mvchary

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8 years, 306 days

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These are questions asked by mvchary

In the process of simplification I have the following multi-variable polynomial:

y:=-8*C*d1^2*(-2+d1)*(-1+d1)^3*r*L*R^3+(d1^4*(-2+d1)^2*L^2-4*C*(-2+d1)*(4*d1^3-13*d1^2+16*d1-8)*(-1+d1)^2*r^2*L+4*C^2*(-2+d1)^2*(-1+d1)^4*r^4)*R^2+(2*d1^4*(-2+d1)^2*r*L^2-2*C*(-2+d1)*(5*d1^3-24*d1^2+32*d1-16)*(-1+d1)^2*r^3*L+4*C^2*(-2+d1)^2*(-1+d1)^4*r^5)*R+d1^4*(-2+d1)^2*r^2*L^2-2*C*(-2+d1)*(d1^3-6*d1^2+8*d1-4)*(-1+d1)^2*r^4*L+C^2*(-2+d1)^2*(-1+d1)^4*r^6

This polynomial contains several (-2+d1), (-1+d1) terms with varying powers in each term. My question here is how to take out common terms and then form compact multi-variable polynomial (without having physical inspection).

 

Thank you for your help.

 

MVC

 

 

I am solving "Fx=0" for geting "roots:x" using "solve(Fx,x)". Solution is in the form of "a+sqrt(b)", "a-sqrt(b)". One solution "f1" is given below.

f1:=1/2*(-8*R*d1^2*r^2*C+10*d1*r^2*C*R+5*d1*r^3*C+2*r*L*d1^2-2*C*r^3+2*R*L*d1^2-R*L*d1^3-r*L*d1^3-4*C*r^2*R+2*R*d1^3*r^2*C-4*r^3*d1^2*C+r^3*d1^3*C+sqrt(26*r^6*d1^4*C^2+41*r^6*d1^2*C^2-44*r^6*d1^3*C^2-20*C^2*r^6*d1+16*C^2*r^5*R-16*C*r^4*L-176*r^5*d1^3*C^2*R+164*r^5*d1^2*C^2*R-74*r^4*d1^4*C*L+136*r^4*d1^3*C*L-136*r^4*d1^2*C*L-80*C^2*r^5*d1*R+72*C*r^4*L*d1-64*C*r^3*R*L+104*R^2*d1^4*r^4*C^2-176*R^2*d1^3*r^4*C^2+164*R^2*d1^2*r^4*C^2-8*r^6*d1^5*C^2+r^2*L^2*d1^6-4*R^2*L^2*d1^5+104*r^5*d1^4*C^2*R+40*r*L*R^3*d1^5*C-72*r*L*R^3*d1^4*C+56*r*L*R^3*d1^3*C-16*r*L*R^3*d1^2*C+R^2*L^2*d1^6+20*r^4*L*C*d1^5-32*r^4*d1^5*C^2*R^2+2*R*L^2*d1^6*r-2*r^4*L*d1^6*C+4*R^2*d1^6*r^4*C^2+4*R*d1^6*r^5*C^2-306*r^3*d1^4*C*R*L+548*r^3*d1^3*C*L*R-544*r^3*d1^2*C*R*L+288*C*r^3*L*d1*R+16*C^2*r^4*R^2+4*R^2*L^2*d1^4-16*R^2*L*d1^6*r^2*C-10*R*L*d1^6*r^3*C+r^6*d1^6*C^2-32*r^5*d1^5*C^2*R-4*r^2*d1^5*L^2-352*R^2*d1^4*r^2*C*L+580*R^2*d1^3*r^2*C*L-552*R^2*d1^2*r^2*C*L-80*d1*r^4*C^2*R^2-8*R^3*d1^6*L*C*r+88*r^3*L*C*d1^5*R+116*r^2*L*R^2*d1^5*C+4*C^2*r^6-8*r*R*L^2*d1^5+288*d1*r^2*C*R^2*L-64*C*r^2*R^2*L+8*r*L^2*d1^4*R+4*r^2*L^2*d1^4)^(1/2))/(-3*r^2*d1*L*C-6*R*d1*L*C*r+2*L*C*r^2+r^2*d1^2*L*C+4*L*C*r*R+2*R*d1^2*L*C*r);

I used the following Maple syntax

patmatch(f1,XT::algebraic+sqrt(YT::algebraic),'q1');

the answer is "false"

Is there any modification in the syntax "patmatch" is required.

Here, my question is how to separate "a" and "b" in "a+sqrt(b)" (a, b are big expressions involving many variables).

Thanking you advance for your help.

 

I am solving "Fx=0" for geting "roots:x" using "solve(Fx,x)". Solution is in the form of

"a+sqrt(b)", "a-sqrt(b)"

Here my question is how to extract "a", "b" separately (a, b are complex and very big expressions).

 

Thank you in advance for your help.

 

 

I am trying to simplify the following polynomial.

> R1 := collect(((3*d1^2-2*d1-d1^3)*r-3*d1^2+d1^3+2*d1)*R^3+((-6*d1+7*d1^2-d1^3)*r^2+(d1-d1^3-3*d1^2+2)*r)*R^2+((-6*d1+6*d1^2)*r^3+(-4*d1^3+6-7*d1+2*d1^2)*r^2)*R+(2*d1^2-2*d1)*r^4+(-2*d1^2-4*d1+4)*r^3,[R,r,d],recursive);

 

With the "collect along with rucursive" unable to give compact version. In the above polynomial most of the bracket terms will have factors([3*d1^2-2*d1-d1^3]=-d1*(d1-1)*(d1-2)), but the collect command unable give these factors, doing such manual simplification in bigger polynomial case is complex. Is there any way to represent above polynomial in compact form.

 

Thanking you in advance.

 

MVC                       

 

 

I have the following multi-variable polynomial:

F:=(d^4-2)*C+(7*d^3-3*d)*C^2-(10*d^4-4*d)*L^2+(d-d^2)*L^3+(R+z^2)*x1+(10*d^3-4*d)*L;

Here my question is how to (i) generate "F" in the following form-> F:=k1*C+k2*L+k3*x1; (ii) How to find the coeficient terms of  "C", "L", "x1".

 

Thanking you in advance.

 

MVC

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