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

• johnson123
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
johnson123

## 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)

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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?).

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## 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.

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