Looking for install support/advice with Maxima
- Subject: Looking for install support/advice with Maxima
- From: Jay Belanger
- Date: 04 Dec 2002 11:25:33 -0600
Kim Lux <lux@diesel-research.com> writes:
> Hi.
Hi.
> I also installed clisp 2.30. to cover the lisp dependency. I've got
> nothing against Gnu lisp, but I cannot find RH RPMs and I don't know how
> to build it.
I have some rpms (built for RedHat 8.0) of the latest cvs gcl in
ftp://vh213601.truman.edu/pub/Maxima
I also have rpms for clisp, but it is clisp 2.30, which, as CY said,
doesn't play nicely with maxima 5.9.0rc3. (I have the latest cvs
maxima, which seems to work nicely with clisp 2.30, but I usually use
gcl.)
Jay
> BTW: the purpose of this installation is to solve the following matrix
> for a, b and r:
...
> I'd like a general symbolic solution, but if that is not available, I
> could supply values for the three known x,y pairs.
I'm not sure why you're using a matrix, or what it means in general
to solve a matrix. It looks like you want to solve the equations
(x1-a)^2 + (y1-b)^2 = r^2
(x2-a)^2 + (y2-b)^2 = r^2
(x3-a)^2 + (y3-b)^2 = r^2
for a, b and r. At the end of this message is what I got from
Maxima. (It looks as if using specific values of x1, etc., might not
be a bad idea.)
Jay
(C1) eqns:[(x1-a)^2 + (y1-b)^2 = r^2, (x2-a)^2 + (y2-b)^2=r^2, (x3-a)^2+(y3-b)^2=r^2]$
(C2) vars:[a,b,r]$
(C3) solve(eqns,vars);
2 2 2 2 2 2
(D3) [[a = - ((Y2 - Y1) Y3 + (- Y2 + Y1 - x2 + x1 ) Y3 + Y1 Y2
2 2 2 2 2
+ (- Y1 + x3 - x1 ) Y2 + (x2 - x3 ) Y1)
/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2 + (2 x3 - 2 x2) Y1),
2 2 2 2
b = ((x2 - x1) Y3 + (x1 - x3) Y2 + (x3 - x2) Y1 + (x2 - x1) x3
2 2 2 2
+ (x1 - x2 ) x3 + x1 x2 - x1 x2)/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2
2 4 4 2 4 2 4
+ (2 x3 - 2 x2) Y1), r = - SQRT(Y2 Y3 - 2 Y1 Y2 Y3 + Y1 Y3 + x2 Y3
4 2 4 3 3 2 3 2 3
- 2 x1 x2 Y3 + x1 Y3 - 2 Y2 Y3 + 2 Y1 Y2 Y3 + 2 Y1 Y2 Y3
2 3 3 2 3 3 3 2 3
- 2 x2 Y2 Y3 + 4 x1 x2 Y2 Y3 - 2 x1 Y2 Y3 - 2 Y1 Y3 - 2 x2 Y1 Y3
3 2 3 4 2 3 2 2 2 2
+ 4 x1 x2 Y1 Y3 - 2 x1 Y1 Y3 + Y2 Y3 + 2 Y1 Y2 Y3 - 6 Y1 Y2 Y3
2 2 2 2 2 2 2 2 2 2
+ 2 x3 Y2 Y3 - 2 x2 x3 Y2 Y3 - 2 x1 x3 Y2 Y3 + 2 x2 Y2 Y3
2 2 2 2 2 3 2 2 2
- 2 x1 x2 Y2 Y3 + 2 x1 Y2 Y3 + 2 Y1 Y2 Y3 - 4 x3 Y1 Y2 Y3
2 2 2 2 2
+ 4 x2 x3 Y1 Y2 Y3 + 4 x1 x3 Y1 Y2 Y3 + 2 x2 Y1 Y2 Y3 - 8 x1 x2 Y1 Y2 Y3
2 2 4 2 2 2 2 2 2
+ 2 x1 Y1 Y2 Y3 + Y1 Y3 + 2 x3 Y1 Y3 - 2 x2 x3 Y1 Y3
2 2 2 2 2 2 2 2 2 2
- 2 x1 x3 Y1 Y3 + 2 x2 Y1 Y3 - 2 x1 x2 Y1 Y3 + 2 x1 Y1 Y3
2 2 2 2 2 2 2 2 3 2
+ 2 x2 x3 Y3 - 4 x1 x2 x3 Y3 + 2 x1 x3 Y3 - 2 x2 x3 Y3
2 2 2 2 3 2 4 2 3 2
+ 2 x1 x2 x3 Y3 + 2 x1 x2 x3 Y3 - 2 x1 x3 Y3 + x2 Y3 - 2 x1 x2 Y3
2 2 2 3 2 4 2 4 2 3
+ 2 x1 x2 Y3 - 2 x1 x2 Y3 + x1 Y3 - 2 Y1 Y2 Y3 + 2 Y1 Y2 Y3
2 3 3 2 3 3 2
- 2 x3 Y2 Y3 + 4 x1 x3 Y2 Y3 - 2 x1 Y2 Y3 + 2 Y1 Y2 Y3
2 2 2 2 2 2
+ 2 x3 Y1 Y2 Y3 + 4 x2 x3 Y1 Y2 Y3 - 8 x1 x3 Y1 Y2 Y3 - 4 x2 Y1 Y2 Y3
2 2 2 4 2 2
+ 4 x1 x2 Y1 Y2 Y3 + 2 x1 Y1 Y2 Y3 - 2 Y1 Y2 Y3 + 2 x3 Y1 Y2 Y3
2 2 2 2 2
- 8 x2 x3 Y1 Y2 Y3 + 4 x1 x3 Y1 Y2 Y3 + 2 x2 Y1 Y2 Y3 + 4 x1 x2 Y1 Y2 Y3
2 2 2 2 2 2 2
- 4 x1 Y1 Y2 Y3 - 2 x2 x3 Y2 Y3 + 4 x1 x2 x3 Y2 Y3 - 2 x1 x3 Y2 Y3
2 2 3 2 2
+ 4 x1 x2 x3 Y2 Y3 - 8 x1 x2 x3 Y2 Y3 + 4 x1 x3 Y2 Y3 - 2 x1 x2 Y2 Y3
3 4 2 3 3 2 3
+ 4 x1 x2 Y2 Y3 - 2 x1 Y2 Y3 - 2 x3 Y1 Y3 + 4 x2 x3 Y1 Y3 - 2 x2 Y1 Y3
2 2 2 2 2 3
- 2 x2 x3 Y1 Y3 + 4 x1 x2 x3 Y1 Y3 - 2 x1 x3 Y1 Y3 + 4 x2 x3 Y1 Y3
2 2 4 3
- 8 x1 x2 x3 Y1 Y3 + 4 x1 x2 x3 Y1 Y3 - 2 x2 Y1 Y3 + 4 x1 x2 Y1 Y3
2 2 2 4 2 4 4 2 4 3 3
- 2 x1 x2 Y1 Y3 + Y1 Y2 + x3 Y2 - 2 x1 x3 Y2 + x1 Y2 - 2 Y1 Y2
2 3 3 2 3 4 2 2 2 2
- 2 x3 Y1 Y2 + 4 x1 x3 Y1 Y2 - 2 x1 Y1 Y2 + Y1 Y2 + 2 x3 Y1 Y2
2 2 2 2 2 2 2 2 2
- 2 x2 x3 Y1 Y2 - 2 x1 x3 Y1 Y2 + 2 x2 Y1 Y2 - 2 x1 x2 Y1 Y2
2 2 2 4 2 3 2 3 2 2 2 2
+ 2 x1 Y1 Y2 + x3 Y2 - 2 x2 x3 Y2 - 2 x1 x3 Y2 + 2 x2 x3 Y2
2 2 2 2 2 2 2 2 2
+ 2 x1 x2 x3 Y2 + 2 x1 x3 Y2 - 4 x1 x2 x3 Y2 + 2 x1 x2 x3 Y2
3 2 2 2 2 3 2 4 2 2 3
- 2 x1 x3 Y2 + 2 x1 x2 Y2 - 2 x1 x2 Y2 + x1 Y2 - 2 x3 Y1 Y2
3 2 3 4 3
+ 4 x2 x3 Y1 Y2 - 2 x2 Y1 Y2 - 2 x3 Y1 Y2 + 4 x2 x3 Y1 Y2
3 2 2 2 2 2
+ 4 x1 x3 Y1 Y2 - 2 x2 x3 Y1 Y2 - 8 x1 x2 x3 Y1 Y2 - 2 x1 x3 Y1 Y2
2 2 2 2 2 4
+ 4 x1 x2 x3 Y1 Y2 + 4 x1 x2 x3 Y1 Y2 - 2 x1 x2 Y1 Y2 + x3 Y1
4 2 4 4 2 3 2 3 2
- 2 x2 x3 Y1 + x2 Y1 + x3 Y1 - 2 x2 x3 Y1 - 2 x1 x3 Y1
2 2 2 2 2 2 2 2 3 2
+ 2 x2 x3 Y1 + 2 x1 x2 x3 Y1 + 2 x1 x3 Y1 - 2 x2 x3 Y1
2 2 2 2 4 2 3 2 2 2 2
+ 2 x1 x2 x3 Y1 - 4 x1 x2 x3 Y1 + x2 Y1 - 2 x1 x2 Y1 + 2 x1 x2 Y1
2 4 4 2 4 3 3 2 3 2 3
+ x2 x3 - 2 x1 x2 x3 + x1 x3 - 2 x2 x3 + 2 x1 x2 x3 + 2 x1 x2 x3
3 3 4 2 3 2 2 2 2 3 2 4 2
- 2 x1 x3 + x2 x3 + 2 x1 x2 x3 - 6 x1 x2 x3 + 2 x1 x2 x3 + x1 x3
4 2 3 3 2 4 2 4
- 2 x1 x2 x3 + 2 x1 x2 x3 + 2 x1 x2 x3 - 2 x1 x2 x3 + x1 x2
3 3 4 2
- 2 x1 x2 + x1 x2 )/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2
2 2 2 2 2
+ (2 x3 - 2 x2) Y1)], [a = - ((Y2 - Y1) Y3 + (- Y2 + Y1 - x2 + x1 ) Y3
2 2 2 2 2 2
+ Y1 Y2 + (- Y1 + x3 - x1 ) Y2 + (x2 - x3 ) Y1)
/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2 + (2 x3 - 2 x2) Y1),
2 2 2 2
b = ((x2 - x1) Y3 + (x1 - x3) Y2 + (x3 - x2) Y1 + (x2 - x1) x3
2 2 2 2
+ (x1 - x2 ) x3 + x1 x2 - x1 x2)/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2
2 4 4 2 4 2 4
+ (2 x3 - 2 x2) Y1), r = SQRT(Y2 Y3 - 2 Y1 Y2 Y3 + Y1 Y3 + x2 Y3
4 2 4 3 3 2 3 2 3
- 2 x1 x2 Y3 + x1 Y3 - 2 Y2 Y3 + 2 Y1 Y2 Y3 + 2 Y1 Y2 Y3
2 3 3 2 3 3 3 2 3
- 2 x2 Y2 Y3 + 4 x1 x2 Y2 Y3 - 2 x1 Y2 Y3 - 2 Y1 Y3 - 2 x2 Y1 Y3
3 2 3 4 2 3 2 2 2 2
+ 4 x1 x2 Y1 Y3 - 2 x1 Y1 Y3 + Y2 Y3 + 2 Y1 Y2 Y3 - 6 Y1 Y2 Y3
2 2 2 2 2 2 2 2 2 2
+ 2 x3 Y2 Y3 - 2 x2 x3 Y2 Y3 - 2 x1 x3 Y2 Y3 + 2 x2 Y2 Y3
2 2 2 2 2 3 2 2 2
- 2 x1 x2 Y2 Y3 + 2 x1 Y2 Y3 + 2 Y1 Y2 Y3 - 4 x3 Y1 Y2 Y3
2 2 2 2 2
+ 4 x2 x3 Y1 Y2 Y3 + 4 x1 x3 Y1 Y2 Y3 + 2 x2 Y1 Y2 Y3 - 8 x1 x2 Y1 Y2 Y3
2 2 4 2 2 2 2 2 2
+ 2 x1 Y1 Y2 Y3 + Y1 Y3 + 2 x3 Y1 Y3 - 2 x2 x3 Y1 Y3
2 2 2 2 2 2 2 2 2 2
- 2 x1 x3 Y1 Y3 + 2 x2 Y1 Y3 - 2 x1 x2 Y1 Y3 + 2 x1 Y1 Y3
2 2 2 2 2 2 2 2 3 2
+ 2 x2 x3 Y3 - 4 x1 x2 x3 Y3 + 2 x1 x3 Y3 - 2 x2 x3 Y3
2 2 2 2 3 2 4 2 3 2
+ 2 x1 x2 x3 Y3 + 2 x1 x2 x3 Y3 - 2 x1 x3 Y3 + x2 Y3 - 2 x1 x2 Y3
2 2 2 3 2 4 2 4 2 3
+ 2 x1 x2 Y3 - 2 x1 x2 Y3 + x1 Y3 - 2 Y1 Y2 Y3 + 2 Y1 Y2 Y3
2 3 3 2 3 3 2
- 2 x3 Y2 Y3 + 4 x1 x3 Y2 Y3 - 2 x1 Y2 Y3 + 2 Y1 Y2 Y3
2 2 2 2 2 2
+ 2 x3 Y1 Y2 Y3 + 4 x2 x3 Y1 Y2 Y3 - 8 x1 x3 Y1 Y2 Y3 - 4 x2 Y1 Y2 Y3
2 2 2 4 2 2
+ 4 x1 x2 Y1 Y2 Y3 + 2 x1 Y1 Y2 Y3 - 2 Y1 Y2 Y3 + 2 x3 Y1 Y2 Y3
2 2 2 2 2
- 8 x2 x3 Y1 Y2 Y3 + 4 x1 x3 Y1 Y2 Y3 + 2 x2 Y1 Y2 Y3 + 4 x1 x2 Y1 Y2 Y3
2 2 2 2 2 2 2
- 4 x1 Y1 Y2 Y3 - 2 x2 x3 Y2 Y3 + 4 x1 x2 x3 Y2 Y3 - 2 x1 x3 Y2 Y3
2 2 3 2 2
+ 4 x1 x2 x3 Y2 Y3 - 8 x1 x2 x3 Y2 Y3 + 4 x1 x3 Y2 Y3 - 2 x1 x2 Y2 Y3
3 4 2 3 3 2 3
+ 4 x1 x2 Y2 Y3 - 2 x1 Y2 Y3 - 2 x3 Y1 Y3 + 4 x2 x3 Y1 Y3 - 2 x2 Y1 Y3
2 2 2 2 2 3
- 2 x2 x3 Y1 Y3 + 4 x1 x2 x3 Y1 Y3 - 2 x1 x3 Y1 Y3 + 4 x2 x3 Y1 Y3
2 2 4 3
- 8 x1 x2 x3 Y1 Y3 + 4 x1 x2 x3 Y1 Y3 - 2 x2 Y1 Y3 + 4 x1 x2 Y1 Y3
2 2 2 4 2 4 4 2 4 3 3
- 2 x1 x2 Y1 Y3 + Y1 Y2 + x3 Y2 - 2 x1 x3 Y2 + x1 Y2 - 2 Y1 Y2
2 3 3 2 3 4 2 2 2 2
- 2 x3 Y1 Y2 + 4 x1 x3 Y1 Y2 - 2 x1 Y1 Y2 + Y1 Y2 + 2 x3 Y1 Y2
2 2 2 2 2 2 2 2 2
- 2 x2 x3 Y1 Y2 - 2 x1 x3 Y1 Y2 + 2 x2 Y1 Y2 - 2 x1 x2 Y1 Y2
2 2 2 4 2 3 2 3 2 2 2 2
+ 2 x1 Y1 Y2 + x3 Y2 - 2 x2 x3 Y2 - 2 x1 x3 Y2 + 2 x2 x3 Y2
2 2 2 2 2 2 2 2 2
+ 2 x1 x2 x3 Y2 + 2 x1 x3 Y2 - 4 x1 x2 x3 Y2 + 2 x1 x2 x3 Y2
3 2 2 2 2 3 2 4 2 2 3
- 2 x1 x3 Y2 + 2 x1 x2 Y2 - 2 x1 x2 Y2 + x1 Y2 - 2 x3 Y1 Y2
3 2 3 4 3
+ 4 x2 x3 Y1 Y2 - 2 x2 Y1 Y2 - 2 x3 Y1 Y2 + 4 x2 x3 Y1 Y2
3 2 2 2 2 2
+ 4 x1 x3 Y1 Y2 - 2 x2 x3 Y1 Y2 - 8 x1 x2 x3 Y1 Y2 - 2 x1 x3 Y1 Y2
2 2 2 2 2 4
+ 4 x1 x2 x3 Y1 Y2 + 4 x1 x2 x3 Y1 Y2 - 2 x1 x2 Y1 Y2 + x3 Y1
4 2 4 4 2 3 2 3 2
- 2 x2 x3 Y1 + x2 Y1 + x3 Y1 - 2 x2 x3 Y1 - 2 x1 x3 Y1
2 2 2 2 2 2 2 2 3 2
+ 2 x2 x3 Y1 + 2 x1 x2 x3 Y1 + 2 x1 x3 Y1 - 2 x2 x3 Y1
2 2 2 2 4 2 3 2 2 2 2
+ 2 x1 x2 x3 Y1 - 4 x1 x2 x3 Y1 + x2 Y1 - 2 x1 x2 Y1 + 2 x1 x2 Y1
2 4 4 2 4 3 3 2 3 2 3
+ x2 x3 - 2 x1 x2 x3 + x1 x3 - 2 x2 x3 + 2 x1 x2 x3 + 2 x1 x2 x3
3 3 4 2 3 2 2 2 2 3 2 4 2
- 2 x1 x3 + x2 x3 + 2 x1 x2 x3 - 6 x1 x2 x3 + 2 x1 x2 x3 + x1 x3
4 2 3 3 2 4 2 4
- 2 x1 x2 x3 + 2 x1 x2 x3 + 2 x1 x2 x3 - 2 x1 x2 x3 + x1 x2
3 3 4 2
- 2 x1 x2 + x1 x2 )/((2 x2 - 2 x1) Y3 + (2 x1 - 2 x3) Y2
+ (2 x3 - 2 x2) Y1)]]
(C4)
>
> In english, the problem is this: I've got three x,y pairs that lie on a
> circle. I'd like to know the x,y co ordinates of the center of that
> circle (a,b) as well as the radius of it. (Obviously if I have a and b,
> I could calculate r...)
>
> BTW Maxima looks great. I can't wait to try it.
>
>
> Thanks
>
> Kim Lux
>
>
>
>
>
>
>
>
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