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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