Abstract Algebra | Writing a polynomial gcd as a combination -- example.
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- čas přidán 5. 08. 2024
- We give an example of Bezout's identity in polynomials. This involves the extended Euclidean algorithm for polynomials.
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Thank you for this, My prof has really checked out with covid and basically just assigns questions from the textbook (which is terrible, I think he wrote it himself, without an editor) There's lots of things in the book that have unexplained examples and this helped immensely. Thank you.
I'm in awe of your presentation skills.
Thank you very much. I understand very well.
Nice explanation sir...thank you
Tidy writing is tidy thinking. Thanks!
TYSM its my exam tomorrow and i was literally struggling to get this concept into my head....
as a person currently studying ntru cryptosystem and struggling, thank you, you practically saved my life
Sir plz make vedios on complex variable integration....
Can u please explain Abel Ruffini insolvability theorem ?
QUESTIONS AND CLARITY I agree
i have one doubt... when he started evaluating for for Z11, how did he put 10mod11 equals -1. I tried looking on the internet that whether we can do that or not, im unable to anything similar. Can anyone help me out?
If you divide 10 by 11, you can do 10-11= -1 so remainder is -1.
Difference between -1 and 10 is 11. So -1 and 10 are congruent mod 11. Or 10 = -1 (mod11)
I love polynomial arithmetic for some reason. I never find it tedious, it's very relaxing to me.
9:39
Why you didn't considered 11/25 ??
the gcd of two polynomials f(x) and g(x) is the monic polynomial of highest possible degree that divides both f(x) and g(x). monic means that there should be no coefficient (i.e. there should only be a coefficient of 1) in front of the leading term, hence he ignores the 11/25. it also makes showing that the remainder is zero easier. he takes care of the 11/25 in the proceeding steps at 11:01 when multiplying 25/11 to g(x). if you included the 11/25 it should work out the same way and cancel out somewhere so that the gcd is monic.
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Next time, please tell if you make a change --> you made a change to f(x) at 2:21