An Implementation Method of Boolean Gröbner Bases and Comprehensive Boolean Gröbner Bases on General Computer Algebra Systems

2014 ◽  
pp. 531-536 ◽  
Author(s):  
Akira Nagai ◽  
Shutaro Inoue
Keyword(s):  
Computer Algebra ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Computer Algebra Systems ◽  
Implementation Method ◽  
General Computer

scholarly journals Distributive laws between the operads Lie and Com

2020 ◽  
Vol 30 (08) ◽  
pp. 1565-1576
Author(s):  
Murray Bremner ◽  
Vladimir Dotsenko
Keyword(s):  
Lie Algebras ◽  
Computer Algebra ◽  
Gröbner Bases ◽  
Classification Problem ◽  
Grobner Bases ◽  
Polynomial Rings ◽  
Associative Algebras ◽  
Distributive Law ◽  
Free Modules

Using methods of computer algebra, especially, Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet–Loday formula deforming the Poisson operad into the associative operad.

scholarly journals AMulet 2.0 for Verifying Multiplier Circuits

2021 ◽  
pp. 357-364
Author(s):  
Daniela Kaufmann ◽  
Armin Biere
Keyword(s):  
Computer Algebra ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Reduction Algorithm ◽  
Elimination Theory ◽  
Verification Tool ◽  
Polynomial Reduction ◽  
Fully Automatic ◽  
Automatic Tool ◽  
The Given

AbstractAMulet 2.0 is a fully automatic tool for the verification of integer multipliers using computer algebra. Our tool models multiplier circuits given as and-inverter graphs as a set of polynomials and applies preprocessing techniques based on elimination theory of Gröbner bases. Finally it uses a polynomial reduction algorithm to verify the correctness of the given circuit. AMulet 2.0 is a re-factorization and improved re-implementation of our previous multiplier verification tool AMulet 1.0.

Sign in / Sign up

Export Citation Format

Share Document