Jason Grout wrote:
> William Stein wrote:
>> On Thu, Aug 28, 2008 at 11:06 PM, Robert Dodier <[EMAIL PROTECTED]> wrote:
>>> On 8/28/08, William Stein <[EMAIL PROTECTED]> wrote:
>>>
>>>> Sage uses Maxima's solve command, and Maxima's solve
>>>> command is pretty wimpy, and we (Sage developers) intend
>>>> to write our own new solve command that can deal with
>>>> more general equations.
>>> Go nuts, man. Hope you can write it in Python since that will
>>> make it easier to port to Lisp.
>>>
>> We might start with Sympy's solve command, which is in Python,
>> and which also can't solve the above equations:
>>
>> sage: from sympy import *
>> sage: x,y = var('x,y')
>> sage: sympy.solve([x==0, 1-exp(y)==0],[x,y])
>> {}
>> sage: solve([y*sin(x)==0, cos(x)==0],x,y)
>> {}
>>
>
> For reference, it seems that axiom can't solve these either (at least
> with my naive attempts):
>
> (9) -> solve([x=0,1-exp(y)=0],[x,y])
> (9) ->
> (9) [[]]
> Type: List List Equation Expression
> Integer
> (10) -> solve([y*sin(x)=0,cos(x)=0],[x,y])
> (10) ->
> (10) [[]]
> Type: List List Equation Expression
> Integer
>
>
> while mathematica gives solutions:
>
> In[1]:= Solve[{x == 0, 1 - Exp[y] == 0}, {x, y}]
>
> Solve::ifun: Inverse functions are being used by Solve, so some
> solutions may
> not be found; use Reduce for complete solution information.
>
> Out[1]= {{x -> 0, y -> 0}}
>
> In[2]:= Solve[{y*Sin[x] == 0, Cos[x] == 0}, {x, y}]
>
> Solve::ifun: Inverse functions are being used by Solve, so some
> solutions may
> not be found; use Reduce for complete solution information.
>
> -Pi Pi
> Out[2]= {{y -> 0, x -> ---}, {y -> 0, x -> --}}
> 2 2
In fact, Mathematica can give general solutions:
In[3]:= Reduce[{x == 0, 1 - Exp[y] == 0}, {x, y}]
Out[3]= C[1] \[Element] Integers && x == 0 && y == (2 I) Pi C[1]
In[4]:= Reduce[{y*Sin[x] == 0, Cos[x] == 0}, {x, y}]
Out[4]= C[1] \[Element] Integers &&
-Pi Pi
> (x == --- + 2 Pi C[1] || x == -- + 2 Pi C[1]) && y == 0
2 2
(translation: the first is x==0 and y==(2*I)*C*Pi, where C is an
integer, etc.)
Jason
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