Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Cartesian Vector Notation01:28

Cartesian Vector Notation

1.9K
Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
1.9K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.2K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.2K
Summation Notation01:25

Summation Notation

348
Sigma notation, also known as summation notation, provides a concise method for representing the sum of a sequence of terms that follow a regular pattern. It utilizes the uppercase Greek letter sigma (∑), A typical expression is:In this form, k the index of summation is 1, the starting value, and n the ending value. The term ak​ represents the general term of the sequence.For example, the increasing sequence 5, 7, 9, ..., 23 over 10 terms can be expressed as:This simplifies the...
348
Scalar Notation01:28

Scalar Notation

1.2K
Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be added or subtracted separately using scalar notation. For instance, force, a vector quantity, can be broken down into its x and y components, called rectangular components, and then the magnitude and direction of these components can be determined using trigonometric functions.
Consider a man pulling a rope from a hook in the northeast direction. The...
1.2K
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

767
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment....
767
Relating Angular And Linear Quantities - II01:05

Relating Angular And Linear Quantities - II

7.0K
In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the relation:
7.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Separability of the Coupled-Cluster Excited State Equations: The Case of Excitonic Couplings.

The journal of physical chemistry. A·2026
Same author

SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian with Size-Intensive Picture Change.

Journal of chemical theory and computation·2026
Same author

Machine-Learning Interatomic Potentials Achieving CCSD(T) Accuracy for Systems with Extended Covalent Networks and van der Waals Interactions.

Journal of chemical theory and computation·2026
Same author

Dissecting non-radiative decay in donor-functionalized radicals with a mode-resolved model.

Physical chemistry chemical physics : PCCP·2025
Same author

Towards Multireference Equivalents of the HEAT Thermochemical Protocol.

Journal of computational chemistry·2025
Same author

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets.

Journal of chemical theory and computation·2025
Same journal

The x-ray absorption spectrum of the propargyl radical C3H3●.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. I. Conformer- and isomer-resolved infrared spectra.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. II. Isomer-resolved unimolecular dynamics.

The Journal of chemical physics·2026
Same journal

Quantum state-to-state dynamics studies of the C(3P) + OH(X2Π) → CO(a3Π) + H(2S) reaction based on a new HCO(12A″) potential energy surface.

The Journal of chemical physics·2026
Same journal

Time-resolved ultrabroadband far-to-mid-infrared spectroscopy directly reveals doorway-mediated vibrational energy flow in an energetic crystal (β-HMX).

The Journal of chemical physics·2026
Same journal

Anomalous phase behaviors near the multiphase coexistence point in 1-alkyl-3-methylimidazolium ionic liquids.

The Journal of chemical physics·2026
See all related articles
  1. Home
  3. Sequant Framework For Symbolic And Numerical Tensor Algebra. I. Core Capabilities.
  1. Home
  3. Sequant Framework For Symbolic And Numerical Tensor Algebra. I. Core Capabilities.

Related Experiment Video

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

SeQuant framework for symbolic and numerical tensor algebra. I. Core capabilities.

Bimal Gaudel1, Robert G Adam2, Ajay Melekamburath1

  • 1Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA.

The Journal of Chemical Physics
|April 13, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

SeQuant is an open-source library for symbolic algebra of tensors. Its graph-theoretic tensor network canonicalizer efficiently handles symmetries, optimizing tensor expression simplification and numerical evaluation.

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Related Experiment Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K

Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Data Science

Background:

  • Symbolic algebra of tensors is crucial for various scientific domains.
  • Existing methods for tensor network (TN) manipulation can be computationally intensive, especially with symmetries.

Purpose of the Study:

  • Introduce SeQuant, an open-source library for symbolic tensor algebra.
  • Enhance the efficiency of tensor expression simplification and numerical evaluation.

Main Methods:

  • Developed a graph-theoretic tensor network (TN) canonicalizer.
  • Implemented support for non-covariant TNs and parametrically dependent tensor modes.
  • Integrated compiler-like components for optimization and direct numerical interpretation.

Main Results:

  • Achieved faster handling of TNs with symmetries compared to group-theoretic methods.
  • Enabled routine simplification of conventional tensor expressions.
  • Optimized the application of Wick's theorem for canonicalizing tensor products.
  • Facilitated manipulation of intermediate representations for numerical evaluation.

Conclusions:

  • SeQuant offers a novel approach to symbolic tensor algebra with significant performance improvements.
  • The library effectively bridges symbolic manipulation and numerical evaluation.
  • Provides advanced features for complex tensor structures relevant to modern simulations and data science.