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);
solve(eqn,x)

ans =
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;
isAlways(eqn)

ans =
  logical
   1

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

ans =
  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]);
isAlways(A == B)

ans =
  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);
isAlways(A == B)

ans =
  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 function returns a logical array with elements set to logical 1 (true) where A and B are equal; otherwise, it returns 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

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.