The problem is the definition of 'parameter' vs 'variable'.
Solve seems to define a 'parameter' as a variable that doesn't happen to be listed in the vars list.
What is really needed here are _three_ different sets: 'variables' that are mentioned in the vars list, 'variables' that aren't mentioned in the vars list, and 'parameters'.
It should be possible to solve a system of equations without producing explicit solutions of _all_ of the 'variables'; just the 'variables' whose values are actually requested.
Thus, solve might conceivably call eliminate to eliminate the variables that aren't mentioned in the vars list, and then solve for the remaining variables whose values are explicitly requested.
I just tried 'eliminate' in this fashion & not only does it seem to work, but it's pretty fast for this particular task.
At 10:38 AM 6/12/2013, Stavros Macrakis wrote:
>Can you suggest concise language that would clarify this? Even for someone as sophisticated as you, apparently my language ("Solve only gives solutions valid for all values of parameters (as opposed to variables)") wasn't clear enough.
>
> -s
>
>On Wed, Jun 12, 2013 at 1:01 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
>Thanks, Stavros, for putting up with my density!
>
>I get it now.
>
>However, the documentation on 'solve', 'linsolve', etc., need to be fixed to document this behavior.
>
>I just did '? solve', and the documentation said nothing about this issue.
>
>At 09:52 AM 6/12/2013, Stavros Macrakis wrote:
>>Extraneous equations add parameters. As I said, solve gives solutions that are correct for all values of all parameters.
>>
>>Thus:
>>
>> solve([x=0],[x]) => [[x=0]]
>>
>>but
>>
>> solve([x=0,y=2],[x]) => []
>>
>>because there is no solution for all values of y, which is considered a parameter, since it is not listed as a variable.
>>
>>In your example, you have equations like h0 = g0 + f0 - e0 which are composed entirely of parameters.
>>
>> -s
>>
>>On Wed, Jun 12, 2013 at 12:21 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
>>Your comment doesn't appear to me to be relevant to the particular set of equations that I gave.
>>
>>The equations are all linear, and solve works fine without the extraneous equations:
>>
>>(%i22) eqn12;
>>(%o22) [d0 = c0 + b0, d1 = c1 + b1, d2 = c2 + b2]
>>(%i23) d;
>>(%o23) [d0, d1, d2]
>>(%i24) solve(eqn12,d);
>>(%o24) [[d0 = c0 + b0, d1 = c1 + b1, d2 = c2 + b2]]
>>(%i25)
>>
>>How can the extraneous (linear) equations screw up solve?
>>
>>At 09:08 AM 6/12/2013, Stavros Macrakis wrote:
>>>Solve only gives solutions valid for all values of parameters (as opposed to variables). For example:
>>>
>>>(%i12) solve([x=a,x=-a],[x]); <<< no solutions for all a
>>>(%o12) []
>>>(%i13) solve([x=a,x=-a],[x,a]); <<< make a into a variable
>>>(%o13) [[x = 0, a = 0]]
>>>
>>>On Wed, Jun 12, 2013 at 11:38 AM, Henry Baker <hbaker1 at pipeline.com> wrote:
>>>Solve doesn't work, either!
>>>
>>>(%i7) d;
>>>(%o7) [d0, d1, d2]
>>>(%i8) eqns;
>>>(%o8) [d0 = c0 + b0, d1 = c1 + b1, d2 = c2 + b2, h0 = g0 + f0 - e0,
>>>h1 = g1 + f1 - e1, h2 = g2 + f2 - e2, f0 = e0 + b0, f1 = e1 + b1,
>>>f2 = e2 + b2, g0 = e0 + c0, g1 = e1 + c1, g2 = e2 + c2]
>>>(%i9) solve(eqns,d);
>>>(%o9) []
>>>(%i10)