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Terui Lab
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A computer algebra lab that handles mathematical expressions on computers and combines this with numerical computation.
AboutAbout the lab
Combining symbolic and numerical computation to reach meaningful answers.
The Terui Lab studies computer algebra, particularly the theory and applications of symbolic-numeric computation.
Computer algebra is the direct handling of mathematical expressions by computer, or the theory behind it.
Symbolic-numeric computation brings numerical methods into problems that exact symbolic computation could not solve, in order to reach meaningful answers.
In computer algebra, the lab also emphasizes finishing computations in practical time, and develops theories and methods for this.
Key terms
- Symbolic-numeric computation
- An approach that brings numerical methods into problems that exact computer algebra could not solve, in order to reach meaningful answers
- Gröbner basis
- A tool in computer algebra for rearranging a system of polynomial equations into a form that is easier to solve
- Inverse kinematics
- The problem of finding how far each joint of a robot arm must move to place the tip of the arm at a target position
- Approximate GCD
- For several polynomials whose coefficients contain errors, the greatest common divisor that can be regarded as nearly common to all of them
- Computer algebra
- Handling mathematical expressions directly on a computer, or the theory for doing so
ResearchResearch themes
The lab studies the theory and applications of computer algebra, which handles mathematical expressions directly on computers. It also incorporates numerical methods, aiming to give meaningful answers to problems that exact computation could not solve.
*Illustrative imageSolving Robot Arm Motion with Algebra
In joint research with the Social Robotics Lab at the University of Tsukuba, the lab studies methods that use Gröbner basis computation to solve inverse kinematics and trajectory planning problems for arm-type robots. It works on solving them efficiently while rigorously guaranteeing the existence of solutions.
*Illustrative imageLocalization for Asteroid Exploration Rovers
In joint research with the Social Robotics Lab at the University of Tsukuba, the lab studies methods for estimating the relative positions of small swarm robots exploring an asteroid, based on the strength of the radio signals they send to each other. It works on reducing nonlinear simultaneous equations to simultaneous linear equations so they can be solved efficiently, as well as on methods for evaluating errors.
*Illustrative imageExact Linear Computation for Matrices
In joint research, the lab develops algorithms that efficiently compute generalized eigenspaces and Jordan chains for matrices with integer or rational entries. The algorithms are based on residue analysis of the resolvent and use tools such as the minimal annihilating polynomial.
*Illustrative imageIterative Algorithms for Approximate Polynomial GCD
In joint research, the lab computes approximate GCDs of univariate polynomials with an iterative algorithm that reduces the problem to constrained optimization. It has succeeded in developing an algorithm that computes extremely efficiently, with accuracy comparable to conventional optimization methods.
MembersFaculty
- Associate ProfessorAkira Terui
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Kreis Maxima” Birgit 18 / CC BY-SA 4.0 (cropped)
- Solving Robot Arm Motion with Algebra: “John Siegel making a 17ft long Robot Arm for NASA” Victoria Lee Croasdell / CC BY-SA 4.0 (cropped)
- Localization for Asteroid Exploration Rovers: “20180915 - European Rover Challenge - DxO” Jakub Hałun / CC BY-SA 4.0 (cropped)
- Exact Linear Computation for Matrices: “DEC PDP-10 (DECsystem 10) mainframe computer system at Living Computer Museum (strongly edited image)” Joe Mabel / CC BY-SA 3.0 (cropped)
- Iterative Algorithms for Approximate Polynomial GCD: “Slide Rule-Karoly Szabo” The original uploader was Tamas Szabo at English Wikipedia. / CC BY-SA 2.5 (cropped)
- Related lab (及川 一誠 研究室): “Crouzeix-Raviart-Finite-Elemente-Lösung” Grawiuton / CC0 (cropped)
- Related lab (桑原 敏郎 研究室): “Matematička gimnazija - Mathematical Gymnasium Belgrade - MGB - Physics Laboratory 1” MGB / Public domain (cropped)
- Related lab (竹山 美宏 研究室): “Portal Math Banner Background ka” User:Alsandro / CC0 (cropped)
- Related lab (竹内 耕太 研究室): “Classroom blackboard at Cornell University, Ithaca, NY 25” LBM1948 / CC BY-SA 4.0 (cropped)
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