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Re: [Maxima-discuss] About the solve() command, particular example
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From: Isaac H. D. <anj...@gm...> - 2015-02-13 19:41:31
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Ok thanks!
I'm a bit confused on what he's trying to do, he has 3 equations with 2
unknowns. But it looks like he wanted to solve the problem treating the
known values as arbitrary. But still, 3 eqs. with 2 unknowns seems
overdetermined system to me with no solution...
He said that by hand he gets a nice solution.
a is supposed to be the radius of the circumscribed circle into the
triangle whose tips are (x,y), (z,s) and (r,t).
(d,c), what he's looking for would be the center of such circle.
2015-02-13 14:29 GMT-03:00 Barton Willis <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.
>
>
>
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