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Question: How can I simplify multivariate rational expressions?

Question:How can I simplify multivariate rational expressions?

ignacios 10 Maple 2024
multivariate simplification trig
March 09 2024
2


 

I have the following expressions:

m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(cos(theta)^2*a^2-(1/3)*r^2)/(r^2+cos(theta)^2*a^2)^9

m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(cos(theta)^2*a^2-(1/3)*r^2)/(r^2+cos(theta)^2*a^2)^9

 (1)

(a^8*(r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8-80*m^3*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(1/3)*(28*(-30*sin(theta)^2*a^4*m*r^5*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(32*(-5*a^2*m^3-m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^6*r^2*cos(theta)^6+(14*(-260*sin(theta)^2*a^6*m*r^3*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4-80*a^4*m^3*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5)

(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (2)

The two expressions are the same because:

simplify(m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(a^2*cos(theta)^2-(1/3)*r^2)/(r^2+a^2*cos(theta)^2)^9-(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5))

0

 (3)

But I don't get the expression (1) from (2) with the help of simplify() command:

simplify((a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5))

(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (4)

Why not? Is there any solution for this?

 

NULL


 

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