Kevin Dragnet

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These are answers submitted by Kevin Dragnet

eqns := {x1^2+y1^2 = r^2, x2^2+y2^2 = r^2, x3^2+y3^2 = r^2, x4^2+y4^2 = r^2}

{x1^2+y1^2 = r^2, x2^2+y2^2 = r^2, x3^2+y3^2 = r^2, x4^2+y4^2 = r^2}

(1)

expression := 4*x1*x2^2*x3-4*x1*x2*x3*x4+4*x1*x3*y2^2-4*x1*x3*y2*y4-4*x2^2*x3^2-4*x2^2*y2^2+4*x2^2*y2*y4+4*x2*x3^2*x4+4*x2*x4*y2^2-4*x2*x4*y2*y4-4*x3^2*y2^2+4*x3^2*y2*y4-4*y2^4+8*y2^3*y4-4*y2^2*y4^2

4*x1*x2^2*x3-4*x1*x2*x3*x4+4*x1*x3*y2^2-4*x1*x3*y2*y4-4*x2^2*x3^2-4*x2^2*y2^2+4*x2^2*y2*y4+4*x2*x3^2*x4+4*x2*x4*y2^2-4*x2*x4*y2*y4-4*x3^2*y2^2+4*x3^2*y2*y4-4*y2^4+8*y2^3*y4-4*y2^2*y4^2

(2)

simplify(expression, eqns)

-4*x2^3*x4+(8*r^2-4*x4^2-4*y2*y4)*x2^2+4*x4*(r^2-x1*x3+x3^2-y2*y4)*x2+4*r^2*x4^2-8*(r^2-y2*y4)*(r^2-(1/2)*x3*(x1-x3))

(3)

NULL

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NULL

expression := (((1/2)*z+1/2)*Ts+Cf*Rz*(z-1)*Ts^2*(z+1)^2)/((4*(z-1))*((1/4)*(z+1)^2*(Lg+L)*Ts^2+(1/2)*Cf*Rf*(z-1)*(z+1)*(Lg+L)*Ts+Lg*Cf*L*(z-1)^2))

(1/4)*(((1/2)*z+1/2)*Ts+Cf*Rz*(z-1)*Ts^2*(z+1)^2)/((z-1)*((1/4)*(z+1)^2*(Lg+L)*Ts^2+(1/2)*Cf*Rf*(z-1)*(z+1)*(Lg+L)*Ts+Lg*Cf*L*(z-1)^2))

(1)

expandedExpression := normal(expression, expanded)

(2*Cf*Rz*Ts^2*z^3+2*Cf*Rz*Ts^2*z^2-2*Cf*Rz*Ts^2*z-2*Cf*Rz*Ts^2+Ts*z+Ts)/(4*Cf*L*Rf*Ts*z^3+4*Cf*Lg*Rf*Ts*z^3+8*Cf*L*Lg*z^3-4*Cf*L*Rf*Ts*z^2-4*Cf*Lg*Rf*Ts*z^2+2*L*Ts^2*z^3+2*Lg*Ts^2*z^3-24*Cf*L*Lg*z^2-4*Cf*L*Rf*Ts*z-4*Cf*Lg*Rf*Ts*z+2*L*Ts^2*z^2+2*Lg*Ts^2*z^2+24*Cf*L*Lg*z+4*Cf*L*Rf*Ts+4*Cf*Lg*Rf*Ts-2*L*Ts^2*z-2*Lg*Ts^2*z-8*Cf*L*Lg-2*L*Ts^2-2*Lg*Ts^2)

(2)

numerator := collect(numer(expandedExpression), z)

2*Ts^2*Cf*Rz*z^3+2*Ts^2*Cf*Rz*z^2+Ts*(-2*Cf*Rz*Ts+1)*z+Ts*(-2*Cf*Rz*Ts+1)

(3)

denominator := collect(normal(denom(expandedExpression), expanded), z)

(4*Cf*L*Rf*Ts+4*Cf*Lg*Rf*Ts+8*Cf*L*Lg+2*L*Ts^2+2*Lg*Ts^2)*z^3+(-4*Cf*L*Rf*Ts-4*Cf*Lg*Rf*Ts-24*Cf*L*Lg+2*L*Ts^2+2*Lg*Ts^2)*z^2+(-4*Cf*L*Rf*Ts-4*Cf*Lg*Rf*Ts+24*Cf*L*Lg-2*L*Ts^2-2*Lg*Ts^2)*z+4*Cf*L*Rf*Ts+4*Cf*Lg*Rf*Ts-8*Lg*Cf*L-2*L*Ts^2-2*Lg*Ts^2

(4)

numerator/denominator

(2*Ts^2*Cf*Rz*z^3+2*Ts^2*Cf*Rz*z^2+Ts*(-2*Cf*Rz*Ts+1)*z+Ts*(-2*Cf*Rz*Ts+1))/((4*Cf*L*Rf*Ts+4*Cf*Lg*Rf*Ts+8*Cf*L*Lg+2*L*Ts^2+2*Lg*Ts^2)*z^3+(-4*Cf*L*Rf*Ts-4*Cf*Lg*Rf*Ts-24*Cf*L*Lg+2*L*Ts^2+2*Lg*Ts^2)*z^2+(-4*Cf*L*Rf*Ts-4*Cf*Lg*Rf*Ts+24*Cf*L*Lg-2*L*Ts^2-2*Lg*Ts^2)*z+4*Cf*L*Rf*Ts+4*Cf*Lg*Rf*Ts-8*Lg*Cf*L-2*L*Ts^2-2*Lg*Ts^2)

(5)

NULL

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