We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption protocols.

We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption protocols.

Polynomial and rational solutions for linear ordinary differential equations can be obtained by algorithmic methods. For instance, the maple package DEtools provides efficient functions polysols and ratsols to find polynomial and rational solutions for a given linear ordinary differential equation with rational function coefficients. A natural analogue of the notion of linear ordinary different...

Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants exclude from solution set. The nondegenerate locus of a is set points where codimension matches number equations. Computing classically done through ideal-theoretic operations commutative algebra as saturati...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

A large number of mathematical models in engineering and physical sciences employ Partial Differential Equations (PDEs). The sheer number of operations required in numerically integrating PDEs in these applications has motivated the search for faster methods of computing. The conventional uniprocessor computers are often unable to fulfill the performance requirements for these computation inten...

People tend to slow down after they commit an error, a phenomenon known as post-error slowing (PES). It has been proposed that slowing after negative feedback or unforeseen errors is linked to the activity of the locus coeruleus-norepinephrine (LC-NE) system, but there is little direct evidence for this hypothesis. Here, we assessed the causal role of the noradrenergic system in modulating PES ...

1 We study the Newton polyhedron of the discriminant for a system of polynomial equations, whose coefficients depend on parameters.

We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system f1 = · · · = fn = 0, with fi ∈ C[x1, . . . , xn], and a polydisc ∆ ⊂ C, our method aims to certify the existence of k solutions (counted with multiplicity) within the polydisc. In case of success, it yields the correct result u...