Naive question, but gotta ask: can Gröbner basis get over the "in general, a polynomial of degree >=5 can't be solved algebraically" hump?
Given that the above is a theorem (from Galois IIRC) I'd assume the answer is no.
And given that any system of polynomial equations in multiple variables - even of low degree - eventually subsume to a univariate polynomial of very high degree , then ... what are Gröbner actually useful for?
Given that the above is a theorem (from Galois IIRC) I'd assume the answer is no.
And given that any system of polynomial equations in multiple variables - even of low degree - eventually subsume to a univariate polynomial of very high degree , then ... what are Gröbner actually useful for?