children

Subexpressions or terms of symbolic expression

Starting in R2020b, the syntax subexpr = children(expr) for a scalar input expr returns subexpr as a nonnested cell array instead of a vector. You can use subexpr = children(expr,ind) to index into the returned cell array of subexpressions. For more information, see Version History.

Syntax

subexpr = children(expr)

subexpr = children(A)

subexpr = children(___,ind)

Description

subexpr = children(expr) returns a nonnested cell array containing the child subexpressions of the symbolic expression expr. For example, the child subexpressions of a sum are its terms.

subexpr = children(A) returns a nested cell array containing the child subexpressions of each expression in the symbolic matrix A.

subexpr = children(___,ind) returns the child subexpressions of a symbolic expression expr or a symbolic matrix A as a cell array indexed by ind.

Examples

Find Child Subexpressions of Symbolic Expression

Find the child subexpressions of the symbolic expression $$x^2+xy+y^2$$. The subexpressions are returned in a nonnested cell array. children uses internal sorting rules when returning the subexpressions. You can index into each element of the cell array by using subexpr{i}, where i is the cell index. The child subexpressions of a sum are its terms.

syms x y
subexpr = children(x^2 + x*y + y^2)

subexpr=1×3 cell array
    {[x*y]}    {[x^2]}    {[y^2]}

s1 = subexpr{1}

s1 = $$x\hspace{0.17em}y$$

s2 = subexpr{2}

s2 = $$x^2$$

s3 = subexpr{3}

s3 = $$y^2$$

You can also index into each element of the subexpressions by specifying the index ind in the children function.

s1 = children(x^2 + x*y + y^2,1)

s1 = $$x\hspace{0.17em}y$$

s2 = children(x^2 + x*y + y^2,2)

s2 = $$x^2$$

s3 = children(x^2 + x*y + y^2,3)

s3 = $$y^2$$

To convert the cell array of subexpressions into a vector, you can use the command [subexpr{:}].

V = [subexpr{:}]

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

Find Child Subexpressions of Equation

Find the child subexpressions of the equation $$x^2+xy=y^2+1$$. The child subexpressions of the equation are returned in a 1-by-2 cell array. Index into all elements of the cell array. The subexpressions of an equation are the left and right sides of that equation.

syms x y
subexpr = children(x^2 + x*y == y^2 + 1)

subexpr=1×2 cell array
    {[x^2 + y*x]}    {[y^2 + 1]}

subexpr{:}

ans = $$x^2+y\hspace{0.17em}x$$

ans = $$y^2+1$$

Next, find the child subexpressions of the inequality $$\sin (x)<\cos (x)$$. Index into all elements of the returned cell array. The child subexpressions of an inequality are the left and right sides of that inequality.

subexpr = children(sin(x) < cos(x))

subexpr=1×2 cell array
    {[sin(x)]}    {[cos(x)]}

subexpr{:}

ans = $$\sin \left(x\right)$$

ans = $$\cos \left(x\right)$$

Find Child Subexpressions of Integral

Find the child subexpressions of an integral $${\int }_a^{b}f(x)dx$$. The child subexpressions are returned as a cell array of symbolic expressions.

syms f(x) a b
subexpr = children(int(f(x),a,b))

subexpr=1×4 cell array
    {[f(x)]}    {[x]}    {[a]}    {[b]}

V = [subexpr{:}]

V = $$\left(\begin{array}{cccc}f\left(x\right)& x& a& b\end{array}\right)$$

Plot Taylor Approximation of Expression

Find the Taylor approximation of the $$\cos (x)$$ function near $$x=2$$.

syms x
t = taylor(cos(x),x,2)

t = 
$$\cos \left(2\right)+\frac{\sin \left(2\right)\hspace{0.17em}{\left(x-2\right)}^3}{6}-\frac{\sin \left(2\right)\hspace{0.17em}{\left(x-2\right)}^5}{120}-\sin \left(2\right)\hspace{0.17em}\left(x-2\right)-\frac{\cos \left(2\right)\hspace{0.17em}{\left(x-2\right)}^2}{2}+\frac{\cos \left(2\right)\hspace{0.17em}{\left(x-2\right)}^4}{24}$$

The Taylor expansion has six terms that are separated by $$+$$ or $$–$$ sign.

Plot the $$\cos (x)$$ function. Use children to separate out the terms of the expansion. Show that the Taylor expansion approximates the function more closely as more terms are included.

fplot(cos(x),[0 4])
hold on
s = 0;
for i = 1:6
    s = s + children(t,i);
    fplot(s,[0 4],'--')
end
legend({'cos(x)','1 term','2 terms','3 terms','4 terms','5 terms','6 terms'})

Find Child Subexpressions of Elements of Matrix

Call the children function to find the child subexpressions of the following symbolic matrix input. The result is a 2-by-2 nested cell array containing the child subexpressions of each element of the matrix.

syms x y
symM = [x + y, sin(x)*cos(y); x^3 - y^3, exp(x*y^2) + 3]

symM = 
$$\left(\begin{array}{cc}x+y& \cos \left(y\right)\hspace{0.17em}\sin \left(x\right)\\ x^3-y^3& {\mathrm{e}}^{x\hspace{0.17em}{y}^2}+3\end{array}\right)$$

s = children(symM)

s=2×2 cell array
    {1×2 cell}    {1×2 cell}
    {1×2 cell}    {1×2 cell}

To unnest or access the elements of the nested cell array s, use braces. For example, the {1,1}-element of s is a 1-by-2 cell array of symbolic expressions.

s11 = s{1,1}

s11=1×2 cell array
    {[x]}    {[y]}

Unnest each element of s using braces. Convert the nonnested cell arrays to vectors using square brackets.

s11vec = [s{1,1}{:}]

s11vec = $$\left(\begin{array}{cc}x& y\end{array}\right)$$

s21vec = [s{2,1}{:}]

s21vec = $$\left(\begin{array}{cc}{x}^3& -y^3\end{array}\right)$$

s12vec = [s{1,2}{:}]

s12vec = $$\left(\begin{array}{cc}\cos \left(y\right)& \sin \left(x\right)\end{array}\right)$$

s22vec = [s{2,2}{:}]

s22vec = $$\left(\begin{array}{cc}{\mathrm{e}}^{x\hspace{0.17em}{y}^2}& 3\end{array}\right)$$

If each element of the nested cell array s contains a nonnested cell array of the same size, then you can also use the ind input argument to access the elements of the nested cell array. The index ind allows children to access each column of subexpressions of the symbolic matrix input symM.

scol1 = children(symM,1)

scol1=2×2 cell array
    {[x  ]}    {[cos(y)    ]}
    {[x^3]}    {[exp(x*y^2)]}

[scol1{:}].'

ans = 
$$\left(\begin{array}{c}x\\ x^3\\ \cos \left(y\right)\\ {\mathrm{e}}^{x\hspace{0.17em}{y}^2}\end{array}\right)$$

scol2 = children(symM,2)

scol2=2×2 cell array
    {[y   ]}    {[sin(x)]}
    {[-y^3]}    {[3     ]}

[scol2{:}].'

ans = 
$$\left(\begin{array}{c}y\\ -y^3\\ \sin \left(x\right)\\ 3\end{array}\right)$$

Input Arguments

expr — Input expression

symbolic number | symbolic variable | symbolic function | symbolic expression

Input expression, specified as a symbolic number, variable, function, or expression.

A — Input matrix

symbolic matrix

Input matrix, specified as a symbolic matrix.

ind — Index of child subexpressions to return

positive integer

Index of child subexpressions to return, specified as a positive integer.

• If children(expr) returns a nonnested cell array of child subexpressions, then indexing with children(expr,ind) returns the ind-th element of the cell array.

• If children(A) returns a nested cell array of child subexpressions, where each cell element has the same size, then indexing with children(A,ind) returns the ind-th column of the nonnested cell array.

Version History

Introduced in R2012a

R2020b: children returns cell arrays

In versions before R2020b, the syntax subexpr = children(expr) returns a vector subexpr that contains the child subexpressions of the scalar symbolic expression expr. The syntax subexpr = children(A) returns a nonnested cell array subexpr that contains the child subexpressions of the symbolic matrix A.

Starting in R2020b, the syntax subexpr = children(expr) returns subexpr as a cell array instead of a vector, and the syntax subexpr = children(A) returns subexpr as a nested cell array instead of a nonnested cell array. You can use subexpr = children(expr,ind) to index into the returned cell arrays of subexpressions. For example, see Plot Taylor Approximation of Expression. You can also unnest and access the elements of a cell array by indexing into the cell array using curly braces. To convert subexpr from a nonnested cell array to a vector, you can use the command [subexpr{:}].