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Katharine
03/31/10 11:42am

Hi there,

I am trying to solve for the points of intersection of a line with the surface z=a(x^2+y^2)^{3/4} using Mathematica (for my radiation transfer program - the line is the path of a photon). I'm a newbie to Mathematica, but this is what I wrote:

Solve[a*{(xp + m*vx)^2 + (yp + m*vy)^2}^{3/4} - (zp + m*vz) == 0, m]

I then get 6 solutions, which are all the same, which is weird as I was expecting them to be different as the surface is paraboloid-like. Here's an example of the first:

{m -> Root[
a^4 xp^6 + 3 a^4 xp^4 yp^2 + 3 a^4 xp^2 yp^4 + a^4 yp^6 -
zp^4 + (6 a^4 vx xp^5 + 6 a^4 vy xp^4 yp + 12 a^4 vx xp^3 yp^2 +
12 a^4 vy xp^2 yp^3 + 6 a^4 vx xp yp^4 + 6 a^4 vy yp^5 -
4 vz zp^3) #1 + (15 a^4 vx^2 xp^4 + 3 a^4 vy^2 xp^4 +
24 a^4 vx vy xp^3 yp + 18 a^4 vx^2 xp^2 yp^2 +
18 a^4 vy^2 xp^2 yp^2 + 24 a^4 vx vy xp yp^3 +
3 a^4 vx^2 yp^4 + 15 a^4 vy^2 yp^4 -
6 vz^2 zp^2) #1^2 + (20 a^4 vx^3 xp^3 + 12 a^4 vx vy^2 xp^3 +
36 a^4 vx^2 vy xp^2 yp + 12 a^4 vy^3 xp^2 yp +
12 a^4 vx^3 xp yp^2 + 36 a^4 vx vy^2 xp yp^2 +
12 a^4 vx^2 vy yp^3 + 20 a^4 vy^3 yp^3 -
4 vz^3 zp) #1^3 + (-vz^4 + 15 a^4 vx^4 xp^2 +
18 a^4 vx^2 vy^2 xp^2 + 3 a^4 vy^4 xp^2 +
24 a^4 vx^3 vy xp yp + 24 a^4 vx vy^3 xp yp +
3 a^4 vx^4 yp^2 + 18 a^4 vx^2 vy^2 yp^2 +
15 a^4 vy^4 yp^2) #1^4 + (6 a^4 vx^5 xp +
12 a^4 vx^3 vy^2 xp + 6 a^4 vx vy^4 xp + 6 a^4 vx^4 vy yp +
12 a^4 vx^2 vy^3 yp + 6 a^4 vy^5 yp) #1^5 + (a^4 vx^6 +
3 a^4 vx^4 vy^2 + 3 a^4 vx^2 vy^4 + a^4 vy^6) #1^6 &, 1]}

Also there's this #1 symbol everywhere in the solutions. 1# is the first argument of a pure function, but what is that here? I would like to have a analytical solution as this would be faster to use in the code. Do these 1#s mean that's not possible?

Thanks for any help!

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Subject (listing for '#1s in soln for intersection of line with surface')
Author Date Posted
#1s in soln for intersection of line with surface Katharine 03/31/10 11:42am
Re: #1s in soln for intersection of line with s... yehuda ben-s... 04/02/10 05:09am
Re: Re: #1s in soln for intersection of line wi... Katharine 04/02/10 08:45am
Re: Re: Re: #1s in soln for intersection of lin... yehuda ben-s... 04/03/10 4:01pm
Re: #1s in soln for intersection of line with s... Peter Pein 04/04/10 07:23am
Re: Re: #1s in soln for intersection of line wi... Katharine 04/04/10 5:57pm
Re: Re: Re: #1s in soln for intersection of lin... Peter Pein 04/06/10 09:05am
Re: Re: Re: #1s in soln for intersection of lin... yehuda ben-s... 04/06/10 11:08am
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