solve equtions in maxima (algorithms, description of implementationin clisp)

You can read the code, trace functions, e.g.

:lisp (trace solve1a)

read the user documentation

and read this

http://www.cs.berkeley.edu/~fateman/papers/simplifier.txt

you can also read a chapter in my thesis, "Essays in Algebraic 
Simplification"  mit-lcs-tr-095
which is online in various places.


?????? ????????? wrote:
> Hi.
>
> Thank you for attention to this message.
> Could you describe the principles of Maxima's simplifier (structure, algorithms, sequence of function calls to simplify expression before solving the equation). For example, we have some as an input for   solving system. What simplification functions and in which order are called to simplify this expression (from file rat3e.lisp, solve.lisp)?
>  
> Best regards,
> Mihail D
>
> -----Original Message-----
> From: Richard Fateman <fateman at cs.berkeley.edu>
> To: ?????? ????????? <mihail_denisenko at mail.ru>
> Date: Tue, 13 Oct 2009 07:23:19 -0700
> Subject: Re: [Maxima] solve equtions in maxima (algorithms, description ofimplementation
> in clisp)
>
>   
>> ?????? ????????? wrote:
>>     
>>> Hi, all.
>>>
>>> If we try to solve equations of kind: (x+a)/(x+a)=1, a - fixed number,
>>> then the answer should be "all numbers, excepting x=-a". Maxima outputs the result "all", it does not exclude wrong solution x=-a. As I understand,
>>> Maxima simplifies expression and (x+a)/(x+a) and gets 1=1. So it answers "all".
>>>
>>> Could you advise how to avoid this error? Maybe could you tell me functions that do this simplification (is it possible to torn off such simplification)?
>>>
>>>   
>>>       
>> If you turn off simplification, you will not be able to do much at all 
>> with Maxima. Solve does not even see (x+a)/(x+a).  It is reduced to 1 by 
>> the simplifier.
>>
>> In this case the limit as x-> -a  of (x+a)/(x+a)  is equal to 1. There 
>> are probably worse examples with truly extraneous roots.
>>
>> Sometimes, but not always,  the extraneous roots can be identified by 
>> back-substitution, but in this case, the equation is already simplified 
>> to 1=1.
>> Sometimes the solutions from solve are too clever for the simplifier to 
>> verify.
>>
>> You are welcome to improve these programs, as long as you do not break 
>> anything that already works.
>>
>> RJF
>>
>>
>>     
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