Related papers: Symbolic tensor calculus on manifolds: a SageMath …
SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer…
In mathematics, many notations have been invented for the concise representation of mathematical formulae. Tensor index notation is one of such notations and has been playing a crucial role in describing formulae in mathematical physics.…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective. We propose to describe these latent manifolds as implicit submanifolds of some ambient latent space. Based…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
In previous work, we presented a symbolic execution method which starts with a concrete model of the program but progressively abstracts away details only when these are known to be irrelevant using interpolation. In this paper, we extend…
We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…
We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this…
We introduce FlagAlgebraToolbox, an extension of SageMath capable of automating flag algebra calculations and optimizations. FlagAlgebraToolbox has a simple interface, can handle a wide range of combinatorial theories, can numerically…
Symbolic computation is the science of computing with symbolic objects (terms, formulae, programs, algebraic objects, geometrical objects, etc). Powerful symbolic algorithms have been developed during the past decades and have played an…
We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the…
This volume contains papers presented at the Ninth International Symposium on Symbolic Computation in Software Science, SCSS 2021. Symbolic Computation is the science of computing with symbolic objects (terms, formulae, programs,…
We introduce in this paper a manifold optimization framework that utilizes semi-Riemannian structures on the underlying smooth manifolds. Unlike in Riemannian geometry, where each tangent space is equipped with a positive definite inner…
In this paper we study the computation of both algebraic and non-algebraic tensor functions under the tensor-tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both…