Related papers: Symbolic Computing with Grassman Variables
We give a precise, computable formula for comparing $\lambda$-invariants between modular forms in the anticyclotomic indefinite setting where the Selmer groups have positive rank. This is an improvement of Hatley-Lei \cite{HL19, HL21} where…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally…
The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration…
Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF,…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
In the current work, the author present a symbolic algorithm for finding the determinant of any general nonsingular cyclic heptadiagonal matrices and inverse of anti-cyclic heptadiagonal matrices. The algorithms are mainly based on the work…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends.…
The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
We report on the computation of invariants, covariants, and contravariants of cubic surfaces. All algorithms are implemented in the computer algebra system magma.
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and…
We present a new symbolic execution semantics of probabilistic programs that include observe statements and sampling from continuous distributions. Building on Kozen's seminal work, this symbolic semantics consists of a countable collection…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matrix (ASM) varieties. The package also introduces tools for…
I introduce batman, a Python package for modeling exoplanet transit light curves. The batman package supports calculation of light curves for any radially symmetric stellar limb darkening law, using a new integration algorithm for models…