displayFormula

Create a 3-by-3 matrix. Multiply the matrix by the scalar coefficient K^2.

syms K A
A = [-1, 0, 1; 1, 2, 0; 1, 1, 0];
B = K^2*A

B = 
$$\left(\begin{array}{ccc}-K^2& 0& K^2\\ K^2& 2\hspace{0.17em}{K}^2& 0\\ K^2& K^2& 0\end{array}\right)$$

The result automatically shows the multiplication being carried out element-wise.

Show the multiplication formula without evaluating the operations by using displayFormula. Input the formula as a string. The variable A in the string is replaced by its values.

displayFormula("F = K^2*A")

$$F=K^2\hspace{0.17em}\left(\begin{array}{ccc}-1& 0& 1\\ 1& 2& 0\\ 1& 1& 0\end{array}\right)$$

Create a 3-by-3 matrix and a 3-by-1 vector. Create a symbolic equation that multiplies the matrix and the vector.

syms A [3 3]
syms v B [3 1]
eqn = B == A*v

eqn = 
$$\left(\begin{array}{c}{B}_1=A_{1,1}\hspace{0.17em}{v}_1+A_{1,2}\hspace{0.17em}{v}_2+A_{1,3}\hspace{0.17em}{v}_3\\ B_2=A_{2,1}\hspace{0.17em}{v}_1+A_{2,2}\hspace{0.17em}{v}_2+A_{2,3}\hspace{0.17em}{v}_3\\ B_3=A_{3,1}\hspace{0.17em}{v}_1+A_{3,2}\hspace{0.17em}{v}_2+A_{3,3}\hspace{0.17em}{v}_3\end{array}\right)$$

The result shows the multiplication being carried out where the elements of the matrix and the vector are combined.

Show the multiplication formula without combining the elements by using displayFormula. Input the formula as a string.

displayFormula("B == A*v")

$$\left(\begin{array}{c}{B}_1\\ B_2\\ B_3\end{array}\right)=\left(\begin{array}{ccc}{A}_{1,1}& A_{1,2}& A_{1,3}\\ A_{2,1}& A_{2,2}& A_{2,3}\\ A_{3,1}& A_{3,2}& A_{3,3}\end{array}\right)\hspace{0.17em}\left(\begin{array}{c}{v}_1\\ v_2\\ v_3\end{array}\right)$$

Define a string that describes a differential equation.

S = "m*diff(y,t,t) == m*g-k*y";

Create a string array that combines the differential equation and additional text. Display the formula along with the text.

symstr = ["'The equation of motion is'"; S;"'where k is the elastic coefficient.'"];
displayFormula(symstr)

$$\mathrm{The equation of motion is}$$

$$m\hspace{0.17em}\frac{{\partial }^2}{\partial t^2}\mathrm{ }y=m\hspace{0.17em}g-k\hspace{0.17em}y$$

$$\mathrm{where k is the elastic coefficient.}$$

Create a string S representing a symbolic expression.

S = "exp(2*pi*i)";

Create another string symstr that contains S.

symstr = "1 + S + S^2 + cos(S)"

symstr = 
"1 + S + S^2 + cos(S)"

Display symstr as a formula without evaluating the operations by using displayFormula. S in symstr is replaced by its value.

displayFormula(symstr)

$$1+{\mathrm{e}}^{2\hspace{0.17em}\pi \hspace{0.17em}\mathrm{i}}+{\left({\mathrm{e}}^{2\hspace{0.17em}\pi \hspace{0.17em}\mathrm{i}}\right)}^2+\cos \left({\mathrm{e}}^{2\hspace{0.17em}\pi \hspace{0.17em}\mathrm{i}}\right)$$

To evaluate the strings S and symstr as symbolic expressions, use str2sym.

S = str2sym(S)

S = $$1$$

expr = str2sym(symstr)

expr = $$S+\cos \left(S\right)+S^2+1$$

Substitute the variable S with its value by using subs. Evaluate the result in double precision using double.

double(subs(expr))

ans = 
3.5403

Define a string that represents a quadratic formula with the coefficients a, b, and c.

syms a b c k
symstr = "a*x^2 + b*x + c";

Display the quadratic formula, replacing a with k.

displayFormula(symstr,a,k)

$$k\hspace{0.17em}{x}^2+b\hspace{0.17em}x+c$$

Display the quadratic formula again, replacing a, b, and c with 2, 3, and -1, respectively.

displayFormula(symstr,[a b c],[2 3 -1])

$$2\hspace{0.17em}{x}^2+3\hspace{0.17em}x-1$$

To solve the quadratic equation, convert the string into a symbolic expression using str2sym. Use solve to find the zeros of the quadratic equation.

f = str2sym(symstr);
sol = solve(f)

sol = 
$$\left(\begin{array}{c}-\frac{b+\sqrt{b^2-4\hspace{0.17em}a\hspace{0.17em}c}}{2\hspace{0.17em}a}\\ -\frac{b-\sqrt{b^2-4\hspace{0.17em}a\hspace{0.17em}c}}{2\hspace{0.17em}a}\end{array}\right)$$

Use subs to replace a, b, and c in the solution with 2, 3, and -1, respectively.

solValues = subs(sol,[a b c],[2 3 -1])

solValues = 
$$\left(\begin{array}{c}-\frac{\sqrt{17}}{4}-\frac{3}{4}\\ \frac{\sqrt{17}}{4}-\frac{3}{4}\end{array}\right)$$