## 15 Reputation

8 years, 270 days

## Polynomial simplifications...

Maple 9

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).

MVC

## Roots dis-isolate the terms within roots...

Maple 9

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');

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).

## Polynomial roots simplifications...

Maple 9

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).

## Polynomial simplification...

Maple 9

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.

MVC

## Selecting identical terms...

Maple

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".