Maple 17 Questions and Posts

These are Posts and Questions associated with the product, Maple 17

Hey guys, I'm a new Maple user and I've been struggling to figure the collect command out.

I made a smaller example to show what I am looking for

I want to find out a way to use collect command and go from "c" output to "d", choosing the terms I want to be collected as common factors.

I'm also uploading the files if it's of any help, The one called question is the example in the picture above and final objeticve is the big expression that I`m trying to factor.

In the final objective file I'm looking for a way to make the "i" output be factored like this as:

Wi δ Wi (...) + Wi δ Wf (...) + Wi δ θi (...) + Wi δ θf (...) + Wf δ Wf (...) + Wf δ Wi (...) + Wf δ θi (...) + Wf δ θf (...) + ...

 

Thanks in advance

Download Final_objective.mw

Download Question_about_collect_and_factor.mw

 

Dear Users,

I have a set of linear equations which can be presented as A(alpha,n) x(alpha)=b(alpha,n), where 'n' is the dimension of the square matric A.

For a particular value of "n" and "alpha", I can solve the unknown vector x. Further, I can differentiate Ax=b with respect to alpha to find out the rate of change of variable x with respect to alpha.

The above exercise reads, Ax'=b'-xA', which gives the unknown vector x', for a given value of alpha and n.

If I chose different values of n while fixing alpha=alpha0, the rate of change of x with alpha ( x' ) does not converge with 'n'. I noticed that x (alpha=alpha0) converges with n, also x(alpha=alpha0+ delta alpha) also converges with 'n'. I am interested in the query why x' does not converge, in spite of the fact that x converges? Any comments regarding the same are highly appreciated.

 

Thanks,

Grv

Hi MaplePrimes,

I'm trying to explore the polynomial r = n^2+n+39.  where n is an integer

I want restrictions on n such that r will factor into two trinomials.

Here is how far I got - 

prime_poly_39_explore.mw

The 'has' function may be helpful.

Any help is appreciated.

Regards,

Matt

 

I believe this is a bug:

 
(((Q(a)^3)^(5/4))^(15/7))^(6/8);
subsindets(%, anything^rational, proc(x) if type(x, specfunc(anything, Q)^rational) then 'Q(x)' else 'x' fi end)<>
subsindets(%, specfunc(anything, Q)^rational, Q);

Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?

Hi all, I want to evaluate the integral G2. I am using the evalf command, but maple is unable to evaluate it. What am I missing here?

 

G2 := -.5*(int(Re(-(0.8823529412e-2*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta)))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))*(-.5*cos(.3926990818+.5*theta)*sin(-.3926990818+.5*theta)+.5*sin(.3926990818+.5*theta)*cos(-.3926990818+.5*theta))/sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(1.017602550-3.872635115*exp(-.2960360476-(1.*I)*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta))*(-0.6282080040e-1-(0.6282080040e-1*I)*(.5*cos(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)+.5*sin(-.3926990818+.5*theta)*cos(.3926990818+.5*theta)/sin(.3926990818+.5*theta)^2)*sin(.3926990818+.5*theta)/sin(-.3926990818+.5*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)))))*(-.5-.5*cos(2.*theta))+.5*Im(-(0.8823529412e-2*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta)))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))*(-.5*cos(.3926990818+.5*theta)*sin(-.3926990818+.5*theta)+.5*sin(.3926990818+.5*theta)*cos(-.3926990818+.5*theta))/sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(1.017602550-3.872635115*exp(-.2960360476-(1.*I)*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta))*(-0.6282080040e-1-(0.6282080040e-1*I)*(.5*cos(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)+.5*sin(-.3926990818+.5*theta)*cos(.3926990818+.5*theta)/sin(.3926990818+.5*theta)^2)*sin(.3926990818+.5*theta)/sin(-.3926990818+.5*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)))))*sin(2.*theta), theta = 0. .. .7853981635))

I'm trying to solve this to set of equations :

EQ1:=-1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4:

EQ2 :=-1186578.220*R*k^2*wr-312683.0293*k^5-288960.9621*k^3*R:

using a loop for different value of R in the range this range (wr=0..10,k=0..10)

eqns:={EQ1,EQ2}:
for i from 1 by 1 to 101 do R:=(i-1):S:=fsolve(eqns,{k, wr},{wr=0..10,k=0..10}):v(i):=(subs(S,(wr)));w(i):=(subs(S,(k)))end do:

but i get this instead :

Error, invalid input: subs received fsolve({-312683.0293*k^5, -1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4}, {k, wr}, {k = 0 .. 10, wr = 0 .. 10}), which is not valid for its 1st argument

is there another way to solves this equations more easly .


 

``

restart;

N := 2

2

(1)

H1 := B*H(Zeta)/A+C*H(Zeta)/A+E/A

B*H(Zeta)/A+C*H(Zeta)/A+E/A

(2)

expand(subs(diff(H(Zeta), Zeta) = B*H(Zeta)/A+C*H(Zeta)/A+E/A, diff(H1, Zeta)))

B^2*H(Zeta)/A^2+2*B*C*H(Zeta)/A^2+B*E/A^2+C^2*H(Zeta)/A^2+C*E/A^2

(3)

s := sum(alpha[i]*(d+H(Zeta))^i, i = -N .. N)+sum(beta[i]*(d+H(Zeta))^(-i), i = 1 .. N)

alpha[-2]/(d+H(Zeta))^2+alpha[-1]/(d+H(Zeta))+alpha[0]+alpha[1]*(d+H(Zeta))+alpha[2]*(d+H(Zeta))^2+beta[1]/(d+H(Zeta))+beta[2]/(d+H(Zeta))^2

(4)

``

s1 := expand(subs(diff(H(Zeta), Zeta) = B*H(Zeta)/A+C*H(Zeta)/A+E/A, diff(s, Zeta)))

-2*alpha[-2]*B*H(Zeta)/((d+H(Zeta))^3*A)-2*alpha[-2]*C*H(Zeta)/((d+H(Zeta))^3*A)-2*alpha[-2]*E/((d+H(Zeta))^3*A)-alpha[-1]*B*H(Zeta)/((d+H(Zeta))^2*A)-alpha[-1]*C*H(Zeta)/((d+H(Zeta))^2*A)-alpha[-1]*E/((d+H(Zeta))^2*A)+alpha[1]*B*H(Zeta)/A+alpha[1]*C*H(Zeta)/A+alpha[1]*E/A+2*alpha[2]*d*B*H(Zeta)/A+2*alpha[2]*d*C*H(Zeta)/A+2*alpha[2]*d*E/A+2*alpha[2]*B*H(Zeta)^2/A+2*alpha[2]*C*H(Zeta)^2/A+2*alpha[2]*H(Zeta)*E/A-beta[1]*B*H(Zeta)/((d+H(Zeta))^2*A)-beta[1]*C*H(Zeta)/((d+H(Zeta))^2*A)-beta[1]*E/((d+H(Zeta))^2*A)-2*beta[2]*B*H(Zeta)/((d+H(Zeta))^3*A)-2*beta[2]*C*H(Zeta)/((d+H(Zeta))^3*A)-2*beta[2]*E/((d+H(Zeta))^3*A)

(5)

s2 := expand(subs(diff(H(Zeta), Zeta) = B*H(Zeta)/A+C*H(Zeta)/A+E/A, diff(s1, Zeta)))

alpha[1]*B^2*H(Zeta)/A^2+alpha[1]*B*E/A^2+alpha[1]*C^2*H(Zeta)/A^2+alpha[1]*C*E/A^2+6*alpha[-2]*E^2/((d+H(Zeta))^4*A^2)+2*alpha[-1]*E^2/((d+H(Zeta))^3*A^2)+4*alpha[2]*B^2*H(Zeta)^2/A^2+4*alpha[2]*C^2*H(Zeta)^2/A^2+2*beta[1]*E^2/((d+H(Zeta))^3*A^2)+6*beta[2]*E^2/((d+H(Zeta))^4*A^2)+2*alpha[2]*E^2/A^2+6*alpha[2]*E*B*H(Zeta)/A^2+6*alpha[2]*E*C*H(Zeta)/A^2-2*alpha[-2]*B^2*H(Zeta)/((d+H(Zeta))^3*A^2)-2*alpha[-2]*B*E/((d+H(Zeta))^3*A^2)-2*alpha[-2]*C^2*H(Zeta)/((d+H(Zeta))^3*A^2)-2*alpha[-2]*C*E/((d+H(Zeta))^3*A^2)-alpha[-1]*B^2*H(Zeta)/((d+H(Zeta))^2*A^2)-alpha[-1]*B*E/((d+H(Zeta))^2*A^2)-alpha[-1]*C^2*H(Zeta)/((d+H(Zeta))^2*A^2)-alpha[-1]*C*E/((d+H(Zeta))^2*A^2)+2*alpha[2]*d*B^2*H(Zeta)/A^2+2*alpha[2]*d*B*E/A^2+2*alpha[2]*d*C^2*H(Zeta)/A^2+2*alpha[2]*d*C*E/A^2+8*alpha[2]*B*H(Zeta)^2*C/A^2-beta[1]*B^2*H(Zeta)/((d+H(Zeta))^2*A^2)-beta[1]*B*E/((d+H(Zeta))^2*A^2)-beta[1]*C^2*H(Zeta)/((d+H(Zeta))^2*A^2)-beta[1]*C*E/((d+H(Zeta))^2*A^2)-2*beta[2]*B^2*H(Zeta)/((d+H(Zeta))^3*A^2)-2*beta[2]*B*E/((d+H(Zeta))^3*A^2)-2*beta[2]*C^2*H(Zeta)/((d+H(Zeta))^3*A^2)-2*beta[2]*C*E/((d+H(Zeta))^3*A^2)+6*alpha[-2]*B^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)+6*alpha[-2]*C^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)+2*alpha[-1]*B^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)+2*alpha[-1]*C^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)+2*beta[1]*B^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)+2*beta[1]*C^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)+6*beta[2]*B^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)+6*beta[2]*C^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)+2*alpha[1]*B*C*H(Zeta)/A^2+4*alpha[-1]*B*H(Zeta)^2*C/((d+H(Zeta))^3*A^2)+4*beta[1]*B*H(Zeta)^2*C/((d+H(Zeta))^3*A^2)+12*beta[2]*B*H(Zeta)^2*C/((d+H(Zeta))^4*A^2)-4*alpha[-2]*B*C*H(Zeta)/((d+H(Zeta))^3*A^2)+12*alpha[-2]*E*B*H(Zeta)/((d+H(Zeta))^4*A^2)+12*alpha[-2]*E*C*H(Zeta)/((d+H(Zeta))^4*A^2)-2*alpha[-1]*B*C*H(Zeta)/((d+H(Zeta))^2*A^2)+4*alpha[-1]*E*B*H(Zeta)/((d+H(Zeta))^3*A^2)+4*alpha[-1]*E*C*H(Zeta)/((d+H(Zeta))^3*A^2)+4*alpha[2]*d*B*C*H(Zeta)/A^2-2*beta[1]*B*C*H(Zeta)/((d+H(Zeta))^2*A^2)+4*beta[1]*E*B*H(Zeta)/((d+H(Zeta))^3*A^2)+4*beta[1]*E*C*H(Zeta)/((d+H(Zeta))^3*A^2)-4*beta[2]*B*C*H(Zeta)/((d+H(Zeta))^3*A^2)+12*beta[2]*E*B*H(Zeta)/((d+H(Zeta))^4*A^2)+12*beta[2]*E*C*H(Zeta)/((d+H(Zeta))^4*A^2)+12*alpha[-2]*B*H(Zeta)^2*C/((d+H(Zeta))^4*A^2)

(6)

s22 := expand(subs(diff(H(Zeta), Zeta) = B*H(Zeta)/A+C*H(Zeta)/A+E/A, s^2))

2*alpha[-2]*alpha[1]*d/(d+H(Zeta))^2+2*alpha[-2]*alpha[1]*H(Zeta)/(d+H(Zeta))^2+2*alpha[-2]*alpha[2]*d^2/(d+H(Zeta))^2+2*alpha[-2]*alpha[2]*H(Zeta)^2/(d+H(Zeta))^2+2*alpha[-1]*alpha[1]*d/(d+H(Zeta))+2*alpha[-1]*alpha[1]*H(Zeta)/(d+H(Zeta))+2*alpha[-1]*alpha[2]*d^2/(d+H(Zeta))+2*alpha[-1]*alpha[2]*H(Zeta)^2/(d+H(Zeta))+4*alpha[0]*alpha[2]*d*H(Zeta)+6*alpha[1]*d^2*alpha[2]*H(Zeta)+6*alpha[1]*d*alpha[2]*H(Zeta)^2+2*alpha[1]*d*beta[1]/(d+H(Zeta))+2*alpha[1]*d*beta[2]/(d+H(Zeta))^2+2*alpha[1]*H(Zeta)*beta[1]/(d+H(Zeta))+2*alpha[1]*H(Zeta)*beta[2]/(d+H(Zeta))^2+2*alpha[2]*d^2*beta[1]/(d+H(Zeta))+2*alpha[2]*d^2*beta[2]/(d+H(Zeta))^2+2*alpha[2]*H(Zeta)^2*beta[1]/(d+H(Zeta))+2*alpha[2]*H(Zeta)^2*beta[2]/(d+H(Zeta))^2+alpha[-2]^2/(d+H(Zeta))^4+alpha[-1]^2/(d+H(Zeta))^2+alpha[0]^2+alpha[1]^2*d^2+alpha[1]^2*H(Zeta)^2+alpha[2]^2*d^4+alpha[2]^2*H(Zeta)^4+beta[1]^2/(d+H(Zeta))^2+beta[2]^2/(d+H(Zeta))^4+4*alpha[2]^2*d^3*H(Zeta)+2*alpha[0]*alpha[1]*d+2*alpha[-1]*beta[2]/(d+H(Zeta))^3+4*alpha[2]^2*d*H(Zeta)^3+2*alpha[0]*alpha[2]*d^2+2*alpha[-1]*alpha[0]/(d+H(Zeta))+2*alpha[0]*beta[1]/(d+H(Zeta))+2*alpha[-2]*alpha[-1]/(d+H(Zeta))^3+2*beta[1]*beta[2]/(d+H(Zeta))^3+2*alpha[-2]*beta[2]/(d+H(Zeta))^4+2*alpha[-2]*alpha[0]/(d+H(Zeta))^2+2*alpha[0]*beta[2]/(d+H(Zeta))^2+2*alpha[0]*alpha[2]*H(Zeta)^2+2*alpha[-1]*beta[1]/(d+H(Zeta))^2+2*alpha[0]*alpha[1]*H(Zeta)+2*alpha[1]^2*d*H(Zeta)+2*alpha[1]*d^3*alpha[2]+2*alpha[1]*H(Zeta)^3*alpha[2]+6*alpha[2]^2*d^2*H(Zeta)^2+2*alpha[-2]*beta[1]/(d+H(Zeta))^3+4*alpha[-2]*alpha[2]*d*H(Zeta)/(d+H(Zeta))^2+4*alpha[-1]*alpha[2]*d*H(Zeta)/(d+H(Zeta))+4*alpha[2]*d*H(Zeta)*beta[1]/(d+H(Zeta))+4*alpha[2]*d*H(Zeta)*beta[2]/(d+H(Zeta))^2

(7)

``

eq := expand(K+(1+w)*s-a*s22-b*V*s2)

alpha[-2]/(d+H(Zeta))^2+alpha[-1]/(d+H(Zeta))+beta[1]/(d+H(Zeta))+beta[2]/(d+H(Zeta))^2+alpha[0]+2*w*alpha[2]*d*H(Zeta)-4*a*alpha[2]^2*d^3*H(Zeta)-2*a*alpha[0]*alpha[1]*d-2*a*alpha[-1]*beta[2]/(d+H(Zeta))^3-4*a*alpha[2]^2*d*H(Zeta)^3-2*a*alpha[0]*alpha[2]*d^2-2*a*alpha[-1]*alpha[0]/(d+H(Zeta))-2*a*alpha[0]*beta[1]/(d+H(Zeta))-2*a*alpha[-2]*alpha[-1]/(d+H(Zeta))^3-2*a*beta[1]*beta[2]/(d+H(Zeta))^3-2*a*alpha[-2]*beta[2]/(d+H(Zeta))^4-2*a*alpha[-2]*alpha[0]/(d+H(Zeta))^2-2*a*alpha[0]*beta[2]/(d+H(Zeta))^2-2*a*alpha[0]*alpha[2]*H(Zeta)^2-2*a*alpha[-1]*beta[1]/(d+H(Zeta))^2-2*a*alpha[0]*alpha[1]*H(Zeta)-2*a*alpha[1]^2*d*H(Zeta)-2*a*alpha[1]*d^3*alpha[2]-2*a*alpha[1]*H(Zeta)^3*alpha[2]-6*a*alpha[2]^2*d^2*H(Zeta)^2-2*a*alpha[-2]*beta[1]/(d+H(Zeta))^3-4*b*V*beta[1]*E*B*H(Zeta)/((d+H(Zeta))^3*A^2)-12*b*V*beta[2]*B*H(Zeta)^2*C/((d+H(Zeta))^4*A^2)-12*b*V*alpha[-2]*E*C*H(Zeta)/((d+H(Zeta))^4*A^2)-4*b*V*beta[1]*E*C*H(Zeta)/((d+H(Zeta))^3*A^2)-12*b*V*beta[2]*E*C*H(Zeta)/((d+H(Zeta))^4*A^2)-4*b*V*alpha[-1]*E*C*H(Zeta)/((d+H(Zeta))^3*A^2)-4*b*V*alpha[2]*d*B*C*H(Zeta)/A^2-4*b*V*beta[1]*B*H(Zeta)^2*C/((d+H(Zeta))^3*A^2)-12*b*V*alpha[-2]*E*B*H(Zeta)/((d+H(Zeta))^4*A^2)+4*b*V*alpha[-2]*B*C*H(Zeta)/((d+H(Zeta))^3*A^2)+2*b*V*beta[1]*B*C*H(Zeta)/((d+H(Zeta))^2*A^2)+2*b*V*alpha[-1]*B*C*H(Zeta)/((d+H(Zeta))^2*A^2)-4*b*V*alpha[-1]*B*H(Zeta)^2*C/((d+H(Zeta))^3*A^2)-12*b*V*beta[2]*E*B*H(Zeta)/((d+H(Zeta))^4*A^2)+4*b*V*beta[2]*B*C*H(Zeta)/((d+H(Zeta))^3*A^2)-12*b*V*alpha[-2]*B*H(Zeta)^2*C/((d+H(Zeta))^4*A^2)-4*b*V*alpha[-1]*E*B*H(Zeta)/((d+H(Zeta))^3*A^2)+K+alpha[1]*d+alpha[1]*H(Zeta)+alpha[2]*d^2+alpha[2]*H(Zeta)^2+w*alpha[0]-a*alpha[0]^2-6*b*V*alpha[2]*E*B*H(Zeta)/A^2-6*b*V*alpha[2]*E*C*H(Zeta)/A^2+2*b*V*alpha[-2]*B^2*H(Zeta)/((d+H(Zeta))^3*A^2)+2*b*V*alpha[-2]*B*E/((d+H(Zeta))^3*A^2)+2*b*V*alpha[-2]*C^2*H(Zeta)/((d+H(Zeta))^3*A^2)+2*b*V*alpha[-2]*C*E/((d+H(Zeta))^3*A^2)+b*V*alpha[-1]*B^2*H(Zeta)/((d+H(Zeta))^2*A^2)+b*V*alpha[-1]*B*E/((d+H(Zeta))^2*A^2)+b*V*alpha[-1]*C^2*H(Zeta)/((d+H(Zeta))^2*A^2)+b*V*alpha[-1]*C*E/((d+H(Zeta))^2*A^2)-2*b*V*alpha[2]*d*B^2*H(Zeta)/A^2-2*b*V*alpha[2]*d*B*E/A^2-2*b*V*alpha[2]*d*C^2*H(Zeta)/A^2-2*b*V*alpha[2]*d*C*E/A^2-8*b*V*alpha[2]*B*H(Zeta)^2*C/A^2+b*V*beta[1]*B^2*H(Zeta)/((d+H(Zeta))^2*A^2)+b*V*beta[1]*B*E/((d+H(Zeta))^2*A^2)+b*V*beta[1]*C^2*H(Zeta)/((d+H(Zeta))^2*A^2)+b*V*beta[1]*C*E/((d+H(Zeta))^2*A^2)+2*b*V*beta[2]*B^2*H(Zeta)/((d+H(Zeta))^3*A^2)+2*b*V*beta[2]*B*E/((d+H(Zeta))^3*A^2)+2*b*V*beta[2]*C^2*H(Zeta)/((d+H(Zeta))^3*A^2)+2*b*V*beta[2]*C*E/((d+H(Zeta))^3*A^2)-6*b*V*alpha[-2]*B^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)-6*b*V*alpha[-2]*C^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)-2*b*V*alpha[-1]*B^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)-2*b*V*alpha[-1]*C^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)-2*b*V*beta[1]*B^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)-2*b*V*beta[1]*C^2*H(Zeta)^2/((d+H(Zeta))^3*A^2)-6*b*V*beta[2]*B^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)-6*b*V*beta[2]*C^2*H(Zeta)^2/((d+H(Zeta))^4*A^2)-2*b*V*alpha[1]*B*C*H(Zeta)/A^2-a*alpha[1]^2*H(Zeta)^2-a*alpha[1]^2*d^2-a*beta[1]^2/(d+H(Zeta))^2+w*alpha[-1]/(d+H(Zeta))-a*alpha[-2]^2/(d+H(Zeta))^4-a*beta[2]^2/(d+H(Zeta))^4+w*beta[1]/(d+H(Zeta))+w*alpha[1]*d-a*alpha[2]^2*H(Zeta)^4-a*alpha[2]^2*d^4+w*alpha[2]*d^2-a*alpha[-1]^2/(d+H(Zeta))^2+w*alpha[2]*H(Zeta)^2+w*alpha[1]*H(Zeta)+w*beta[2]/(d+H(Zeta))^2+w*alpha[-2]/(d+H(Zeta))^2+2*alpha[2]*d*H(Zeta)-2*a*alpha[-2]*alpha[1]*d/(d+H(Zeta))^2-2*a*alpha[-2]*alpha[1]*H(Zeta)/(d+H(Zeta))^2-2*a*alpha[-2]*alpha[2]*d^2/(d+H(Zeta))^2-2*a*alpha[-2]*alpha[2]*H(Zeta)^2/(d+H(Zeta))^2-2*a*alpha[-1]*alpha[1]*d/(d+H(Zeta))-2*a*alpha[-1]*alpha[1]*H(Zeta)/(d+H(Zeta))-2*a*alpha[-1]*alpha[2]*d^2/(d+H(Zeta))-2*a*alpha[-1]*alpha[2]*H(Zeta)^2/(d+H(Zeta))-4*a*alpha[0]*alpha[2]*d*H(Zeta)-6*a*alpha[1]*d^2*alpha[2]*H(Zeta)-6*a*alpha[1]*d*alpha[2]*H(Zeta)^2-2*a*alpha[1]*d*beta[1]/(d+H(Zeta))-2*a*alpha[1]*d*beta[2]/(d+H(Zeta))^2-2*a*alpha[1]*H(Zeta)*beta[1]/(d+H(Zeta))-2*a*alpha[1]*H(Zeta)*beta[2]/(d+H(Zeta))^2-2*a*alpha[2]*d^2*beta[1]/(d+H(Zeta))-2*a*alpha[2]*d^2*beta[2]/(d+H(Zeta))^2-2*a*alpha[2]*H(Zeta)^2*beta[1]/(d+H(Zeta))-2*a*alpha[2]*H(Zeta)^2*beta[2]/(d+H(Zeta))^2-2*b*V*alpha[2]*E^2/A^2-4*a*alpha[-2]*alpha[2]*d*H(Zeta)/(d+H(Zeta))^2-4*a*alpha[-1]*alpha[2]*d*H(Zeta)/(d+H(Zeta))-4*a*alpha[2]*d*H(Zeta)*beta[1]/(d+H(Zeta))-4*a*alpha[2]*d*H(Zeta)*beta[2]/(d+H(Zeta))^2-b*V*alpha[1]*B^2*H(Zeta)/A^2-b*V*alpha[1]*B*E/A^2-b*V*alpha[1]*C^2*H(Zeta)/A^2-b*V*alpha[1]*C*E/A^2-6*b*V*alpha[-2]*E^2/((d+H(Zeta))^4*A^2)-2*b*V*alpha[-1]*E^2/((d+H(Zeta))^3*A^2)-4*b*V*alpha[2]*B^2*H(Zeta)^2/A^2-4*b*V*alpha[2]*C^2*H(Zeta)^2/A^2-2*b*V*beta[1]*E^2/((d+H(Zeta))^3*A^2)-6*b*V*beta[2]*E^2/((d+H(Zeta))^4*A^2)

(8)

collect(eq, [H, d], recursive):

eqq := subs(H(Zeta) = H, eq)

alpha[0]-2*a*alpha[0]*alpha[1]*d-2*a*alpha[0]*alpha[2]*d^2-2*a*alpha[1]*d^3*alpha[2]+2*w*alpha[2]*d*H-4*a*alpha[2]^2*d^3*H-2*a*alpha[-1]*beta[2]/(d+H)^3-4*a*alpha[2]^2*d*H^3-2*a*alpha[-1]*alpha[0]/(d+H)-2*a*alpha[0]*beta[1]/(d+H)-2*a*alpha[-2]*alpha[-1]/(d+H)^3-2*a*beta[1]*beta[2]/(d+H)^3-2*a*alpha[-2]*beta[2]/(d+H)^4-2*a*alpha[-2]*alpha[0]/(d+H)^2-2*a*alpha[0]*beta[2]/(d+H)^2-2*a*alpha[0]*alpha[2]*H^2-2*a*alpha[-1]*beta[1]/(d+H)^2-2*a*alpha[0]*alpha[1]*H-2*a*alpha[1]^2*d*H-2*a*alpha[1]*H^3*alpha[2]-6*a*alpha[2]^2*d^2*H^2-2*a*alpha[-2]*beta[1]/(d+H)^3+alpha[-2]/(d+H)^2+alpha[-1]/(d+H)+beta[1]/(d+H)+beta[2]/(d+H)^2+alpha[1]*H+alpha[2]*H^2-2*a*alpha[-2]*alpha[1]*d/(d+H)^2-2*a*alpha[-2]*alpha[1]*H/(d+H)^2-2*a*alpha[-2]*alpha[2]*d^2/(d+H)^2-2*a*alpha[-2]*alpha[2]*H^2/(d+H)^2-2*a*alpha[-1]*alpha[1]*d/(d+H)-2*a*alpha[-1]*alpha[1]*H/(d+H)-2*a*alpha[-1]*alpha[2]*d^2/(d+H)-2*a*alpha[-1]*alpha[2]*H^2/(d+H)-4*a*alpha[0]*alpha[2]*d*H-6*a*alpha[1]*d^2*alpha[2]*H-6*a*alpha[1]*d*alpha[2]*H^2-2*a*alpha[1]*d*beta[1]/(d+H)-2*a*alpha[1]*d*beta[2]/(d+H)^2-2*a*alpha[1]*H*beta[1]/(d+H)-2*a*alpha[1]*H*beta[2]/(d+H)^2-2*a*alpha[2]*d^2*beta[1]/(d+H)-2*a*alpha[2]*d^2*beta[2]/(d+H)^2-2*a*alpha[2]*H^2*beta[1]/(d+H)-2*a*alpha[2]*H^2*beta[2]/(d+H)^2-4*b*V*alpha[-1]*B*H^2*C/((d+H)^3*A^2)-12*b*V*beta[2]*E*B*H/((d+H)^4*A^2)+4*b*V*beta[2]*B*C*H/((d+H)^3*A^2)-12*b*V*alpha[-2]*B*H^2*C/((d+H)^4*A^2)-4*b*V*alpha[-1]*E*B*H/((d+H)^3*A^2)-12*b*V*beta[2]*B*H^2*C/((d+H)^4*A^2)-4*b*V*beta[1]*E*C*H/((d+H)^3*A^2)-12*b*V*alpha[-2]*E*C*H/((d+H)^4*A^2)-4*b*V*beta[1]*E*B*H/((d+H)^3*A^2)-12*b*V*beta[2]*E*C*H/((d+H)^4*A^2)-4*b*V*alpha[-1]*E*C*H/((d+H)^3*A^2)-4*b*V*alpha[2]*d*B*C*H/A^2-4*b*V*beta[1]*B*H^2*C/((d+H)^3*A^2)-12*b*V*alpha[-2]*E*B*H/((d+H)^4*A^2)+4*b*V*alpha[-2]*B*C*H/((d+H)^3*A^2)+2*b*V*beta[1]*B*C*H/((d+H)^2*A^2)+2*b*V*alpha[-1]*B*C*H/((d+H)^2*A^2)-a*alpha[1]^2*H^2+w*beta[2]/(d+H)^2-a*beta[2]^2/(d+H)^4+w*alpha[-2]/(d+H)^2-a*alpha[-1]^2/(d+H)^2+w*beta[1]/(d+H)-a*alpha[-2]^2/(d+H)^4+2*alpha[2]*d*H-a*alpha[2]^2*H^4+w*alpha[2]*H^2+w*alpha[-1]/(d+H)+w*alpha[1]*H-a*beta[1]^2/(d+H)^2+K+alpha[1]*d+alpha[2]*d^2+w*alpha[0]-a*alpha[0]^2-6*b*V*alpha[2]*E*B*H/A^2-6*b*V*alpha[2]*E*C*H/A^2+2*b*V*alpha[-2]*B^2*H/((d+H)^3*A^2)+2*b*V*alpha[-2]*B*E/((d+H)^3*A^2)+2*b*V*alpha[-2]*C^2*H/((d+H)^3*A^2)+2*b*V*alpha[-2]*C*E/((d+H)^3*A^2)+b*V*alpha[-1]*B^2*H/((d+H)^2*A^2)+b*V*alpha[-1]*B*E/((d+H)^2*A^2)+b*V*alpha[-1]*C^2*H/((d+H)^2*A^2)+b*V*alpha[-1]*C*E/((d+H)^2*A^2)-2*b*V*alpha[2]*d*B^2*H/A^2-2*b*V*alpha[2]*d*C^2*H/A^2-8*b*V*alpha[2]*B*H^2*C/A^2+b*V*beta[1]*B^2*H/((d+H)^2*A^2)+b*V*beta[1]*B*E/((d+H)^2*A^2)+b*V*beta[1]*C^2*H/((d+H)^2*A^2)+b*V*beta[1]*C*E/((d+H)^2*A^2)+2*b*V*beta[2]*B^2*H/((d+H)^3*A^2)+2*b*V*beta[2]*B*E/((d+H)^3*A^2)+2*b*V*beta[2]*C^2*H/((d+H)^3*A^2)+2*b*V*beta[2]*C*E/((d+H)^3*A^2)-6*b*V*alpha[-2]*B^2*H^2/((d+H)^4*A^2)-6*b*V*alpha[-2]*C^2*H^2/((d+H)^4*A^2)-2*b*V*alpha[-1]*B^2*H^2/((d+H)^3*A^2)-2*b*V*alpha[-1]*C^2*H^2/((d+H)^3*A^2)-2*b*V*beta[1]*B^2*H^2/((d+H)^3*A^2)-2*b*V*beta[1]*C^2*H^2/((d+H)^3*A^2)-6*b*V*beta[2]*B^2*H^2/((d+H)^4*A^2)-6*b*V*beta[2]*C^2*H^2/((d+H)^4*A^2)-2*b*V*alpha[1]*B*C*H/A^2-2*b*V*alpha[2]*d*B*E/A^2-2*b*V*alpha[2]*d*C*E/A^2-a*alpha[1]^2*d^2+w*alpha[1]*d-a*alpha[2]^2*d^4+w*alpha[2]*d^2-2*b*V*alpha[2]*E^2/A^2-4*a*alpha[-2]*alpha[2]*d*H/(d+H)^2-4*a*alpha[-1]*alpha[2]*d*H/(d+H)-4*a*alpha[2]*d*H*beta[1]/(d+H)-4*a*alpha[2]*d*H*beta[2]/(d+H)^2-b*V*alpha[1]*B^2*H/A^2-b*V*alpha[1]*C^2*H/A^2-6*b*V*alpha[-2]*E^2/((d+H)^4*A^2)-2*b*V*alpha[-1]*E^2/((d+H)^3*A^2)-4*b*V*alpha[2]*B^2*H^2/A^2-4*b*V*alpha[2]*C^2*H^2/A^2-2*b*V*beta[1]*E^2/((d+H)^3*A^2)-6*b*V*beta[2]*E^2/((d+H)^4*A^2)-b*V*alpha[1]*B*E/A^2-b*V*alpha[1]*C*E/A^2

(9)

collect(eqq, {d+H})

Error, (in collect) cannot collect d+H

 

``

NULL

``


 

Download SHAFEEG2.mwSHAFEEG2.mw

Maple does not simplify the expression A*[sin(x)]^2+A*[cos(x)]^2=A, where A is any expression.

How can I make it do so? 

 

Thanks,

Maple 17 64-bit on Windows 8

Hello!! Please help me,I need to solve a system of linear algebraic equations by running, and I solved the built-in command solve

restart;
with(plots):
f:=unapply(-x^2+1,x);
mu[1]:=unapply(1/(t^2+1),t);
mu[2]:=unapply(1/(t-5),t); 
g:=unapply(t^3-7*x,[t,x]);
l:=2; T:=3;
n:=10: m:=n: 
h:=evalf(l/n); 
tau:=evalf(T/m);
for k from 0 to n do 
x[k]:=h*k:
end do: 
for j from 0 to m do 
t[j]:=tau*j: 
end do:
ss:=evalf({seq(seq((y[k,j+1]-y[k,j])/tau=(y[k-1,j]-2*y[k,j]+y[k+1,j])/h^2+g(t[j],x[k]),k=1..n-1),j=0..m-1),seq(y[0,j]=mu[1](t[j]),j=1..m),seq(y[k,0]=f(x[k]),k=0..n),seq(y[n,j]=mu[2](t[j]),j=1..m)});
#s:=evalf(solve(ss,{seq(seq(y[k,j],k=0..n),j=0..m)}));

 

Good evening!!! I have a task to implement the task of Cauchy by the method of Milne, wrote the code, but did not understand it until the end, help to understand? what's wrong?
First calculate four "initial" values by the method of Runge-Kutta methods, then use the method of Milne, the Fact that two times running, perhaps extra?

restart;
with(plots):
a:=0; b:=1; eps:=evalf(10^(-3)):
f:=unapply(2*x*(x^2+y),x,y);
G:=simplify(dsolve({diff(y(x),x)=f(x,y(x)),y(a)=1}));                    
N:=15: h:=(b-a)/N:
for i from 0 to N do 
x[i]:=a+i*h: 
end do:
y[0]:=1;
s[0]:=1;
for i from 0 to 2 do 
t[1]:=evalf(h*f(x[i],y[i])):
t[2]:=evalf(h*f(x[i]+h/2,y[i]+t[1]/2)): 
t[3]:=evalf(h*f(x[i]+h/2,y[i]+t[2]/2)):
t[4]:=evalf(h*f(x[i]+h,y[i]+t[3])):
y[i+1]:=evalf(y[i]+(t[1]+2*t[2]+2*t[3]+t[4])/6):
q[1]:=evalf(h*f(x[i],s[i])):
q[2]:=evalf(h*f(x[i]+h/2,s[i]+q[1]/2)): 
q[3]:=evalf(h*f(x[i]+h/2,s[i]+q[2]/2)):
q[4]:=evalf(h*f(x[i]+h,s[i]+q[3])):
s[i+1]:=evalf(s[i]+(q[1]+2*q[2]+2*q[3]+q[4])/6):
end do;
for i from 3 to N-1 do 
y[i+1]:=evalf(y[i-3]+((4*h)/3)*(2*f(x[i],y[i])-f(x[i-1],y[i-1])+2*f(x[i-2],y[i-2]))):
s[i+1]:=evalf(s[i-1]+(h/3)*(f(x[i+1],y[i+1])+4*f(x[i],s[i])+f(x[i-1],s[i-1]))):
d[i+1]:=abs(y[i+1]-s[i+1])/29:
if abs(d[i+1]) < eps then y[i]:=y[i]:
else y[i]:=s[i];
end if: end do;
s1:=plot(rhs(G),x=a..b,color=yellow):
s2:=pointplot({seq([x[k],y[k]],k=0..N)}): 
display(s1,s2);

 

I want to write a procedure called Resistance which calculates and displays the equivalent resistance to three resistors R1, R2 and R3

If the resistances are connected in series then Rser = R1 + R2 + R3

If the resistances are connected in parallel then (R1 * R2 * R3) / (R1 * R2 + R1 * R3 + R2 * R3) and after that, I must write an algorithm which I will test this resistance but it does not work please help me
 

"Resistance:=proc(R1,R2,R3) local Rser,Rpar,R; if(R=Rser)then Rser:=R1+R2+R3;   elif(R=Rpar)jthen Rpar:=(R1*R2*R3)/((R1*R2+R1*R3++R2*R3));  end if;  end proc;"

Error, unable to parse

"Resistance:=proc(R1,R2,R3) local Rser,Rpar,R; if(R=Rser)then Rser:=R1+R2+R3;   elif(R=Rpar) jthen Rpar:=(R1*R2*R3)/(R1*R2+R1*R3++R2*R3);  end if;  end proc;"

 

R1 := readstat(entrer*la*valeur*de*R1); R2 := readstat(entret*la*valeur*de*R2); R3 := readstat(entrer*la*valeur*de*R3); Resistance(R1, R2, R3); printf("la valeur en serie est:%f", Rser); printf("la valeur parallele est:%f", Rpar)

``


 

Download RESISTANCE.mw

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