Re:AbstractAlgebra: Computer algebra package for Julia language
by red_trumpet on Friday March 20, 2020 @12:37PM
(#22638946)
This is the feature list from the link:
- Use of Julia multiprecision integers and rationals
- Finite fields (prime order, naive implementation only)
- Number fields (naive implementation only)
- Univariate polynomials
- Multivariate polynomials
- Relative and absolute power series
- Laurent series
- Fraction fields
- Residue rings, including Z/nZ
- Matrices and linear algebra
What exactly do you consider "numerical" here? AFAIU those are all standard constructions from abstract algebra and number theory.
Re:AbstractAlgebra: Computer algebra package for Julia language
by abjKT26nO8 on Friday March 20, 2020 @12:42PM
(#22638990)
You're mostly right, with one (or two) exception: > Matrices and linear algebra. This isn't abstract algebra. It's used in abstract algebra, but that's true for linear algebra in almost any branch of mathematics. Also, depending on what exactly they implemented for Univariate polynomials, this part may also be numerical.
Re:AbstractAlgebra: Computer algebra package for Julia language
by omaranto on Friday March 20, 2020 @01:29PM
(#22639466)
Did you look at the documentation? The matrices implemented have their elements in arbitrary commutative rings (well, not arbitrary, somebody has to implement them in Julia, of course, but they have a bunch). I think its fair to call that abstract algebra; I wouldn't it numeric. In my university, that's how we teach linear algebra to math majors but not to engineers, for example.
Still neat, though!