On Dec 6, 2006, at 11:34 PM, William Stein wrote:
>
> On Wed, 06 Dec 2006 23:20:56 -0800, Robert Bradshaw
> <[EMAIL PROTECTED]> wrote:
>> First, let me say that I like this proposal.
>> On Dec 6, 2006, at 5:03 PM, William Stein wrote:
>>> Sage calculus
>>> f = alg expr
>>>
>>> f.subs(var, val, ...)
>>> f.subs(dict)
>>> f.subs(list of pairs)
>>> implement recursively, with base case functions of 1 var and vars
>>> and
>>> constants being clear.
>>
>> I would vote for f.subs(var=val, ...) as well.
>>
>>> f.function(*args) - returns a callable version of f, which otherwise
>>> works in same way. Output is result of subs.
>>> this just another formal function, but with a call method.
>>> Also, function((vars...),expr) makes an evaluatable function.
>>
>> The motivation for not providing a call function to begin with is
>> that the arguments have not been specified yet? I still think f(x,y)
>> = sin(x)*cos(x+y+3) is the most "natural" syntax, but alas it
>> requires the preprocessor.
>
> If we wanted, we could always add that later on top of what I
> proposed.
> It would just be:
>
> f = (sin(x)*cos(x+y+3)).function(x,y)
>
> or
>
> dummy = sin(x*) * cos(x+y+3)
> f = dummy.function(x,y)
>
> Either might be doable with the preprocessor, though I shudder...
I think either are very doable via the preprocessor, but we can hold
off for now.
>
> Also, with my proposal one could also already type
>
> f = function( (x,y), sin(x)*cos(x+y+3) )
>
> which is nice since in Mathematica one types "f = Function[ {x,y},
> Sin[x]*Cos[x+y+3] ]".
> Here this would be implemented via:
>
> def function( vars, expr):
> return expr.function(*vars)
I do think this is the cleanest pure python way of doing things.
>
>
>>> f.derivative(var) - we completely implement.
>>
>> Even if we implement this (which should be relatively easy), should
>> we pass the results to maxima to try and simplify it? On that note,
>> should we have a f.simplify(), etc. method?
>
> Yes. Indeed, we should definitely have
>
> f.simplify(numerous options) -- feed exp that defines f to maxima
> (or
> maple or mathematica),
> run various simplify commands, then parse the result.
>
> Note that Maxima has dozens (?) of variants of simply and expand
> commands
> with all
> kinds of funny names, which is confusing, and which I hope to
> remedy with
> SAGE.
>
> William
Yes, lots of at-the-fingertips documentation on the many different
versions of simplify will put us head and shoulders above every other
CAS in that regard.
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