Tropical geometry has recently found several applications in the analysis of neural networks with piecewise linear activation functions. This article presents a new look at the problem of tropical ...

Polynomial division can also be performed when there is a remainder. In such cases, the remainder can be written as a term divided by the divisor, forming a rational expression.

Peter Shor revolutionized public-key infrastructure (PKI) using concepts that trace back to 4,000-year-old Babylonian mathematics and culminated in futuristic quantum computing. Here, we explore the ...

Abstract Let A A be the linear transformation on the linear space V in the field P, Vλi V λ be the root subspace corresponding to the characteristic polynomial of the eigenvalue λi λ i , and Wλi W λ ...

A new algorithm is presented for directly determining both the quotient and the remainder associated with the division of one polynomial matrix by another. The procedure requires that the denominator ...

Abstract We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute on encrypted data for any desired functions without needing to decrypt the data or ...

Learn what the remainder theorem is, how to prove it, and how to apply it to polynomial division problems.

In the polynomial division, the original data forms the input polynomial, a predefined polynomial serves as the divisor, and the remainder polynomial gives the final check value. An n -bit CRC ...