How to use coeffs to a minimum power

Hello,

Stemming from a recent post here I wanted to ask a question about using coeffs. As the title says, is it possible to set coeffs to find all coefficients of an equation up to a power of the variable (or a minimum power if a larger power exists) for instance:

syms x
y = x + 3;
[c p] = coeffs(y,x,'all')

c = 

p = 

However in my application I need to collect all terms of x^2 from a series of equations, so for the above I would want something like:

c = (0, 1, 3)

p = (x^2, x, 1)

to make it easy. Is it possible to force coeffs to go upto a minimum power of x without altering the equation itself?

Answer 1

[Star Strider]

One approach —

syms x 
eqn(1,:) = 5*x^2 + 2*x + 8;
eqn(2,:) = 42*x^3 + 3*x^2 + 3;

eqn

eqn = 

for k = 1:numel(eqn)
    [cfs,px] = coeffs(eqn(k),'All');
    xsq = find(ismember(px, x^2));                          % Index Oof 'x^2' Terms
    xsqcf{k} = cfs(xsq);                                    % Coefficient Of 'x^2' Term
end

xsqcf{1}

ans = 

5

xsqcf{2}

ans = 

3

I have not tested this for robustness to other conditions. It works here.

.

[Connor LeClaire]

Will this return 0 if there is no x^2 term in one of the equations?

[Star Strider]

Yes!

syms x 
eqn(1,:) = 5*x^2 + 2*x + 8;
eqn(2,:) = 42*x^3 + 3*x^2 + 3;
eqn(3,:) = x^3 + 42*x - pi;

eqn

eqn = 

for k = 1:numel(eqn)
    [cfs,px] = coeffs(eqn(k),'All');
    xsq = find(ismember(px, x^2));                          % Index Oof 'x^2' Terms
    xsqcf{k} = cfs(xsq);                                    % Coefficient Of 'x^2' Term
end

xsqcf{1}

ans = 

5

xsqcf{2}

ans = 

3

xsqcf{3}

ans = 

0

If the desired result is to have it return something else, that can be substitured for the 0 —

subzero = @(x) (double(x) == 0) .* sym(pi)^sym(pi);
Result = subzero([xsqcf{3}])

Result = 

.

[Connor LeClaire]

Sorry I meant if the order of the equation is less than the desired term (equation order = 1, desired term = x^2) will it return 0?

Example: get x^2 coefficient for the equation: y = x+3

sorry I should've been more clear, as if the order of the equation is >= desired term order, coeffs includes 0 as the coefficient of the intermediate term if flagged with all, however it does not extend to any higher order.

[Star Strider]

Do the experiment —

syms x 
eqn(1,:) = 5*x^2 + 2*x + 8;
eqn(2,:) = 42*x^3 + 3*x^2 + 3;
eqn(3,:) = 42*x - pi;

eqn

eqn = 

for k = 1:numel(eqn)
    [cfs,px] = coeffs(eqn(k),'All');
    xsq = find(ismember(px, x^2));                          % Index Oof 'x^2' Terms
    xsqcf{k} = cfs(xsq);                                    % Coefficient Of 'x^2' Term
end

xsqcf{1}

ans = 

5

xsqcf{2}

ans = 

3

xsqcf{3}

 
ans =
 
Empty sym: 1-by-0
 

So in that instance, it returns an empty array element. A zero value can be substituted if desired —

for l = 1:numel(xsqcf)
    if isempty(xsqcf{k})
        xsqcf{k} = 0;
    end
end

Result = [xsqcf{:}]

Result = 

Loops sre efficient, so there is no specific reason to use cellfun here.

.

[Connor LeClaire]

Awesome thanks!!!!

[Star Strider]

As always, my pleasure!

.