How to count number of terms in a symbolic expression?

I have a long symbolic expression composed of many terms. How is it possible to count the total number of terms of my expression and then choose the ith term?

syms x y
z=x*y+cos(x*y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2;

for example here the z is composed of 7 terms and the 3rd term is x*sin(x).

Answer 1

[Walter Roberson]

syms x y
z=x*y+cos(x*y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2;
terms = children(z)

terms = 1×7 cell array
    {[-x]}    {[-y]}    {[cos(x)*sin(x)]}    {[x*y]}    {[x*cos(x*y)]}    {[x*sin(x)]}    {[2]}

nterms = length(terms)

nterms = 7

terms{3}

ans = 

children(z, 3)

ans = 

[Walter Roberson]

Notice the "third" term as far as MATLAB is concerned is not x*sin(x)

MATLAB re-arranges terms according to algebraic equivalences, into its own preferred order. The rules for ordering are not published, and can be contextual.

[Walter Roberson]

Further example:

syms x
f = 6 + x - 3 - 2 - 1

as far as the symbolic toolbox is concerned this is the same as

 f = x

The toolbox always folds rational and symbolic floating point numbers

5 + 2*sqrt(sym('3.2'))

will get completely executed to scalar

5 + 2*sqrt(sym(3.2))

will execute to an expression. sym(3.2) is converted to sym(32)/sym(10) and sqrt of a rational is not fully evaluated

Answer 2

[VBBV]

syms x y
z='x*y+cos(x*y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2'

z = 'x*y+cos(x*y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2'

C = strsplit(z,{'+','-'}) 

C = 1×7 cell array
    {'x*y'}    {'cos(x*y)*x'}    {'x*sin(x)'}    {'sin(x)*cos(x)'}    {'x'}    {'y'}    {'2'}

length(C)

ans = 7

C{3} % 3rd term

ans = 'x*sin(x)'

[Torsten]

Seems difficult to convert z as a symbolic expression to a string while keeping the order of the terms (see Walter Roberson's comment).

[VBBV]

yes, the order of precedence for the operators is what Matlab considers in the symbolic expression. @Walter Roberson is correct.

[Walter Roberson]

Consider

syms x y
z='x*y+cos(x-y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2'

z = 'x*y+cos(x-y)*x+x*sin(x)+sin(x)*cos(x)-x-y+2'

C = strsplit(z,{'+','-'}) 

C = 1×8 cell array
    {'x*y'}    {'cos(x'}    {'y)*x'}    {'x*sin(x)'}    {'sin(x)*cos(x)'}    {'x'}    {'y'}    {'2'}

length(C)

ans = 8

C{3} % 3rd term

ans = 'y)*x'

The pattern matching has to be a lot more complicated to extract expressions. Indeed, it can be proven that it cannot be done using traditional regular expressions -- not unless you are willing to impose a maximum nesting depth (and use terribly messy expressions.) Some programming languages such as perl add regexp constructs that extend the pattern capabilities to make it possible; if MATLAB has those facilities I am overlooking them.

[VBBV]

@Walter Roberson +1