eq

Define symbolic equation

Syntax

A == B

eq(A,B)

Description

A == B defines a symbolic equation. Use the equation as input to functions such as solve, assume, fcontour, and subs.

eq(A,B) is equivalent to A == B.

Examples

Define and Solve Equation

Solve this trigonometric equation. Define the equation by using the == operator.

syms x
eqn = sin(x) == cos(x);
xsol = solve(eqn,x)

xsol = 
$$\frac{\pi }{4}$$

Plot Symbolic Equation

Plot the equation $$\sin (x^2)=\sin (y^2)$$ by using fimplicit. Define the equation by using the == operator.

syms x y
eqn = sin(x^2) == sin(y^2);
fimplicit(eqn)

Test Equality of Symbolic Expressions

Test the equality of two symbolic expressions by using isAlways.

syms x
eqn = x + 1 == x + 1;
tf = isAlways(eqn)

tf = logical
   1

eqn = sin(x)/cos(x) == tan(x);
tf = isAlways(eqn)

tf = logical
   1

Test Equality of Symbolic Matrices

Check the equality of two symbolic matrices by using isAlways.

A = sym(hilb(3));
B = sym([1 1/2 5; 1/2 2 1/4; 1/3 1/8 1/5]);
tf = isAlways(A == B)

tf = 3×3 logical array

   1   1   0
   1   0   1
   1   0   1

Compare a matrix and a scalar. The == operator expands the scalar into a matrix of the same dimensions as the input matrix.

A = sym(hilb(3));
B = sym(1/2);
tf = isAlways(A == B)

tf = 3×3 logical array

   0   1   0
   1   0   0
   0   0   0

Input Arguments

A — Input

number | vector | matrix | array | symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic array | symbolic function | symbolic matrix function | symbolic expression

Input, specified as a number, vector, matrix, or array, or a symbolic number, scalar variable, matrix variable, array, function, matrix function, or expression.

B — Input

number | vector | matrix | array | symbolic number | symbolic scalar variable | symbolic matrix variable | symbolic array | symbolic function | symbolic matrix function | symbolic expression

Input, specified as a number, vector, matrix, or array, or a symbolic number, scalar variable, matrix variable, array, function, matrix function, or expression.

Tips

• Calling == or eq for nonsymbolic A and B invokes the MATLAB^® eq function. This MATLAB eq function returns a logical array with elements set to logical 1 (true) where A and B are equal; otherwise, elements of the returned array are logical 0 (false).

• If both A and B are arrays, then they must have the same dimensions. A == B returns an array of equations A(i,j,...) == B(i,j,...).

Version History

Introduced in R2012a

R2026a: Symbolic functions must have matching arguments in equations

When you define a symbolic equation involving symbolic functions using the eq (==) operator, the symbolic functions on both sides of the equation must have the same function arguments. For example, this code now returns an error because the left side of the symbolic equation is a symbolic function with t as its argument, while the right side contains a symbolic function with a and t as its arguments.

syms x(t) k(a,t)
eq = diff(x,t) == -k*t

Error using symfun/privResolveArgs (line 247)
Symbolic function input arguments must match.

Error in sym/privComparison (line 889)
            args = privResolveArgs(A, B);
                   ^^^^^^^^^^^^^^^^^^^^^
Error in  ==  (line 350)
            X = privComparison(A, B, '_equal', 'FALSE', 'FALSE');
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In previous releases, the same code returned the equation 0 == 1, which is always invalid and represents a contradiction.

syms x(t) k(a,t)
eq = diff(x,t) == -k*t

eq =
 
0 == 1

R2022a: Define equation of symbolic matrix functions

The eq function accepts input arguments of type symfunmatrix.

R2021a: Define equation of symbolic matrix variables

The eq function accepts input arguments of type symmatrix.