MATLAB: Symbolic simplification issue with exact division of polynomial by monomial

simplificationsymbolic

I am writing a code and at some point I have an exact division of a polynomial with a monomial; however, simplification does not seem to work

Ex:

((x1 + y2 – x1*y2)*(- x2^2*y1 + x2^2 + x2*y1^2 – y1^2)*(2*x1 + x2 + y1 – x1*x2 – x1*y1 – 1))/(x2 – y1) does not simplify.

However, notice that the middle factor in numerator (- x2^2*y1 + x2^2 + x2*y1^2 – y1^2) is divisible by (x2-y1) and MATLAB; indeed, simplifies (- x2^2*y1 + x2^2 + x2*y1^2 – y1^2)/(x2 -y1) and gives x2 + y1 – x2*y1.

How could I get around this issue?

Best Answer

Sometimes, you have to lead it gently by the hand if you want it to do everything:

syms x1 x2 y1 y2 
f = ((x1 + y2 - x1*y2)*(- x2^2*y1 + x2^2 + x2*y1^2 - y1^2)*(2*x1 + x2 + y1 - x1*x2 - x1*y1 - 1))/(x2 - y1);
f1 = expand(f);
f1 = simplify(collect(f1))
f1 =
(x1 + y2 - x1*y2)*(x2 + y1 - x2*y1)*(2*x1 + x2 + y1 - x1*x2 - x1*y1 - 1)

Is that the sort of result you want?

Related Solutions

MATLAB: Using fsolve over a range of equations.

Solve the equations once and then plug in the values.

for z = 100:105
  x1=velprof(z,y1);
  x2=velprof(z,y2);
  x3=velprof(z,y3);
  x4=velprof(z,y4);
  c = [ (((x3*y4-x4*y3)*x2^2+(-x3^2*y4+x4^2*y3)*x2+x3*x4*y2*(-x4+x3))*x1^3+((-x3*y4+x4*y3)*x2^3+(-x4^3*y3+x3^3*y4)*x2+y2*x3*x4^3-x3^3*x4*y2)*x1^2+((x3^2*y4-x4^2*y3)*x2^3+(x4^3*y3-x3^3*y4)*x2^2+x3^2*x4^2*y2*(-x4+x3))*x1-x3*x2*x4*y1*(-x4+x3)*(x2-x4)*(x2-x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((-y2+y1)*x4^2+(y2-y4)*x1^2-x2^2*(y1-y4))*x3^3+((-y1+y2)*x4^3+(y4-y2)*x1^3+x2^3*(y1-y4))*x3^2+((y3-y2)*x1^2+x2^2*(y1-y3))*x4^3+((y2-y3)*x1^3-x2^3*(y1-y3))*x4^2+x1^2*x2^2*(y3-y4)*(x1-x2))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y4-y3)*x2+(y2-y4)*x3-x4*(y2-y3))*x1^3+((y3-y4)*x2^3+(y4-y2)*x3^3+x4^3*(y2-y3))*x1+((-y1+y4)*x3+x4*(y1-y3))*x2^3+((y1-y4)*x3^3-x4^3*(y1-y3))*x2-x3*x4*(-x4+x3)*(x3+x4)*(-y2+y1))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)), ...
  (((y3-y4)*x2+(y4-y2)*x3+x4*(y2-y3))*x1^2+((y4-y3)*x2^2+(y2-y4)*x3^2-x4^2*(y2-y3))*x1+((y1-y4)*x3-x4*(y1-y3))*x2^2+((-y1+y4)*x3^2+x4^2*(y1-y3))*x2+x3*x4*(-y2+y1)*(-x4+x3))/((-x4+x3)*(x2-x4)*(x2-x3)*(x1-x4)*(x1-x3)*(x1-x2)) ];
  disp(z)
  disp(c)
end

MATLAB: How to sum the elements of a symbolic vector

syms x1 x2
X = [1, x1, x2, x1^2, x2^2, x1*x2], 
out=char(X(1))
for k=2:numel(X)
  out=[out  '+'  char(X(k))]
end

Best Answer

Related Solutions

MATLAB: Using fsolve over a range of equations.

MATLAB: How to sum the elements of a symbolic vector

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