lhs

Left side (LHS) of equation

Syntax

lhsEqn = lhs(eqn)

Description

lhsEqn = lhs(eqn) returns the left side of the symbolic equation eqn. The value of eqn also can be a symbolic condition, such as x > 0. If eqn is an array, then lhs returns an array of the left sides of the equations in eqn.

Conditions that use the > or >= operator are internally rewritten using the < or <= operator. Therefore, lhs returns the original right side. For example, lhs(x > 0) returns 0.

Examples

Find Left Side of Equation

Find the left side of the equation $2\mathit{y}={\mathit{x}}^2$ by using lhs.

First, declare the equation.

syms x y
eqn = 2*y == x^2

eqn = $$2\hspace{0.17em}y=x^2$$

Find the left side of eqn by using lhs.

lhsEqn = lhs(eqn)

lhsEqn = $$2\hspace{0.17em}y$$

Find Left Side of Condition

Find the left side of the condition $\mathit{x}+\mathit{y}<1$ by using lhs.

First, declare the condition.

syms x y
cond = x + y < 1

cond = $$x+y<1$$

Find the left side of cond by using lhs.

lhsCond = lhs(cond)

lhsCond = $$x+y$$

Find Left Side of Equations in Array

For an array that contains equations and conditions, lhs returns an array of the left sides of those equations or conditions. The output array is the same size as the input array.

Find the left side of the equations and conditions in the vector V.

syms x y
V = [y^2 == x^2, x ~= 0, x*y >= 1]

V = $$\left(\begin{array}{ccc}{y}^2=x^2& x\ne 0& 1\le x\hspace{0.17em}y\end{array}\right)$$

lhsV = lhs(V)

lhsV = $$\left(\begin{array}{ccc}{y}^2& x& 1\end{array}\right)$$

Because any condition using the >= operator is internally rewritten using the <= operator, the sides of the last condition in V are exchanged.

Find Left Side of Equation Involving Symbolic Matrix Variables

Find the left side of a symbolic equation that involves symbolic matrix variables.

Create the symbolic matrix variables and the symbolic equation.

syms A [2 2] matrix
syms B [2 1] matrix
syms C [1 2] matrix
eqn = B*C == A*A - 2*A + eye(2)

eqn = $$B\hspace{0.17em}C={\mathrm{I}}_2-2\hspace{0.17em}A+A^2$$

Find the left side of the equation by using lhs.

lhsEqn = lhs(eqn)

lhsEqn = $$B\hspace{0.17em}C$$

Input Arguments

eqn — Equation or condition

symbolic equation | symbolic condition | vector of symbolic equations or conditions | matrix of symbolic equations or conditions | multidimensional array of symbolic equations or conditions

Equation or condition, specified as a symbolic equation or condition, or a vector, matrix, or multidimensional array of symbolic equations or conditions.

Data Types: sym | symfun | symmatrix | symfunmatrix

Version History

Introduced in R2017a

R2025a: Get left and right sides of symbolic equation that includes piecewise expressions

You can use the lhs and rhs functions to get the left and right sides of a symbolic equation that includes piecewise expressions. For an example, see Solve System of Equations with Piecewise Expressions.

R2022b: Find left side of symbolic equation or condition involving symbolic matrix variables and matrix functions

The lhs function accepts a symbolic equation or condition involving symbolic matrix variables and matrix functions as an input argument. The input data type can be symmatrix or symfunmatrix. For an example, see Find Left Side of Equation Involving Symbolic Matrix Variables.