ijuptilk

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These are questions asked by ijuptilk

Hi, I have the equation below and I'm trying to use "collect " to get the coefficient of dudy^2 and dvdx^2. I tried

aa1 := subs({gamma[1] = alpha[3]-alpha[2], gamma[2] = alpha[6]-alpha[5]}, collect(aa, {dudy^2, dvdx^2}))

But is not collecting the coefficient of dvdx^2. Please can someone help?

aa := alpha[1]*(cos(theta(x, y, t))^4*dudx^2+2*cos(theta(x, y, t))^3*dudx*sin(theta(x, y, t))*dvdx+2*cos(theta(x, y, t))^3*dudx*sin(theta(x, y, t))*dudy+2*cos(theta(x, y, t))^2*dudx*sin(theta(x, y, t))^2*dvdy+cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dvdx^2+2*cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dvdx*dudy+2*cos(theta(x, y, t))*sin(theta(x, y, t))^3*dvdx*dvdy+cos(theta(x, y, t))^2*sin(theta(x, y, t))^2*dudy^2+2*cos(theta(x, y, t))*sin(theta(x, y, t))^3*dudy*dvdy+sin(theta(x, y, t))^4*dvdy^2)+(alpha[2]+alpha[3]+gamma[2])*(-dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*thetadot-(1/2)*dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*dudy+(1/2)*dudx*cos(theta(x, y, t))*sin(theta(x, y, t))*dvdx+(1/2)*cos(theta(x, y, t))^2*dvdx*thetadot-(1/4)*cos(theta(x, y, t))^2*dvdx^2+(1/2)*cos(theta(x, y, t))^2*dudy*thetadot+(1/4)*cos(theta(x, y, t))^2*dudy^2-(1/2)*sin(theta(x, y, t))^2*dvdx*thetadot+(1/4)*sin(theta(x, y, t))^2*dvdx^2-(1/2)*sin(theta(x, y, t))^2*dudy*thetadot-(1/4)*sin(theta(x, y, t))^2*dudy^2+dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*thetadot-(1/2)*dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*dvdx+(1/2)*dvdy*sin(theta(x, y, t))*cos(theta(x, y, t))*dudy)+alpha[4]*(dudx^2+(1/2)*dvdx^2+dvdx*dudy+(1/2)*dudy^2+dvdy^2)+(alpha[5]+alpha[6])*(cos(theta(x, y, t))^2*dudx^2+2*cos(theta(x, y, t))*dudx*((1/2)*dvdx+(1/2)*dudy)*sin(theta(x, y, t))+cos(theta(x, y, t))^2*((1/2)*dvdx+(1/2)*dudy)^2+2*cos(theta(x, y, t))*((1/2)*dvdx+(1/2)*dudy)*dvdy*sin(theta(x, y, t))+sin(theta(x, y, t))^2*((1/2)*dvdx+(1/2)*dudy)^2+sin(theta(x, y, t))^2*dvdy^2)+gamma[1]*(sin(theta(x, y, t))^2*thetadot^2+sin(theta(x, y, t))^2*dudy*thetadot-sin(theta(x, y, t))^2*dvdx*thetadot+(1/4)*sin(theta(x, y, t))^2*dudy^2-(1/2)*sin(theta(x, y, t))^2*dudy*dvdx+(1/4)*sin(theta(x, y, t))^2*dvdx^2+cos(theta(x, y, t))^2*thetadot^2-cos(theta(x, y, t))^2*dvdx*thetadot+cos(theta(x, y, t))^2*dudy*thetadot+(1/4)*cos(theta(x, y, t))^2*dvdx^2-(1/2)*cos(theta(x, y, t))^2*dudy*dvdx+(1/4)*cos(theta(x, y, t))^2*dudy^2)+xi*(cos(theta(x, y, t))^2*dudx+2*cos(theta(x, y, t))*sin(theta(x, y, t))*((1/2)*dvdx+(1/2)*dudy)+sin(theta(x, y, t))^2*dvdy);

Please, how do I fix this? I have

n := Vector[row]([cos(theta(x, y, t)), sin(theta(x, y, t))]);

and Tried :

sum(Multiply(n[i], n[i]), i = 1 .. 2)

But received: "Error, bad index into Vector".

Please how do I compute the div n,  (n.curl n), (n.curl n)^2 and (n x curl n) and  (n x curl n)^2 given the information below: 

restart; restart; with(VectorCalculus); with(LinearAlgebra);

I.e.,

n = (cos(theta(x,y), sin(theta(x,y), 0).

I tried 

divn := Divergence(proc (x, y, z) options operator, arrow; `<,>`(n) end proc);

but received: Error, (in VectorCalculus:-Divergence) the procedure must evaluate to a Vector

Please why does 

roots(x^5 - C__1*x^4 -C__2*x^3 -C__3*x^2 -C__4*x +C__5, x);

returns  [ ]?

Please how  can I use getdata to extract only 200x2 of 208x2 matrix from maple to excel.

For instance I have:

Q:= ( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

It returns  208x2,  200x2 200x2 matrices and I can't extract it using 

`<|>`( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

because the matrices have different dimension. Please, how can make 208x2 matrix to 200x2?

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