- Referenced in 185 articles
- specific types: A Tucker tensor can be expressed as the product of a core tensor ... each mode, and a Kruskal tensor can be expressed as the sum of rank...
- Referenced in 16 articles
- calculation. Riegeom can efficiently simplify generic tensor expressions written in the indicial format. It addresses ... dimension dependent relations of Riemann tensor polynomials. There are tools to manipulate tensors such ... mathematical formulation of canonical form of tensor expressions described elsewhere. Riegeom is implemented over...
- Referenced in 18 articles
- facilitate the translation of tensor expressions into C++ without compromizing speed. A tensor here...
- Referenced in 77 articles
- flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element...
- Referenced in 171 articles
- manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential ... polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results...
- Referenced in 25 articles
- maintain the structure of the input expression as long as possible. This facilitates the application ... form to the subblocks of the local tensor in discontinuous Galerkin problems. This ... enables us to preserve the tensor structure of expressions longer through the compilation process than ... those tensor operations in the second stage. TSFC also efficiently traverses complicated expressions, and experimental...
- Referenced in 14 articles
- following features and capabilities: Manipulation of tensor expressions with and without indices; Implicit ... calculation of covariant derivatives; Automatic application of tensor symmetries; Riemannian metrics and curvatures; Differential forms...
- Referenced in 35 articles
- generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible...
- Referenced in 12 articles
- simplification. Nature of problem: Simplification of tensor expressions taking into account multiterm linear identities, symmetry...
- Referenced in 9 articles
- curvature of Cartan connection leads to wrong expressions. On the other hand , the FINSLER package ... example. Furthermore, the problem of simplifying tensor expressions is treated. This paper is intended...
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- problem: Manipulation and simplification of tensor expressions (or any expression in terms of indexed objects...
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- symbols for complicated expressions, such as covariant derivative and strength tensor for gauge fields. Supersymmetric...
- Referenced in 43 articles
- symmetric groups. It has facilities for converting expressions from one symmetric function basis to another ... standard operations such as scalar products, inner tensor (or Kronecker) products, and plethysm. Beginning with...
- Referenced in 2 articles
- rapid composition of high-performance tensor expressions, appearing for example in many-body quantum mechanics ... allows users to compose tensor expressions of arbitrary complexity in native C++ code that closely...
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- using Unicode in identifiers, implemented tensor expressions commonly look very similar to their mathematical writing ... number of bugs in implementations. Operations on tensors are often compiled into the minimum assembly...
- Referenced in 8 articles
- user-level interface elegantly expresses arbitrary-dimensional generalized tensor contractions in the form...
- Referenced in 4 articles
- main features are: Consistent integration of tensors with symbolic indices and index contractions in Mathematica ... manipulate (expand, collect, differentiate etc.) such expressions. Arbitrary tensors and index types can be defined...
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- package for the manipulation of algebraic expressions of tensors in general relativity. In this paper ... packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses ... potential for manipulation of indexed algebraic tensor expressions in a flexible software environment...
- Referenced in 2 articles
- declare and apply tensor and tensor expression symmetries. Kronecker, generalized Kronecker and Levi-Civita routines...
- Referenced in 15 articles
- high rank tensor integrals with up to three propagators, and gives compact expressions...