- #1
johnson123
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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.
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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 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)=a^{2}b, the algebraic degree of a is 2 and the algebraic degree of b is 1.
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.