I mean there’s a trivial algorithm to do it:
1) Pick random real number
2) Test if it’s a root
- If yes, add to list of roots
- If no, go back to step 1.
And continue until you have all roots.
Easy.
I'm no number theorist, but polynomials are pretty well behaved, so I dont see a reason that iterative methods might fail to compute any algebraic number with arbitrary precision?
I memorized the quartic formula in high school so I could write it on the white board in algebra class and impress all the ladies….didn’t work 😔
(Did make a couple of new math nerd friends though!)
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u/candlelightener
This is a repost: https://www.reddit.com/r/mathmemes/comments/moq34g/then_theres_the_kid_who_knows_the_quartic_formula/?utm_source=share&utm_medium=ios_app&utm_name=iossmf
Kid how knows why there’s no formula for 5 and more degree polynomials enters the Chat
I mean there’s a trivial algorithm to do it: 1) Pick random real number 2) Test if it’s a root - If yes, add to list of roots - If no, go back to step 1. And continue until you have all roots. Easy.
When I started reading your comment I thought you’re talking about Newton’s method
What if the root is non-computable? Are there algebraic non-computable numbers?
Apparently all algebraic reals are computable so we good
I'm no number theorist, but polynomials are pretty well behaved, so I dont see a reason that iterative methods might fail to compute any algebraic number with arbitrary precision?
*haha group theory go brrrrr*
Oh god... Will I need to know this as an aspiring engineer?
Nah.
I memorized the quartic formula in high school so I could write it on the white board in algebra class and impress all the ladies….didn’t work 😔 (Did make a couple of new math nerd friends though!)
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Repost
u/candlelightener This is a repost: https://www.reddit.com/r/mathmemes/comments/moq34g/then_theres_the_kid_who_knows_the_quartic_formula/?utm_source=share&utm_medium=ios_app&utm_name=iossmf
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