finding the remainder of the division of two symbolic variables

I want to get 2*V^2 from the operation below

syms A V
rem(2*V^2+3A,A)

but it seems like rem() function does not work with symbolic variables. Is there a way to achieve this in another way?

[Torsten]

Besides the fact that "rem" does not work with symbolic variables:

If V is divisible by A, the remainder is 0. So why do you think the result should be 2*V^2 ?

[Elif Cansu Akoguz]

Yes, you are right. But my actual objective is to be able to write a complicated & long symbolic expression in terms of another expression that is meaningful in the context of a theoretical model that I am trying to solve. Say this expression is g(x,y,z,t) and f(x,y,z,t) = g(x,y,z,t)*z+(x+y)^2 holds, however f(x,y,z,t) is too complicated too deduce this equality manually. Functions like simplify() or subexpr() does not help my case either. As a last resort, I am trying to find a way to divide f to g and get z and (x+y)^2 as the mod and the remainder to construct g(x,y,z,t)*z+(x+y)^2 myself.

[Umar]

Hi @Elif Cansu Akoguz ,

To address your query regarding, “But my actual objective is to be able to write a complicated & long symbolic expression in terms of another expression that is meaningful in the context of a theoretical model that I am trying to solve. Say this expression is g(x,y,z,t) and f(x,y,z,t) = g(x,y,z,t)*z+(x+y)^2 holds, however f(x,y,z,t) is too complicated too deduce this equality manually. Functions like simplify() or subexpr() does not help my case either. As a last resort, I am trying to find a way to divide f to g and get z and (x+y)^2 as the mod and the remainder to construct g(x,y,z,t)*z+(x+y)^2 myself.” Please see response below.

Define the symbolic variables and the function:

syms x y z t g;

f = g*z + (x+y)^2; % Define f(x,y,z,t) in terms of g, z, and (x+y)^2

disp(f);

After this step, the function f will be displayed.

Expand the function:

f_expanded = expand(f);

disp(f_expanded);

The expanded form of the function will be displayed after this step.

Extract the coefficients of g in the expanded expression:

coeff_g = coeffs(f_expanded, g);

disp(coeff_g);

The coefficients of g in the expanded expression will be displayed.

Extract the quotient and remainder:

quotient = coeff_g(1)*g; % Extract the quotient

remainder = coeff_g(2); % Extract the remainder

disp(quotient);

disp(remainder);

The quotient and remainder will be displayed after this step.

Reconstruct the function:

[quotient, remainder] = quorem(f_expanded, g);

reconstructed_f = g*quotient + remainder;

disp(reconstructed_f);

The reconstructed function after applying the quotient and remainder will be displayed. Please see attached.

[Elif Cansu Akoguz]

Thanks for your answer but the problem with this approach is that it starts from an expression of f in terms of g which should normally be unknown in the beginning. Deducing that expression is the whole point of this exercise. Let me give you a more concrete example:

Assume I want to rewrite the f function below as f=z*(1+bL)^2+t;

syms bL bH A V;
f=(A^2*bL^2 + 2*A^2*bL + A^2 + 4*bH^2*bL^2 - 8*bH*bL + 4)/(8*(bH*bL - 1)^2);
coeffs(f,(1+bL)^2)

Error using mupadengine/feval2sym_NaNsingularity
Invalid indeterminate.

Error in sym/coeffs (line 59)
cSym = feval2sym_NaNsingularity(symengine, 'symobj::coeffs',p.s, args{:});

I want to be able to deduce z=A^2 from this but coeffs function does not take arguements like (1+bL)^2 as input.

[Umar]

Hi @ Elif Cansu Akoguz,

If you manually expand the expression and then extract the coefficients, you can deduce the value of z as A^2 in the rewritten function. Let me illustrate it with example,

syms bL bH A V z t;
f = (A^2*bL^2 + 2*A^2*bL + A^2 + 4*bH^2*bL^2 - 8*bH*bL + 4)/(8*(bH*bL - 1)^2);
% Expand the expression
expanded_f = expand(f);
% Extract the coefficients
coeff_z = coeffs(expanded_f, A^2);
z = coeff_z(1); % Assuming z is the coefficient of A^2
% Verify the result
rewritten_f = z*(1+bL)^2 + t;

This approach will bypass the limitation of the coeffs function with complex arguments. Hope this helps.

Answer 1

[Aditya]

Hi @Elif Cansu Akoguz,

you can use "quorem" function to get the Quotient and remainder for a particular expression:

here is an example on how to do it:

[q, r] = quorem(expr, A, A);

To read more about this function refer to this link:

• https://in.mathworks.com/help/symbolic/sym.quorem.html