Mathematics
Mathematics, 20.07.2019 01:30, shyshy6184

In this problem, you will show that every polynomial parametric curve in the plane r2 satisfies a polynomial cartesian equation. let x = p(t) and y = q(t) where p, q ∈ p(r) are fixed polynomials. note that each expression x iy j is a polynomial p(t) i q(t) j in the variable t. (a) find a function l: z≥0 × z≥0 → z≥0 (i. e. a function that takes in a pair of nonnegative integers (m, n) and returns a nonnegative integer l(m, n)) so that if 0 ≤ i ≤ m and 0 ≤ j ≤ n, then x iy j = p(t) i q(t) j ∈ pl(m, n) (r). of course your choice of l will need to depend on p and q somehow, but that is fine because they are fixed throughout this problem. (b) choose m and n judiciously so th

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In this problem, you will show that every polynomial parametric curve in the plane r2 satisfies a po...

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