Related papers: Scalar actions in Lean's mathlib
The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean's mechanism of instance parameters. Related mechanisms for typeclasses are available in other…
We report on the higher-order differential calculus library developed inside the Lean mathematical library mathlib. To support a broad range of applications, we depart in several ways from standard textbook definitions: we allow arbitrary…
Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…
We report on our experience formalizing differential geometry with mathlib, the Lean mathematical library. Our account is geared towards geometers with no knowledge of type theory, but eager to learn more about the formalization of…
Following our previous work, we suggest here a large class of algebras of scalars in which simultaneous and correlated computations can be performed owing to the existence of surjective algebra homomorphisms. This may replace the currently…
This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are…
This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…
We consider a simple instance of action up to homotopy. More precisely, we consider strict actions of DGLAs in degrees -1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
We develop a method for the simulation of scalar field theories with complex actions which is local, simple to implement and can be used in any number of space-time dimensions. For model systems satisfying the $\mathcal{PT}$ symmetry…
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie…
This survey gives an overview of three central algebraic themes related to the study of splines: duality, group actions, and homology. Splines are piecewise polynomial functions of a prescribed order of smoothness on some subdivided domain…
Models on logarithmic lattices have recently been proposed as an alternative approach to the study of multi-scale nonlinear physics. Here, we introduce LogLatt, an efficient MATLAB library for the calculus between functions on…
Task arithmetic is a straightforward yet highly effective strategy for model merging, enabling the resultant model to exhibit multi-task capabilities. Recent research indicates that models demonstrating linearity enhance the performance of…
We present ZFLean, a Lean 4 library for doing core mathematics inside a model of ZFC with the ergonomics expected of typed Mathlib developments. Building on Mathlib's ZFC model, we contribute a relational calculus for sets with rewriting…