k*I), 1 + k*I], {k, 49, 50, 1/2}] I get for the first table <...
373 views

### Parallel PowerMod

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

### How to apply PolynomialMod to a SparseArray?

I have a list bdrs of SparseArrays, whose entries are polynomials in the variable t with ...
87 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 ...
76 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 ...
153 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 ...
655 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 ...
### Variables defined modulo $\pi$ and avoiding singularities; phase plotting for a map
I have the following $2$-dimensional implicitly defined map ...