Algebraic Degree of a & b: F(a,b)=mn

  • Thread starter johnson123
  • Start date
  • Tags
    Degree
In summary, the algebraic degree of a and b in the function F(a,b)=mn is 1. This means that both variables, a and b, are raised to the first power in the function. To find the algebraic degree of a and b in a function, you can look at the highest exponent of each variable. In this case, since both a and b have an exponent of 1, the algebraic degree is 1. The algebraic degree of a and b tells us the number of times each variable appears in the function. In this case, since the algebraic degree is 1, it means that both a and b appear once in the function. Yes, the algebraic degree of a and b
  • #1
johnson123
17
0

Homework Statement



If a and b are algebraic over F of degree m and n, both relatively prime, then

F(a,b)=mn, (i.e. [F(a,b):F]=mn)

any comments are helpfull.
 
Last edited:
Physics news on Phys.org
  • #2
Your post is very incomplete. Are a and b algebraic over a field F? And by "F(a,b)=mn" do you mean "[F(a,b):F]=mn"?

In which case, that m and n are relatively prime is important. Are you trying to say that [F(a,b):F]=[F(a):F][F(b):F]? This is false in general (why?).
 
Last edited:

Related to Algebraic Degree of a & b: F(a,b)=mn

What is the algebraic degree of a and b in the function F(a,b)=mn?

The algebraic degree of a and b in the function F(a,b)=mn is 1. This means that both variables, a and b, are raised to the first power in the function.

How do you find the algebraic degree of a and b in a given function?

To find the algebraic degree of a and b in a function, you can look at the highest exponent of each variable. In this case, since both a and b have an exponent of 1, the algebraic degree is 1.

What does the algebraic degree of a and b tell us about the function F(a,b)=mn?

The algebraic degree of a and b tells us the number of times each variable appears in the function. In this case, since the algebraic degree is 1, it means that both a and b appear once in the function.

Can the algebraic degree of a and b be different in different functions?

Yes, the algebraic degree of a and b can be different in different functions. It depends on the exponents of each variable in the function. For example, in the function F(a,b)=a2b, the algebraic degree of a is 2 and the algebraic degree of b is 1.

Why is the algebraic degree of a and b important in mathematics?

The algebraic degree of a and b is important in mathematics because it helps us understand the complexity and behavior of a function. It also allows us to determine the number of solutions to a given equation and make predictions about the function's graph and behavior.

Similar threads

  • Calculus and Beyond Homework Help
Replies
19
Views
391
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
349
  • Calculus and Beyond Homework Help
Replies
11
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
695
  • Precalculus Mathematics Homework Help
Replies
5
Views
446
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
552
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
Back
Top