MATLAB: How to simplify this complex equation using matlab

large equationsimplify

I am begineer user of Matlab. My friend recommend me to use matlab to solve large calculation. So, I start using it. Can someone give me advice how to solve this problem as shown below. Thank you very much. I'm looking forward to see your advice.

9*a^6*l – ((a^2*l*(b – 1)*(720*b^4*e^2 – 1440*b^3*e^2 + 720*b^2*e^2))/5 – (a^2*l*r*(b – 1)*(120*a^2*b^2*e – 120*a^2*b*e + 1440*b^4*e^2 + 120*b^4*e – 2880*b^3*e^2 – 360*b^3*e + 1440*b^2*e^2 + 240*b^2*e))/5)/r^2 – (9*a^7*l)/5 – a*l*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2)^2 + 6*a^3*l*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2) + b*l*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2)^2 – a^3*l^3*((12*a^2)/l^2 + (2*a*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2))/l^2) + b^3*l^3*((12*a^2)/l^2 + (2*a*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2))/l^2) – 9*a^2*b^4*l + (9*a^2*b^5*l)/5 + a*l*(a*(a – 1)*(a – 2) + 12*a*e*(1/r – 1)*(b – 1)^2)^2 + (9*a^5*l*(a – 1)^2)/5 + 2*a^3*l*(a*(a – 1)*(a – 2) + 12*a*e*(1/r – 1)*(b – 1)^2)*(a – 1) – 6*a*b^2*l*(3*a + a*(a^2 – 1) – 12*a*e*(1/r – 1)*(b – 1)^2) – (a^2*l*(b – 1)*(5*a^4 + 120*a^2*b^2*e + 10*a^2*b^2 – 120*a^2*b*e – 20*a^2*b + 720*b^4*e^2 + 120*b^4*e + 9*b^4 – 1440*b^3*e^2 – 360*b^3*e – 36*b^3 + 720*b^2*e^2 + 240*b^2*e + 44*b^2 – 16*b + 4))/5

Best Answer

syms a b e l r 
Eq = 9*a^6*l - ((a^2*l*(b - 1)*(720*b^4*e^2 - 1440*b^3*e^2 + 720*b^2*e^2))/5 - (a^2*l*r*(b - 1)*(120*a^2*b^2*e - 120*a^2*b*e + 1440*b^4*e^2 + 120*b^4*e - 2880*b^3*e^2 - 360*b^3*e + 1440*b^2*e^2 + 240*b^2*e))/5)/r^2 - (9*a^7*l)/5 - a*l*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2)^2 + 6*a^3*l*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2) + b*l*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2)^2 - a^3*l^3*((12*a^2)/l^2 + (2*a*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2))/l^2) + b^3*l^3*((12*a^2)/l^2 + (2*a*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2))/l^2) - 9*a^2*b^4*l + (9*a^2*b^5*l)/5 + a*l*(a*(a - 1)*(a - 2) + 12*a*e*(1/r - 1)*(b - 1)^2)^2 + (9*a^5*l*(a - 1)^2)/5 + 2*a^3*l*(a*(a - 1)*(a - 2) + 12*a*e*(1/r - 1)*(b - 1)^2)*(a - 1) - 6*a*b^2*l*(3*a + a*(a^2 - 1) - 12*a*e*(1/r - 1)*(b - 1)^2) - (a^2*l*(b - 1)*(5*a^4 + 120*a^2*b^2*e + 10*a^2*b^2 - 120*a^2*b*e - 20*a^2*b + 720*b^4*e^2 + 120*b^4*e + 9*b^4 - 1440*b^3*e^2 - 360*b^3*e - 36*b^3 + 720*b^2*e^2 + 240*b^2*e + 44*b^2 - 16*b + 4))/5
Eqs = simplify(Eq, 'Steps', 250)

Eqs =
(24*a^2*e*l*(b - 1)^2*(4*a - 2*b - 12*b*e + 12*b^2*e - 7*a^2 + 4*a^3 + b^2))/r - (4*a^2*l*(2*a^4 + 120*a^3*b^2*e - 240*a^3*b*e + 120*a^3*e - 6*a^3 - 210*a^2*b^2*e + 420*a^2*b*e - 210*a^2*e + 5*a^2 + 120*a*b^2*e - 240*a*b*e + 120*a*e + 180*b^4*e^2 + 30*b^4*e - 540*b^3*e^2 - 120*b^3*e + 540*b^2*e^2 + 150*b^2*e - 180*b*e^2 - 60*b*e - 1))/5 - (144*a^2*b*e^2*l*(b - 1)^3)/r^2

Related Solutions

MATLAB: I need a final equation… second….

I'm not sure what is meant by "a to ha function are 'Random variable', so I will just phrase the answer as if they are arbitrary constants.

The first key to this is to tell solve() that x and z are to be solved for by adding parameters 'x','z' to the end of the calling sequence.

The solution from solve() might be expressed in terms of some RootOf() of a quadratic equations. I do not recall at the moment how to ask MuPad to expand those equations; in Maple the call to use is allvalues().

Then simplify() -- or in the case of Maple, simplify(%,size), which asks it do look for factorizations and so on.

The output is as follows, again two solutions.

{

x = (1/4263200)*(((1460*h-1460*f)*a+1460*b*(f-g))*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)-4543718560000*(-(1/2131600)*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^3+((1/2131600)*e*a^2-(1/2131600)*b*(d+e)*a+(1/2131600)*b^2*d-(1/4543718560000)*(g-h)*((-e+d)*f+e*g-d*h))*c^2+(a^3*b+(-2*b^2-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f-(1/2131600)*g*h+(1/2131600)*e^2)*a^2+(b^2+(1/1065800)*f^2+(-(1/1065800)*g-(1/1065800)*h)*f+(1/532900)*g*h-(1/2131600)*h^2-(1/2131600)*d^2-(1/2131600)*e^2-(1/2131600)*g^2)*b*a+(-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f+(1/2131600)*d^2-(1/2131600)*g*h)*b^2-(1/4543718560000)*(g-h)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g))*c-a^3*b*e+((d+e)*b^2-(1/2131600)*d*f^2+((1/1065800)*d*h-(1/2131600)*e*(g-h))*f-(1/2131600)*d*h^2-(1/2131600)*(e^2-h*(g-h))*e)*a^2-(b^2*d+(-(1/2131600)*d-(1/2131600)*e)*f^2+((1/1065800)*d*h+(1/1065800)*e*g)*f-(1/2131600)*d^2*e+(-(1/2131600)*h^2-(1/2131600)*e^2)*d-(1/2131600)*e*g^2)*b*a+(-(1/2131600)*e*f^2+(((1/2131600)*g-(1/2131600)*h)*d+(1/1065800)*e*g)*f-(1/2131600)*d^3-(1/2131600)*g*(g-h)*d-(1/2131600)*e*g^2)*b^2+(1/4543718560000)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g)*((-e+d)*f+e*g-d*h))*((a-b)*c-a*e+d*b))/(((a-b)*c-a*e+d*b)*(((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(-2*e*a^2+2*b*(d+e)*a-2*b^2*d+(1/1065800)*(g-h)*((-e+d)*f+e*g-d*h))*c+(h^2+e^2+f^2-2*f*h)*a^2-2*b*(f^2+(-g-h)*f+d*e+g*h)*a+(f^2+d^2-2*f*g+g^2)*b^2-(1/2131600)*((-e+d)*f+e*g-d*h)^2))

z = (1460*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)+((g-h)*d+(h-g)*e)*c^3+((2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f+(-g+2*h)*d^2+(-g-h)*e*d+(2*g-h)*e^2-g^3+h*g^2+(-2131600*a*b+2131600*a^2+h^2)*g-h^3+(2131600*b^2-2131600*a*b)*h)*c^2+(((g-h)*d+(h-g)*e)*f^2+(d^3-d^2*e+(4263200*a*b-e^2-2131600*a^2-2131600*b^2+g^2-h^2)*d+e^3+(4263200*a*b-2131600*a^2+h^2-g^2-2131600*b^2)*e)*f-h*d^3+(2*g-h)*e*d^2+((-g+2*h)*e^2-h*g^2+(-h^2-2131600*b^2)*g+2*h^3+(-4263200*b^2+4263200*a*b+2131600*a^2)*h)*d-e^3*g+(2*g^3-h*g^2+(4263200*a*b+2131600*b^2-h^2-4263200*a^2)*g-2131600*h*a^2)*e)*c+(2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f^3+(d^2*h+(-g-h)*e*d+e^2*g+(2131600*a*b-2131600*b^2)*g+(2131600*a*b-2131600*a^2)*h)*f^2+(-e*d^3+(2*e^2+2131600*a*b+h^2)*d^2+(-e^3+(-8526400*a*b+2131600*b^2-g^2-h^2+2131600*a^2)*e)*d+(g^2+2131600*a*b)*e^2+(2131600*a*b-2131600*b^2)*g^2+(2131600*a*b-2131600*a^2)*h^2+9087437120000*b^2*a^2-4543718560000*b^3*a-4543718560000*a^3*b)*f+e*h*d^3+((-g-h)*e^2+2131600*b^2*g-h^3+(2131600*b^2-2131600*a*b)*h)*d^2+(e^3*g+(h*g^2+(h^2-2131600*b^2)*g-2131600*h*a^2)*e)*d+(-g^3+(-2131600*a*b+2131600*a^2)*g+2131600*h*a^2)*e^2+2131600*b^2*g^3-2131600*b*g^2*a*h+(-2131600*b*a*h^2+4543718560000*b^3*a-4543718560000*b^2*a^2)*g+2131600*a^2*h^3+(4543718560000*a^3*b-4543718560000*b^2*a^2)*h)/(4263200*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(4*(g-h)*(-e+d)*f+(-4*g*h+4*h^2+8526400*b*(a-b))*d-8526400*e*(-(1/2131600)*g^2+(1/2131600)*g*h+a*(a-b)))*c+4263200*((1/1460)*d+a-b-(1/1460)*e)*(-(1/1460)*d+a-b+(1/1460)*e)*f^2+(4*d^2*h-4*(g+h)*e*d+4*e^2*g-8526400*(a-b)*(a*h-g*b))*f+(4263200*b^2-2*h^2)*d^2+(-8526400*a*b+4*g*h)*e*d+(4263200*a^2-2*g^2)*e^2+4263200*(a*h-g*b)^2)

}

and

{

x = (1/4263200)*(((-1460*h+1460*f)*a-1460*b*(f-g))*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)-4543718560000*(-(1/2131600)*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^3+((1/2131600)*e*a^2-(1/2131600)*b*(d+e)*a+(1/2131600)*b^2*d-(1/4543718560000)*(g-h)*((-e+d)*f+e*g-d*h))*c^2+(a^3*b+(-2*b^2-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f-(1/2131600)*g*h+(1/2131600)*e^2)*a^2+(b^2+(1/1065800)*f^2+(-(1/1065800)*g-(1/1065800)*h)*f+(1/532900)*g*h-(1/2131600)*h^2-(1/2131600)*d^2-(1/2131600)*e^2-(1/2131600)*g^2)*b*a+(-(1/2131600)*f^2+((1/2131600)*g+(1/2131600)*h)*f+(1/2131600)*d^2-(1/2131600)*g*h)*b^2-(1/4543718560000)*(g-h)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g))*c-a^3*b*e+((d+e)*b^2-(1/2131600)*d*f^2+((1/1065800)*d*h-(1/2131600)*e*(g-h))*f-(1/2131600)*d*h^2-(1/2131600)*(e^2-h*(g-h))*e)*a^2-(b^2*d+(-(1/2131600)*d-(1/2131600)*e)*f^2+((1/1065800)*d*h+(1/1065800)*e*g)*f-(1/2131600)*d^2*e+(-(1/2131600)*h^2-(1/2131600)*e^2)*d-(1/2131600)*e*g^2)*b*a+(-(1/2131600)*e*f^2+(((1/2131600)*g-(1/2131600)*h)*d+(1/1065800)*e*g)*f-(1/2131600)*d^3-(1/2131600)*g*(g-h)*d-(1/2131600)*e*g^2)*b^2+(1/4543718560000)*((h-g)*f^2+(g^2-h^2+d^2-e^2)*f-d^2*h+(e^2-h*(g-h))*g)*((-e+d)*f+e*g-d*h))*((a-b)*c-a*e+d*b))/(((a-b)*c-a*e+d*b)*(((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(-2*e*a^2+2*b*(d+e)*a-2*b^2*d+(1/1065800)*(g-h)*((-e+d)*f+e*g-d*h))*c+(h^2+e^2+f^2-2*f*h)*a^2-2*b*(f^2+(-g-h)*f+d*e+g*h)*a+(f^2+d^2-2*f*g+g^2)*b^2-(1/2131600)*((-e+d)*f+e*g-d*h)^2))

z = (-1460*(-9685390482496000000*(b^2-(1/2131600)*c^2+(1/1065800)*e*c-(1/2131600)*e^2-(1/2131600)*(f-h)^2)*(a^2-2*a*b+b^2-(1/2131600)*d^2+(1/1065800)*d*e-(1/2131600)*e^2-(1/2131600)*(g-h)^2)*((c-e)*a-(-d+c)*b)^2*(a^2-(1/2131600)*c^2+(1/1065800)*c*d-(1/2131600)*d^2-(1/2131600)*(f-g)^2))^(1/2)+((g-h)*d+(h-g)*e)*c^3+((2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f+(-g+2*h)*d^2+(-g-h)*e*d+(2*g-h)*e^2-g^3+h*g^2+(-2131600*a*b+2131600*a^2+h^2)*g-h^3+(2131600*b^2-2131600*a*b)*h)*c^2+(((g-h)*d+(h-g)*e)*f^2+(d^3-d^2*e+(4263200*a*b-e^2-2131600*a^2-2131600*b^2+g^2-h^2)*d+e^3+(4263200*a*b-2131600*a^2+h^2-g^2-2131600*b^2)*e)*f-h*d^3+(2*g-h)*e*d^2+((-g+2*h)*e^2-h*g^2+(-h^2-2131600*b^2)*g+2*h^3+(-4263200*b^2+4263200*a*b+2131600*a^2)*h)*d-e^3*g+(2*g^3-h*g^2+(4263200*a*b+2131600*b^2-h^2-4263200*a^2)*g-2131600*h*a^2)*e)*c+(2131600*b^2-4263200*a*b-e^2+2131600*a^2-d^2+2*d*e)*f^3+(d^2*h+(-g-h)*e*d+e^2*g+(2131600*a*b-2131600*b^2)*g+(2131600*a*b-2131600*a^2)*h)*f^2+(-e*d^3+(2*e^2+2131600*a*b+h^2)*d^2+(-e^3+(-8526400*a*b+2131600*b^2-g^2-h^2+2131600*a^2)*e)*d+(g^2+2131600*a*b)*e^2+(2131600*a*b-2131600*b^2)*g^2+(2131600*a*b-2131600*a^2)*h^2+9087437120000*b^2*a^2-4543718560000*b^3*a-4543718560000*a^3*b)*f+e*h*d^3+((-g-h)*e^2+2131600*b^2*g-h^3+(2131600*b^2-2131600*a*b)*h)*d^2+(e^3*g+(h*g^2+(h^2-2131600*b^2)*g-2131600*h*a^2)*e)*d+(-g^3+(-2131600*a*b+2131600*a^2)*g+2131600*h*a^2)*e^2+2131600*b^2*g^3-2131600*b*g^2*a*h+(-2131600*b*a*h^2+4543718560000*b^3*a-4543718560000*b^2*a^2)*g+2131600*a^2*h^3+(4543718560000*a^3*b-4543718560000*b^2*a^2)*h)/(4263200*((1/1460)*g+a-b-(1/1460)*h)*(-(1/1460)*g+a-b+(1/1460)*h)*c^2+(4*(g-h)*(-e+d)*f+(-4*g*h+4*h^2+8526400*b*(a-b))*d-8526400*e*(-(1/2131600)*g^2+(1/2131600)*g*h+a*(a-b)))*c+4263200*((1/1460)*d+a-b-(1/1460)*e)*(-(1/1460)*d+a-b+(1/1460)*e)*f^2+(4*d^2*h-4*(g+h)*e*d+4*e^2*g-8526400*(a-b)*(a*h-g*b))*f+(4263200*b^2-2*h^2)*d^2+(-8526400*a*b+4*g*h)*e*d+(4263200*a^2-2*g^2)*e^2+4263200*(a*h-g*b)^2)

}

Sorry, I know the formatting is not nice, but reformatting it by hand takes too much time.

MATLAB: How to use if inside loop

I think the following will solve your problem.

 Total = zeros(200,1);
 for kk = 1:200
    RY = kk;
    L_B=40;
    L_S=20;
    % Single Reflection Left Side
    if RY < 2*L_B
        R1L=1;     %  1
    elseif 2*L_B<RY && RY< 2*(L_B+L_S)
        R1L=0;     %  3
    elseif 2*(L_B+L_S) < RY && RY< 2*(2*L_B+L_S)
        R1L=1;     %  5
    elseif 2*(2*L_B+L_S) < RY && RY< 2*(2*L_B+2*L_S)
        R1L=0;     %  7
    elseif 2*(2*L_B+2*L_S) < RY && RY< 2*(3*L_B+2*L_S)
        R1L=1;     %  9
    elseif 2*(3*L_B+2*L_S) < RY && RY< 2*(3*L_B+3*L_S)
        R1L=0;     %  11
    elseif 2*(3*L_B+3*L_S) < RY && RY< 2*(4*L_B+3*L_S)
        R1L=1;     %  13
    else
        R1L=0;
    end
    % Single Reflection Right Side
    if RY < 2*L_B
        R1R=1;     %  2
    elseif 2*L_B<RY && RY< 2*(L_B+L_S)
        R1R=0;     %  4
    elseif 2*(L_B+L_S) < RY && RY< 2*(2*L_B+L_S)
        R1R=1;     %  6
    elseif 2*(2*L_B+L_S) < RY && RY< 2*(2*L_B+2*L_S)
        R1R=0;     %  8
    elseif 2*(2*L_B+2*L_S) < RY && RY< 2*(3*L_B+2*L_S)
        R1R=1;     %  10
    elseif 2*(3*L_B+2*L_S) < RY && RY< 2*(3*L_B+3*L_S)
        R1R=0;     %  12
    elseif 2*(3*L_B+3*L_S) < RY && RY< 2*(4*L_B+3*L_S)
        R1R=1;     %  14
    else
        R1R=0;
    end
    Total(kk)=R1L+R1R
 end

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Related Solutions

MATLAB: I need a final equation… second….

MATLAB: How to use if inside loop

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