Re: [Maxima-discuss] About the solve() command, particular example

[Barton W. <wi...@un...>]

When the option variable solveexplicit  is true and Maxima is unable to find a solution, it returns the empty list


    (%i54)  solve(x^99+x+1,x), solveexplicit : true;
    (%o54) []


But with , solveexplicit : false we get a nounform-like result:

    (%i55)  solve(x^99+x+1,x), solveexplicit : false;
    (%o55) [0=x^99+x+1]


The set  {x in complex |  y = 2 } is empty. Regardless of the value of solveexplicit, returns [] for solve(y=1,x):


    (%i57)  solve(y=1,x), solveexplicit : true;
    (%o57) []

    (%i58)  solve(y-1,x), solveexplicit : false;
    (%o58) []


For the system you asked about, eliminating just c & d yields a huge mess that doesn't vanish. So I think


    (%i61) solve([a^2=(x-d)^2+(y-c)^2,a^2=(z-d)^2+(s-c)^2,a^2=(r-d)^2+(t-c)^2],[d,c]);
    (%o61) []


is correct--there is no values for c & d that satisfy the equation. Solving for a, c, and d does give a solution with no parameters.


--Barton
________________________________
From: Isaac Haïk Dunn <anj...@gm...>
Sent: Friday, February 13, 2015 11:05
To: <max...@li...>
Subject: [Maxima-discuss] About the solve() command, particular example

Hello,
Someone (not me) came up with a system of 3 equations with 9 variables (2 unknows and 7 known values for the variables).
When he tried to solve it with Maxima he got an empty list [] as result.
I've read that this means that Maxima is not able to find a solution to the system.
Anyway, this happens when he types:
(%i1) solve([a^2=(x-d)^2+(y-c)^2,a^2=(z-d)^2+(s-c)^2,a^2=(r-d)^2+(t-c)^2],[d,c]);
(%o1)                                 []


So far so good. However when I ask to solve for the 9 unknown (instead of 2 as above), Maxima returns something different than the empty list:

(%i2) solve([a^2=(x-d)^2+(y-c)^2,a^2=(z-d)^2+(s-c)^2,a^2=(r-d)^2+(t-c)^2],[d,c,x,y,z,r,s,t]);
(%o2) [[d = %r1, c = %r2, x = %r3, y =
            2      2                  2
%r2 - sqrt(a  - %r3  + 2 %r1 %r3 - %r1 ), z = %r4, r = %r5,
          2      2                  2
s = sqrt(a  - %r4  + 2 %r1 %r4 - %r1 ) + %r2,
          2      2                  2
t = sqrt(a  - %r5  + 2 %r1 %r5 - %r1 ) + %r2],
                                      2      2                  2
[d = %r6, c = %r7, x = %r8, y = sqrt(a  - %r8  + 2 %r6 %r8 - %r6 ) + %r7,
                             2      2                  2
z = %r9, r = %r10, s = sqrt(a  - %r9  + 2 %r6 %r9 - %r6 ) + %r7,
          2      2                    2
t = sqrt(a  - %r6  + 2 %r10 %r6 - %r10 ) + %r7],
[d = %r11, c = %r12, x = %r13, y = %r12
         2       2                     2
 - sqrt(a  - %r13  + 2 %r11 %r13 - %r11 ), z = %r14, r = %r15,
          2       2                     2
s = sqrt(a  - %r14  + 2 %r11 %r14 - %r11 ) + %r12,
                 2       2                     2
t = %r12 - sqrt(a  - %r15  + 2 %r11 %r15 - %r11 )],
                                         2       2                     2
[d = %r16, c = %r17, x = %r18, y = sqrt(a  - %r18  + 2 %r16 %r18 - %r16 )
                                       2       2                     2
 + %r17, z = %r19, r = %r20, s = sqrt(a  - %r19  + 2 %r16 %r19 - %r16 )
                          2       2                     2
 + %r17, t = %r17 - sqrt(a  - %r20  + 2 %r16 %r20 - %r16 )],
[d = %r21, c = %r22, x = %r23, y = %r22
         2       2                     2
 - sqrt(a  - %r23  + 2 %r21 %r23 - %r21 ), z = %r24, r = %r25,
                 2       2                     2
s = %r22 - sqrt(a  - %r24  + 2 %r21 %r24 - %r21 ),
          2       2                     2
t = sqrt(a  - %r25  + 2 %r21 %r25 - %r21 ) + %r22],
                                         2       2                     2
[d = %r26, c = %r27, x = %r28, y = sqrt(a  - %r28  + 2 %r26 %r28 - %r26 )
                                              2       2
 + %r27, z = %r29, r = %r30, s = %r27 - sqrt(a  - %r29  + 2 %r26 %r29
       2             2       2                     2
 - %r26 ), t = sqrt(a  - %r30  + 2 %r26 %r30 - %r26 ) + %r27],
[d = %r31, c = %r32, x = %r33, y = %r32
         2       2                     2
 - sqrt(a  - %r33  + 2 %r31 %r33 - %r31 ), z = %r34, r = %r35,
                 2       2                     2
s = %r32 - sqrt(a  - %r34  + 2 %r31 %r34 - %r31 ),
                 2       2                     2
t = %r32 - sqrt(a  - %r35  + 2 %r31 %r35 - %r31 )],
                                         2       2                     2
[d = %r36, c = %r37, x = %r38, y = sqrt(a  - %r38  + 2 %r36 %r38 - %r36 )
                                              2       2
 + %r37, z = %r39, r = %r40, s = %r37 - sqrt(a  - %r39  + 2 %r36 %r39
       2                    2       2                     2
 - %r36 ), t = %r37 - sqrt(a  - %r40  + 2 %r36 %r40 - %r36 )]]



As if there was a solution in which case I'm not able to obtain even by setting values to the 7 unknowns (it may be that the values I assign to the 7 supposedly known values make the system having no solution though).

I am curious as to why the empty list is returned in the 1st case but not in the 2nd case.
Thanks.