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Class of mathematical software
available. Tela is a software package similar to MATLAB and GNU Octave, but designed specifically for tensors. Tensor is a tensor package written for the
Tensor_software
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Concept in machine learning
learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data
Tensor_(machine_learning)
Series of system-on-chip processors
2020. The first-generation Tensor chip debuted on the Pixel 6 smartphone series in 2021, and was succeeded by the Tensor G2 chip in 2022, G3 in 2023
Google_Tensor
Interactive theorem prover software
mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration
Proof_assistant
Sequence of operations for a task
representation. Most algorithms are implemented on particular hardware/software platforms and their algorithmic efficiency is tested using real code. The
Algorithm
Software used in mathematical applications
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data. Mathematical knowledge of techniques such as
Mathematical_software
Associative algebra together with a Lie bracket that satisfies Leibniz's law
the tensor algebra of the underlying vector space of the Lie algebra. The tensor algebra is simply the disjoint union (direct sum ⊕) of all tensor products
Poisson_algebra
Study of discrete mathematical structures
algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying
Discrete_mathematics
Application of mathematical methods to other fields
mathematics". The success of modern numerical mathematical methods and software has led to the emergence of computational mathematics, computational science
Applied_mathematics
disseminating proofs. AlphaDev AlphaEvolve AlphaGeometry AlphaProof AlphaTensor DeepSeek-Prover FunSearch Ramanujan machine Artificial intelligence Automated
Mathematics and artificial intelligence
Mathematics_and_artificial_intelligence
Machine learning software library
TensorFlow is a software library for machine learning and artificial intelligence. It can be used across a range of tasks, but is used mainly for training
TensorFlow
Area of mathematics
education Mathematical software List of free educational software for computational mathematics List of open-source software for mathematics National
Computational_mathematics
Type of approximation to an underlying physical theory
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Effective_field_theory
1960 article by Eugene Wigner
Einstein, which would not have been possible without the development of Tensor Analysis by a series of great mathematicians such as Gauss, Riemann, Christoffel
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
Branch of applied probability theory
called decision analysis and is aimed at finding tools, methodologies, and software (decision support systems) to help people make better decisions. In contrast
Decision_theory
Calculus on stochastic processes
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Stochastic_calculus
Branch of mathematics concerning probability
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Probability_theory
Open-source software library for LLM inference
UINT64 // starting position within the tensor_data block, relative to the start of the block // (n+1)-th tensor ... Llama.cpp supports many large language
Llama.cpp
Study of abstract machines and automata
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Automata_theory
Methods of mathematical approximation
are common, and the code is included in most ab initio quantum chemistry software. A related but more accurate method is the coupled cluster method. Perturbation
Perturbation_theory
Calculus of vector-valued functions
(p,q)} tensor can be formed by taking a tensor product of a ( p , 0 ) {\displaystyle (p,0)} tensor and a ( 0 , q ) {\displaystyle (0,q)} tensor, which
Vector_calculus
Organization
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
International Council for Industrial and Applied Mathematics
International_Council_for_Industrial_and_Applied_Mathematics
Branch of functional analysis
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Operator_algebra
Formulation of classical mechanics using momenta
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Hamiltonian_mechanics
Branch of computer science
computational geometry topics List of interactive geometry software List of information graphics software List of numerical computational geometry topics List
Computational_geometry
Physical quantities taking values at each point in space and time
example of a vector field. Strain tensor, representing the deformation of matter caused by stress, is an example of a tensor field. Field theories, mathematical
Field_(physics)
Branch of applied mathematics
manifold that "curves" geometrically, according to the Riemann curvature tensor. The concept of Newton's gravity: "two masses attract each other" replaced
Mathematical_physics
Physical theory with fields invariant under the action of local "gauge" Lie groups
relativity. Its case is somewhat unusual in that the gauge field is a tensor, the Lanczos tensor. Theories of quantum gravity, beginning with gauge gravitation
Gauge_theory
This is a list of open-source software to be used for high-order mathematical calculations. This software has played an important role in the field of
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Branch of mathematics
MIT Press., Chapter 1 Borisenko, A. I.; Tarapov, I. E. (1979). Vector and Tensor Analysis with Applications (Dover Books on Mathematics). Dover Books on
Mathematical_analysis
Physical theory describing classical fields
formulation using tensor fields was found. Instead of using two vector fields describing the electric and magnetic fields, a tensor field representing
Classical_field_theory
Algebra based on a vector space with a quadratic form
algebra generated by V may be written as the tensor algebra ⨁n≥0 V ⊗ ⋯ ⊗ V, that is, the direct sum of the tensor product of n copies of V over all n. Therefore
Clifford_algebra
Set of objects whose state must satisfy limits
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Constraint satisfaction problem
Constraint_satisfaction_problem
Harmonic functions as solutions to Laplace's equation
Mathematical software Arbitrary-precision arithmetic Finite element analysis Tensor software Interactive geometry software Optimization software Statistical
Potential_theory
Concept in theoretical physics
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Renormalization_group
Collection of random variables
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Stochastic_process
Theory of getting acceptably close inexact mathematical calculations
University Press. ISBN 978-0-521-88068-8. Cody, Jr., W.J.; Waite, W. (1980). Software Manual for the Elementary Functions. Prentice-Hall. ISBN 0-13-822064-6
Approximation_theory
Field theory involving topological effects in physics
turns out to be metric independent. The independence of the stress-energy tensor Tαβ of the system from the metric depends on whether the BRST-operator is
Topological quantum field theory
Topological_quantum_field_theory
AI accelerator ASIC by Google
The Tensor Processing Unit (TPU) is a neural processing unit (NPU) application-specific integrated circuit (ASIC) developed by Google for neural network
Tensor_Processing_Unit
Study of the properties of codes and their fitness
feedback logic, normally XOR gates. The decoder can be implemented in software or firmware. The Viterbi algorithm is the optimum algorithm used to decode
Coding_theory
Field of higher mathematics
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Geometric_analysis
Software for a class of mathematical problems
solver is a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical
Solver
Theory of subatomic structure
wrapped into a small circle. Einstein introduced a non-symmetric metric tensor, while much later Brans and Dicke added a scalar component to gravity. These
String_theory
Algebraic structure used in theoretical physics
ordinary ungraded tensor product (except that the result is graded). However, in general, the super tensor product is distinct from the tensor product of A
Superalgebra
Study of rational collective decision-making
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Social_choice_theory
This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed
List of finite element software packages
List_of_finite_element_software_packages
Representation of mechanical stress at every point within a deformed 3D object
Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress
Cauchy_stress_tensor
Quantum field theory enjoying conformal symmetry
of tensor structures, and there is a structure constant for each tensor structure. In the case of two scalar fields and a symmetric traceless tensor of
Conformal_field_theory
Calculus of functions of several variables
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Multivariable_calculus
Framework to describe phase transitions
Mathematical software Arbitrary-precision arithmetic Finite element analysis Tensor software Interactive geometry software Optimization software Statistical
Statistical_field_theory
Branch of mathematics
Hiriart-Urruty, Comparison of public-domain software for black box global optimization. Optimization Methods & Software 13(3), pp. 203–226, 2000. J.D. Pintér
Global_optimization
Methods used to find numerical solutions of ordinary differential equations
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Mathematical approach to quantum physics
perturbative corrections can be coded on computers with symbolic processing software like Mathematica. Let H(0) be the Hamiltonian completely restricted either
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
lists libraries, applications, and other software which enable or support arbitrary-precision arithmetic. Software that supports arbitrary precision computations:
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
French scientific society aiming at promoting applied mathematics
Mathematical software Arbitrary-precision arithmetic Finite element analysis Tensor software Interactive geometry software Optimization software Statistical
Société de mathématiques appliquées et industrielles
Société_de_mathématiques_appliquées_et_industrielles
Branch of numerical analysis
one are discretized. MOL allows standard, general-purpose methods and software, developed for the numerical integration of ordinary differential equations
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Graph representation in quantum mechanics
compression and contraction are both efficient. Tensor network states are the special case in which a tensor network represents a variational wave function
Tensor_network
Quantum mechanics with supersymmetry
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Supersymmetric quantum mechanics
Supersymmetric_quantum_mechanics
Field of mathematics
2019. Dongarra, Jack; Hammarling, Sven (1990). "Evolution of Numerical Software for Dense Linear Algebra". In Cox, M. G.; Hammarling, S. (eds.). Reliable
Numerical_linear_algebra
Overview of mechanics based on the least action principle
nonlinear. This scalar field formulation can be extended to vector fields, tensor fields, and spinor fields. The Lagrangian is the volume integral of the
Analytical_mechanics
Academic association dedicated to the use of mathematics in industry
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Society for Industrial and Applied Mathematics
Society_for_Industrial_and_Applied_Mathematics
and the complex algebra can be constructed from the real one by taking tensor product with the complex numbers.[citation needed] The bosonic part of the
Supersymmetry_algebra
Setting of relativistic physics in geometric algebra
representation is unnecessary for STA. Products of the basis vectors generate a tensor basis containing one scalar { 1 } {\displaystyle \{1\}} , four vectors
Spacetime_algebra
Approach to dimensionality reduction
data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images
Multilinear_subspace_learning
Formulation of classical mechanics
complicated. In a set of curvilinear coordinates ξ = (ξ1, ξ2, ξ3), the law in tensor index notation is the "Lagrangian form" F a = m ( d 2 ξ a d t 2 + Γ a b
Lagrangian_mechanics
European mathematical society
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
European Society for Mathematical and Theoretical Biology
European_Society_for_Mathematical_and_Theoretical_Biology
Physics-mathematics connection
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Particle physics and representation theory
Particle_physics_and_representation_theory
Interdisciplinary field of research
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Mathematical_sociology
Interactive geometry software (IGS) or dynamic geometry environments (DGEs) are computer programs which allow one to create and then manipulate geometric
List of interactive geometry software
List_of_interactive_geometry_software
Theory in theoretical physics
because the stress–energy tensor may be written as an anticommutator of a supercharge and another field. As the stress–energy tensor measures the dependence
Topological_string_theory
Study of vector bundles, principal bundles, and fibre bundles
{\displaystyle R_{\nabla }} , by analogy with the Riemannian curvature tensor in Riemannian geometry which is denoted by R {\displaystyle R} . The letter
Gauge_theory_(mathematics)
Decomposition in multilinear algebra
multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal
Tensor_rank_decomposition
Symmetry between bosons and fermions
Traditional symmetries of physics are generated by objects that transform by the tensor representations of the Poincaré group and internal symmetries. Supersymmetries
Supersymmetry
Numerics including mathematically strict error evaluation
Hypergeometric Functions Rigorously. ACM Transactions on Mathematical Software (TOMS), 45(3), 30. Johansson, Fredrik (2015). Rigorous high-precision computation
Validated_numerics
Japanese counterpart of the Society for Industrial and Applied Mathematics
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Japan Society for Industrial and Applied Mathematics
Japan_Society_for_Industrial_and_Applied_Mathematics
Deep learning library
performance across major cloud platforms. PyTorch defines a class called Tensor (torch.Tensor) to store and operate on homogeneous multidimensional rectangular
PyTorch
which release their software under open-source licenses and are related to artificial intelligence projects. These include software libraries, frameworks
Lists of open-source artificial intelligence software
Lists_of_open-source_artificial_intelligence_software
Algebra of 4D spacetime
Mathematical software Arbitrary-precision arithmetic Finite element analysis Tensor software Interactive geometry software Optimization software Statistical
Algebra_of_physical_space
2026 Android smartphone developed by Google
suggest that Tensor G6 provides additional performance for heavy workloads, and draws less power when connected to cellular networks. With Tensor G6 comes
Pixel_11
Infinitesimal calculus on functions defined on a geometric algebra
can associate the components of a metric tensor, the Christoffel symbols, and the Riemann curvature tensor as follows: g i j = e i ⋅ e j , Γ i j k =
Geometric_calculus
Numerical computation library for Python
import theano from theano import tensor # Declare two symbolic floating-point scalars a = tensor.dscalar() b = tensor.dscalar() # Create a simple expression
Theano_(software)
2026 Android smartphone by Google
previous generation Tensor G4, the same chip found in the Pixel 9 series, to power the phone instead of using the current generation Tensor G5 SoC. This marks
Pixel_10a
Quantum computing company
AI models and quantum software. The AI model compression platform, CompactifAI, delivers compressed AI models by applying tensor network techniques. With
Multiverse_Computing
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Deep backward stochastic differential equation method
Deep_backward_stochastic_differential_equation_method
Theory of stochastic partial differential equations
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Supersymmetric theory of stochastic dynamics
Supersymmetric_theory_of_stochastic_dynamics
Tabular comparison of deep learning software
The following tables compare notable software frameworks, libraries, and computer programs for deep learning applications. Licenses here are a summary
Comparison of deep learning software
Comparison_of_deep_learning_software
American technology company
integrated circuit (ASIC). The architecture was originally introduced as a Tensor Streaming Processor (TSP) but was later rebranded as a Language Processing
Groq
Topics referred to by the same term
space A metric tensor, in differential geometry, which allows defining lengths of curves, angles, and distances in a manifold Metric tensor (general relativity)
Metric
analysis Multilinear algebra Exterior Geometric Tensor Vector Multivariable calculus Exterior Geometric Tensor Vector Numerical analysis Numerical linear algebra
Clifford_analysis
Algorithms for matrix decomposition
negatively. Multilinear algebra Multilinear subspace learning Tensor Tensor decomposition Tensor software Dhillon, Inderjit S.; Sra, Suvrit (2005). "Generalized
Non-negative matrix factorization
Non-negative_matrix_factorization
GPU microarchitecture by Nvidia
accelerated by the Tensor cores, which are used to fill in the blanks in a partially rendered image, a technique known as de-noising. The Tensor cores perform
Turing_(microarchitecture)
GPU microarchitecture by Nvidia
estimated to provide 25 Gbit/s per lane. (Disabled for Titan V) Tensor cores: A tensor core is a unit that multiplies two 4×4 FP16 matrices, and then adds
Volta_(microarchitecture)
2025 Android smartphone developed by Google
subjects. The custom Google Tensor G5 System-on-Chip (SoC) is a noticeable upgrade over the Tensor G4 and other previous Tensor processors. Instead of using
Pixel_10
GPU microarchitecture by Nvidia
processing power (GA100 only, 2x on GA10x) compared to previous Tensor Core generations; the Tensor Core Count is reduced to one per SM. Second-generation ray
Ampere_(microarchitecture)
Method of utilizing water in magnetic resonance imaging
more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming
Diffusion-weighted magnetic resonance imaging
Diffusion-weighted_magnetic_resonance_imaging
Series of embedded computing boards by Nvidia
512-core Ampere GPU with 16 Tensor cores, while the 8 GB variant doubles those numbers to 40/20 TOPs, a 1024-core GPU and 16 Tensor cores. Both have 6 Arm
Nvidia_Jetson
Development platform for rendering graphics
Ampere-, Ada Lovelace- and Blackwell-based GPUs, specifically utilizing the Tensor cores (and new RT cores on Turing and successors) on the architectures for
Nvidia_RTX
ARM-based system-on-chip by Nvidia
with a Blackwell RTX GPU containing 6,144 CUDA cores and fifth-generation Tensor Cores with FP4 precision. The CPU and GPU are connected using Nvidia's NVLink-C2C
Nvidia_RTX_Spark
2022 Android smartphone developed by Google
unveils Pixel 6a with Tensor chipset for $449". GSMArena. 11 May 2022. Johnson, Allison (2022-05-11). "The Pixel 6A includes Google's Tensor chipset and costs
Pixel_6a
travel, tourism, insurance
TENSOR SOFTWARE
TENSOR SOFTWARE
Male
Greek
(ÎœÎντωÏ) Greek name derived from the word menos, MENTOR means "spirit." In mythology, this is the name of the son of Ãlkimos.
Surname or Lastname
English
English : unexplained.
Surname or Lastname
English
English : patronymic from Penn 3 or Paine 1.English : habitational name from Penson in Devon.
Surname or Lastname
English
English : variant of Windsor. This is the spelling used for places so named in Devon and Hampshire.Perhaps also an Americanized spelling of German Winzer.
Surname or Lastname
English
English : perhaps an altered spelling of Janson.Respelling of Danish, Norwegian, and North German Jensen.
Surname or Lastname
English
English : patronymic from a reduced form of the personal name Steven.English : habitational name from a place in Derbyshire, recorded in Domesday Book as Steintune, later as Steineston, from the Old Norse personal name Steinn (meaning ‘stone’) + Old English tūn ‘enclosure’, ‘settlement’.Variant of Steenson 2.
Boy/Male
French
Works in iron.
Surname or Lastname
French
French : unexplained.English : unexplained.Possibly a respelling of Menter, an unexplained name of German origin.
Male
Scandinavian
Scandinavian form of Latin Theodorus, TEODOR means "gift of God."
Surname or Lastname
English
English : variant spelling of Ensor.
Surname or Lastname
English
English : patronymic from the medieval personal name Benne, a pet form of Benedict (see Benn).English : habitational name from a place in Oxfordshire named Benson, from Old English Benesingtūn ‘settlement (Old English tūn) associated with Benesa’, a personal name of obscure origin, perhaps a derivative of Bana meaning ‘slayer’.Jewish (Ashkenazic) : patronymic composed of a pet form of the personal name Beniamin (see Bien, Benjamin) + German Sohn ‘son’.Scandinavian : altered form of such names as Bengtsson, Bendtsen, patronymics from Bengt, Bendt, etc., Scandinavian forms of Benedict.
Male
English
English surname transferred to forename use, BENSON means "son of Ben."
Boy/Male
Muslim
Winner
Surname or Lastname
English
English : variant of Tennyson.
Surname or Lastname
German
German : variant of Tanner 2.English : from Old French teneor, teneur, tenor, ‘holder of a tenement’, hence an equivalent of Tennant.
Surname or Lastname
English
English : probably a variant of Manser.
Surname or Lastname
English
English : habitational name for someone from Edensor in Derbyshire, which derives its name from the genitive case of the Old English personal name Ēadhūn (see Eden 1) + Old English ofer ‘ridge’.
Surname or Lastname
English
English : patronymic from the personal name Henn(e), a short form of Henry 1, Hayne (see Hain 2), or Hendy.Irish : Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).
Boy/Male
Polish Spanish
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : nickname for a peasant who gave himself airs and graces, from Anglo-Norman French segneur ‘lord’ (Latin senior ‘elder’).English and Dutch : distinguishing nickname for the elder of two bearers of the same personal name (for example, a father and son or two brothers), from Latin senior ‘elder’.
TENSOR SOFTWARE
TENSOR SOFTWARE
TENSOR SOFTWARE
TENSOR SOFTWARE
TENSOR SOFTWARE
TENSOR SOFTWARE
TENSOR SOFTWARE
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