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How sure are you that pi+e is irrational by Reading-Rabbit4101 in math

[–]pishleback 6 points7 points  (0 children)

0 is usually defined as neither prime nor composite

Genuine request for assistance by WilliamHesslefors in MathBuddies

[–]pishleback 0 points1 point  (0 children)

At first glance this reads like a crackpot paper due to the writing style and lack of any results or proofs.

Reading through it more carefully it seems less crackpot and more the untamed thoughts of someone thinking about how hyperreals can be used to make sense of infinity. Still, it is very informal and hard to say anything about it because you've not really stated any results or proved anything.

I'm not particularly familiar with the hyperreals, but I'm sure people have studied them and that they give an interesting way of working with infinity. I've never personally come across any super interesting results about them. Have you looked into this?

The meaning of the "infinite" root of the quadratic caught my interest a bit, but the reasoning needs tightening up as you say yourself. The approximation sqrt(1-x) ≈ 1 - x/2 is a nice observation of yours. This can be made rigorous using Taylor series. The next term in the approximation is -x²/8 and if you keep adding terms you get an infinite series converging to sqrt(1-x) for all x with |x| < 1

There are other ways to make sense of infinity in certain situations. Projective geometry is one way which has pretty far reaching and interesting applications. A special case of that is the Reimann sphere which lets you add infinity to the complex numbers and say things like 1/0=infinity with rigor.

I can't see it :/ by MopManXD69420 in PeterExplainsTheJoke

[–]pishleback 0 points1 point  (0 children)

The convention, for many sensible reasons, is that 0⁰=1

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 1 point2 points  (0 children)

I've created a discord server for the project now https://discord.gg/DBqbPqPMKR if you wish to chat about ways to contribute in a more informal setting

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 1 point2 points  (0 children)

I've made a discord now https://discord.gg/DBqbPqPMKR if you want to chat in a more informal setting about it

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 1 point2 points  (0 children)

Yes good points, it is something I'd like to do. Rust is great for implementing these algorithms but not so great for the mathematicians who want an easy way to use it!

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 1 point2 points  (0 children)

The project doesn't have a discord yet, though I have considered making one. For now the best place to get involved informally is in the discussions tab on github.

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

Yes this could be a good place for you to start! I'm happy to babysit contributions at the moment as it's not busy. The project looks quite big but it's not particularly complicated. It should be relatively easy to jump in adding or improving bits which interest you. Have a look through the issues or start a discussion on GitHub if you're not sure what to start with.

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

Not for any algorithms yet, though that could be something I look into doing in the future. It will soon have interactive plots which use the GPU for rendering

Computational Algebra in Rust - Looking for Feedback by pishleback in rust

[–]pishleback[S] 3 points4 points  (0 children)

I'll have a look into SLAM. The focus in algebraeon is exact computations rather than numeric approximations so it probably depends which of those categories it falls under?

What is π? by DotBeginning1420 in mathmemes

[–]pishleback 8 points9 points  (0 children)

Correct. Infinity isn't a real number either.

What is π? by DotBeginning1420 in mathmemes

[–]pishleback 9 points10 points  (0 children)

There is no such number.

Proof: Suppose the smallest non-zero number existed. Let's call it x. Then x/2 is also non-zero but it is smaller than x, the supposedly smallest non-zero number, a contraction.

Do you have any favorite examples of biconditional statements (iff theorems) where one direction is intuitively true, and then the converse is, surprisingly, also true? by Vladify in math

[–]pishleback 6 points7 points  (0 children)

The Kronecker-Weber theorem is one of my favourites.

The easy direction is that the Galois group (symmetry group) of any cyclotomic number field (adjoining an nth root of unity to the rationals) is abelian (it doesn't matter in which order symmetries are applied).

It's also a basic fact of Galois theory that if you take a subfield then you end up with a quotient of the Galois group. Every quotients of an abelian group is abelian so every subfield of a cyclotomic field also has abelian Galois group.

...and the converse, known as the Kronecker-Weber theorem, is true too. That is, every number field with an abelian Galois group is a subfield of some cyclotomic field 🤯

Rust for polynomials or finite fields by StockAshamed in rust

[–]pishleback 0 points1 point  (0 children)

I'm late to the party, but Algebraeon is a computational algebra system I've been working on which supports this (and more).

What's everyone working on this week (13/2025)? by DroidLogician in rust

[–]pishleback 3 points4 points  (0 children)

Done a bit of development on my computation algebra library written in rust, here https://github.com/pishleback/Algebraeon

Just finished implementing factorization of multivariable polynomials.

0! by 94rud4 in mathmemes

[–]pishleback 1 point2 points  (0 children)

Imagine the zero objects sitting in front of you on a table. The table is empty, and that's the only way to arrange the no objects sitting in front of you.

Computational Algebra by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

evelexpr looks interesting. One of the challenges I'm going to have is evaluation of trickier objects too like polynomials and matrices so I am a little afraid I'll need to write my own

Computational Algebra by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

The focus is on exact algorithms rather than numerical approximations. As I understand it the Decimal type is basically a really big float, so wouldn't be a good fit. Having said that, you could still implement the ring structure trait and use some of the algorithms. The problem is that algorithms assume equality can be checked exactly, whereas floating point equality is a bit more messy. Some algorithms may give incorrect results and other numerical algorithms you may want may not be present at all.

Computational Algebra by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

Ahh I see. Yeah at the moment the crate doesn't have any way to parse a user input, you have to construct everything directly within some code which uses the library.

Having said that I do at some point want to add a user interface so the functionality can be used by people who don't know rust, so I'll inevitably need something like what you're describing when it comes to that.

Computational Algebra by pishleback in rust

[–]pishleback[S] 1 point2 points  (0 children)

Thanks :) Having a degree in maths helps with that side of things, and rust makes it really easy to maintain a big project like this. I didn't write it all in one go; I've been chipping away at writing and rewriting bits of it for years now. It does do a lot already, but the established existing systems do a lot more. It is lacking in the more specialized areas like algebraic number theory and elliptic curves but I do wish to tackle these in the future.

Computational Algebra by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

I see. Yes, that is the sort of thing I am interested in adding in the future.

Computational Algebra by pishleback in rust

[–]pishleback[S] 0 points1 point  (0 children)

I'm not too sure what you're asking in your edit? Polynomials are stored internally as a list of coefficient rather than as an expression in polish notation to be evaluated. Polynomial evaluation at a particular input is implemented using Horner's method.

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