Uso do calculo simbólico na Matlab

Use subs to Evaluate Expressions and Functions

Evaluation is one of the most common mathematical operations. Therefore, it is important to understand how and when Symbolic Math Toolbox™ performs evaluations. For example, create a symbolic variable, x, and then assign the expression x^2 to another variable, y.

syms x
y = x^2;

Now, assign a numeric value to x.

x = 2;

This second assignment does not change the value of y, which is still x^2. If later you change the value of x to some other number, variable, expression, or matrix, the toolbox remembers that the value of y is defined as x^2. When displaying results, Symbolic Math Toolbox does not automatically evaluate the value of x^2 according to the new value of x.

y

y =
 x^2

To enforce evaluation of y according to the new value of x, use the subs function.

subs(y)

ans =
  4

Formula Rearrangement and Rewriting

• numden - Extract numerator and denominator

syms s
H = (s^2 + 5*s + 6)/(s^4 + 7*s + 27)

H =
  (s^2 + 5*s + 6)/(s^4 + 7*s + 27)

[N,D] = numden(H)

N =
  s^2 + 5*s + 6
D =
  s^4 + 7*s + 27

• coeffs - Coefficients of polynomial

Coefficients of Univariate Polynomial - Find the coefficients of this univariate polynomial.

n = coeffs(N)

n =
 [ 1, 5, 6]

Atenção!!! Os termos nulos não são inseridos no vetor dos coeficientes.

[d,terms] = coeffs(D)

d =
 [ 1, 7, 27]
terms =
 [ s^4, s, 1]

• sym2poly - Extract vector of all numeric coefficients, including zeros, from symbolic polynomial

Para extrair o vetor com os termos nulos use sym2poly.

n = sym2poly(N)

n =
     1     5     6
d = sym2poly(D)

d =
    1     0     0     7    27