displayFormula

Display symbolic formula from string

Syntax

displayFormula(symstr)

displayFormula(symstr,old,new)

Description

displayFormula(symstr) displays the symbolic formula from the string symstr without evaluating the operations. All workspace variables that are specified in symstr are replaced by their values.

displayFormula(symstr,old,new) replaces only the expression or variable old with new. Expressions or variables other than old are not replaced by their values.

Examples

Multiplication Formula of Matrix and Scalar

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")

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

Multiplication Formula of Matrix and Vector

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")

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

Display Differential Equation

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)

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

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

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

Display and Evaluate Symbolic Expression

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

Display and Solve Quadratic Equation

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

Input Arguments

symstr — String representing symbolic formula

character vector | string scalar | cell array of character vectors | string array

String representing a symbolic formula, specified as a character vector, string scalar, cell array of character vectors, or string array.

You can also combine a string that represents a symbolic formula with regular text (enclosed in single quotation marks) as a string array. For an example, see Display Differential Equation.

old — Expression or variable to be replaced

character vector | string scalar | cell array of character vectors | string array | symbolic variable | symbolic function | symbolic expression | symbolic array

Expression or variable to be replaced, specified as a character vector, string scalar, cell array of character vectors, string array, symbolic variable, function, expression, or array.

new — New value

number | character vector | string scalar | cell array of character vectors | string array | symbolic number | symbolic variable | symbolic expression | symbolic array

New value, specified as a number, character vector, string scalar, cell array of character vectors, string array, symbolic number, variable, expression, or array.

Version History

Introduced in R2019b