How to count number of terms in a symbolic expression?

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Mehdi 2023-12-2

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https://ww2.mathworks.cn/matlabcentral/answers/2055574-how-to-count-number-of-terms-in-a-symbolic-expression

评论： Walter Roberson 2023-12-3

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).

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Answer 1

Walter Roberson 2023-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/2055574-how-to-count-number-of-terms-in-a-symbolic-expression#answer_1364574

编辑：Walter Roberson 2023-12-3

在 MATLAB Online 中打开

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 =

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Walter Roberson 2023-12-3

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 2023-12-3

在 MATLAB Online 中打开

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

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Answer 2

VBBV 2023-12-3

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https://ww2.mathworks.cn/matlabcentral/answers/2055574-how-to-count-number-of-terms-in-a-symbolic-expression#answer_1364569

编辑：VBBV 2023-12-3

在 MATLAB Online 中打开

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)'

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Walter Roberson 2023-12-3

编辑：Walter Roberson 2023-12-3

在 MATLAB Online 中打开

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.