Basic Learning of MATLAB -------- polynomials and their operations

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% Polynomial and Its Operation % use the poly2sym () function to construct the polynomial % instance to construct the polynomial: 2 * x ^ 6 + 3 * x ^ 5 + 4 * x ^ 4 + 8 * x + 1A = [2 3 4 0 0 8 1]; poly2sym () % result ans = 2 * x ^ 6 + 3 * x ^ 5 + 4 * x ^ 4 + 8 * x + 1% polynomial root (that is, the polynomial expression = x corresponding to 0 value) % instance A = [2 3 4 0 0 8 1]; poly2sym (a) % constructor x = roots () % obtain the root of the polynomial % result ans = 2 * x ^ 6 + 3 * x ^ 5 + 4 * x ^ 4 + 8 * x + 1X =-0.7708 + 1.4984i-0.7708- 1.4984i-1.2805 0.7237 + 0.7586i 0.7237-0.7586i-0.1251%, x) % result ans = 1.0e-013 *-0.0111-0.0833i-0.0111 + 0.0833i 0.3453 0.0022 + 0.20.1i 0.0022-0.20.1i 0.0111% as shown in the result, the root obtained is an approximate value instead of an exact value % polynomial derivation polyder (h) % instance A = [2 3 4 0 0 8 1]; poly2sym () % construct polynomial x = polyder (a) % evaluate the polynomial poly2sym (x) % Show the polynomial % result after the derivation: ans = 2 * x ^ 6 + 3 * x ^ 5 + 4 * x ^ 4 + 8 * x + 1X = 12 15 16 0 0 8ans = 12 * x ^ 5 + 15 * x ^ 4 + 16 * x ^ 3 + 8% polynomial valuation polyval (p, x) % Where p represents the polynomial coefficient, X represents the point of the required value % if X is a matrix, polyvalm (p, x) is required) to implement % instance A = [2 3 4 0 0 8 1]; poly2sym (a) % to construct a polynomial polyval (A, [1 2 3 4]) % calculated polynomial value at x = 1 2 3 4% result ans = 2 * x ^ 6 + 3 * x ^ 5 + 4 * x ^ 4 + 8 * x + 1ans = 18 305 2536 12321% when X is a matrix, solve a = [1 0 1]; % x ^ 2 + 1B = [1 2 3; 4 5 6; 7 8 9] polyvalm (a, B) % is actually equivalent to directly replacing the two-dimensional matrix of B with the variable X, returns the Matrix Polynomial % result of B ^ 2 + e x = 1 2 3 4 5 6 7 8 9ans = 31 36 42 66 82 96 102 126 151% rational polynomial residue () the function is used to calculate the representation of rational polynomials % rational polynomials. The molecular denominator polynomials are used to represent % [R, P, K] = residue (B, A), where B represents the coefficients of the molecular polynomials, a Represents the coefficient of the denominator polynomial % instance B = [3 5 3 8]; poly2sym (B) % molecular polynomial A = [4 6 0-5]; poly2sym () % denominator polynomial [R, P, K] = residue (B,) % calculated rational polynomial % result R =-0.3939 + 0.7790i-0.3939-0.7790i 0.9127 P =-1.1230 + 0.6438i-1.1230-0.6438i 0.7460 K = 0.7500% result description B (s) R (1) R (2) R (n) ---- = -------- + .... + -------- + K (s) a (s) S-P (1) S-p (2) S-P (n)

Basic Learning of MATLAB -------- polynomials and their operations