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CCGPS Advanced Algebra

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... Suppose the y j satisfy a polynomial equation P(y j ) =  with coefficients in k. , assume ys occurs. The strategy will be to replace the y j , j < s, by elements z j so that k[z , . . . , zs− , ys ] = k[y , . . . , ys ] and so that when written in terms of the new variables the polynomial P ...
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A Linear Equation System of Two Variables

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System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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