The notion of spectral sequence is an algorithm or computational tool in homological algebra and more generally in homotopy theory which allows to compute chain homology groups/homotopy groups of bi-graded objects from the homology/homotopy of the two graded components.
Notably there is a spectral sequence for computing the homology of the total complex of a double complex from the homology of it…
analysis (differential/integral calculus, functional analysis, topology)
metric space, normed vector space
open ball, open subset, neighbourhood
convergence, limit of a sequence
compactness, sequential compactness
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constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
basic constructions:
strong axioms
further
In real ana…
Campbell Watson; Charles Wachira; Rosie Lickorish; Romeo Kienzler; Blair Edwards; Michael Johnston
3/3/2026
Across disciplines, advances in computational mathematics are transforming how large-scale scientific data is analyzed, interpreted, and translated into deployable workflows. In the Earth and space monitoring domains, extreme weather risk, disaster response, precision agriculture, and solar activity forecasting rely on turning petabytes of satellite and sensor data into actionable insights.
Found…
We propose a new polynomial evaluation algorithm to evaluate a degree-$d$ Boolean polynomial $f(x_n,\ldots,x_1)$ on all elements in some structured sets $S\subseteq \mathbb F_2^n$. This problem has been well-studied for $S=\mathbb F_2^n$ and there are efficient polynomial evaluation algorithms like standard Mobius transform, memory-efficient Mobius transform (EUROCRYPT 2021, TOMS 2024) and fast e…
Determining the complexity of computing Gröbner bases is an important problem in both theory and practice, and solving degrees provide a central measure of this complexity.
We study solving degrees and Gröbner basis computations for affine polynomial systems, with particular emphasis on semi-regular sequences.
We first derive two upper bounds for the maximum Gröbner basis degree of the homogeniz…
basic constructions:
strong axioms
further
constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
The limited principle of omniscience () states that the existential quantification of any decidable proposition is again decidable. That is,
or equivalently
We have not stated the domain of quantification of the variable . If you…
