Replacing variables with dummy variables

Hello everyone,

I have obtained a really long equation in Matlab containing a lot of variables. Is there a function in Matlab that can find N suitable dummy variables in which it can compress the found combinations of the actual variables?

Forex:

y(x) = A*log(x)+A*B*sin(x)+C*e^x

Where:

A = 2*a+b+5*c+2*d

B = c+d/a

C = a^2+c^4/b+b/2

(the actual equation is much longer)

Thanks in advance!

[Adam]

What is wrong with doing it in exactly the way you show? Creating your own variables that roll together a number of other variables into a simpler equation.

[Roy Cornelissen]

Since the obtained answer is: (D*((4*c1^2*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/b^3 + (12*c2^2*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/b^3 + (144*c3^2*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/(5*b^3) + (12*c1*c2*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/b^3 + (16*c1*c3*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/b^3 + (36*c2*c3*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/b^3 + (pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(3*a*b) + (b*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(18*a^3) + (2*c1*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(3*a*b) + (2*c2*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(3*a*b) + (2*c3*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(3*a*b) + (b*c1*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(12*a^3) + (b*c2*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(15*a^3) + (b*c3*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(18*a^3) + (4*c1^2*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(9*a*b) + (3*c2^2*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(5*a*b) + (16*c3^2*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(21*a*b) + (b*c1^2*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(30*a^3) + (b*c2^2*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(42*a^3) + (b*c3^2*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(54*a^3) + (c1*c2*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(a*b) + (16*c1*c3*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(15*a*b) + (4*c2*c3*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2))/(3*a*b) + (b*c1*c2*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(18*a^3) + (b*c1*c3*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(21*a^3) + (b*c2*c3*pi^3*(32*t + 3*pi - 6*pi*t + 51*pi*t^2 - 32*t^2))/(24*a^3)))/2 + (k_rx*((a*(4*t^2 - 2*t + 1))/2 - (16*a*t*(t - 1))/(3*pi)))/(2*b^2) + (b*k_ry*pi^2*(t - 1)^2*(252*c1^2 + 420*c1*c2 + 360*c1*c3 + 630*c1 + 180*c2^2 + 315*c2*c3 + 504*c2 + 140*c3^2 + 420*c3 + 420))/(1260*a^2) + (a*k_rx*(2*c1 + 3*c2 + 4*c3 + 1)^2*(32*t + 3*pi - 6*pi*t + 12*pi*t^2 - 32*t^2))/(12*b^2*pi) - (b*q_xx*pi*(32*t + 3*pi - 6*pi*t + 15*pi*t^2 - 32*t^2)*(252*c1^2 + 420*c1*c2 + 360*c1*c3 + 630*c1 + 180*c2^2 + 315*c2*c3 + 504*c2 + 140*c3^2 + 420*c3 + 420))/(15120*a)

It is not really clear how to compress the variables and coefficients.

Answer 1

[Star Strider]

The only one that I can think of is the Symbolic Math Toolbox coeffs (link) function. Others, such as simplify (link), and related functions linked to on that page, could also be useful.

[Roy Cornelissen]

I tried but Matlab return the following:

Error using symengine The indeterminate is invalid.

[Star Strider]

Please post the code you used, including the syms declaration.

You would likely have to use the expand function first, to get rid of the fractions, and if the result was a fraction, then use numden, and then simplify and coeffs on both the numerator and denominator.