Dear Nils,
Thank you for this hindsight full response. A couple remarks below :
Le jeudi 6 mai 2021 à 08:06:18 UTC+2, Nils Bruin a écrit :
> "and" and "or" in python are not logical operators -- they are flow
> control for expressions; much like the " ... if ... else ..." expression
> is. Their behaviour cannot be overloaded. The bitwise operators "&" and "|"
> would be candidates for overloading.
>
> Concerning the translation from maxima to sage, the string parser may be
> difficult that way. I'm not so sure it can do smart things with infix.
>
it may do ; it already does for the arithmetic operators :
sage: ME=maxima
sage: c=ME("a^b")
sage: c.parent()
Maxima
sage: c.sage()
a^b
sage: [maxima.part(c,u) for u in (0..len(c))]
["^", a, b]
So maybe we can use whatever `maxima` does for "^" as a cookie-cutter for
logical functions ?
> The binary-based interface would be very easy to adapt, though:
>
> sage: M=maxima_calculus
> sage: c=M('a and b')
> sage: c.ecl()
> <ECL: ((MAND SIMP) $A $B)>
>
> Adapting the s-expr based translator would be very straightforward, since
> (as you can see) the and appears in exactly the same way other functions
> would. Example:
>
> sage: c=M('sin(a) + b')
> sage: c.ecl()
> <ECL: ((MPLUS SIMP) ((%SIN SIMP) $A) $B)>
>
Agreed so far.
> The challenge would be that sage calculus never fully completed the
> transition to the s-expr translation.
>
That is a *different* problem. If I understand you correctly, you would
like to complete the transition to the library interface and essentially
kill the pexpect one, thus dispensing with updating it for logical
operators ?
This would leave in the dark all code previously written using
pexpect-specific
features of the Maxima interface. Not so nice...
> It's much more efficient and robust, but the strings-based translation was
> "good enough" for anyone to bother completing the transition. A few
> operations (integrals and limits if I'm not mistaken) do use this layer,
> but other don't (I think simplifications mostly don't). Perhaps this is
> enough motivation to complete the transition, or at least to the degree
> needed for boolean expressions?
>
I agree that such cleanup may be beneficial. But IMHO it won't be neither
fast nor clean... A distinct task ?
The relevant conversion functions are
>
> sage.interfaces.maxima_lib.sr_to_max
> sage.interfaces.maxima_lib.max_to_sr
>
> They use some dictionaries that would need to be preseeded with
> appropriate translation values for MAND and MOR. You'd furthermore have to
> search for occurrences of them in the library to see where they are already
> used.
>
Thank you for the information.
Sincerely,
>
>
> On Wednesday, May 5, 2021 at 2:45:50 PM UTC-7 emanuel.c...@gmail.com
> wrote:
>
>> At least Sympy, Maxima and Mathematica can treat boolean expressions as
>> other expressions. Maxima : :
>>
>> (%i1) display2d:false;
>>
>> (%o1) false
>> (%i2) foo: a and b;
>>
>> (%o2) a and b
>> (%i3) bar: subst([a=(%pi>3), b=(%pi<4)], foo);
>>
>> (%o3) %pi > 3 and %pi < 4
>> (%i4) is(bar);
>>
>> (%o4) unknown
>> (%i5) bar, ev;
>>
>> (%o5) true
>>
>> Sympy:
>>
>> >>> a, b, x=symbols("a, b, x")
>> >>> foo.subs({a:pi>3, b:x<4})
>> x < 4
>> >>> from sympy import *
>> >>> a, b, x=symbols("a, b, x")
>> >>> foo=And(a, b) ; foo
>> a & b
>> >>> foo.subs({a:pi>3, b:x<4})
>> x < 4
>> >>> foo.subs({a:pi>3, b:pi<4})
>> True
>>
>> Thanks to Sage’s and and or “lazy” operators and the interpretation on
>> anything not zero as True, Sage’s expressions containing logical
>> operators gives surprising results :
>>
>> sage: var("a, b")
>> (a, b)
>> sage: foo = a and b ; foo
>> b
>> sage: (x>3) and (x<4)
>> x > 3
>> sage: (pi>3) and (x<4)
>> x < 4
>> sage: (pi>3) and (pi<4)
>> pi < 4
>>
>> bool((pi>3) and (pi<4))
>> True
>>
>> As a consequence, we have no way to translate in sage the boolean
>> expressions sometimes returned by Sympy or Maxima (e. g. Piecewise
>> functions returned by Sympy for some integrations. It ois easy to slap
>> _sage_ methods to Sympy’s logical functions in terms of Python
>> expressions, but :
>>
>> - their interpretation won't be what us expected, and
>>
>> - these expressions won't translate to Maxima in a useful way :
>>
>> sage: "print(%s)"%(a and b)
>> 'print(b)'
>> sage: maxima("print(%s)"%(a and b))
>> b
>>
>> Another (better) solution is to wrap, for example, Sympy’s logical
>> functions in symbolic function, and define suitanle conversion functions.
>> This is easy for Sage<-> sympy translations ; Sage -> maxima translation is
>> also manageable.
>>
>> Where I’m stuck is the Maxima->Sage translation (necessary given the
>> importance of Maxima for a lot of our symbolics) : the current interface
>> isn’”t useable :
>>
>> sage: maxima("a and b")
>> aandb
>> sage: maxima("a and b").sage()
>> aandb
>> sage: maxima("a and b").sage().parent()
>> Symbolic Ring
>> sage: maxima("a and b").sage().variables()
>> (aandb,)
>> sage: maxima("a and b").sage().operator() is None
>> True
>> sage: maxima("a and b").sage().operands()
>> []
>>
>> or worse :
>>
>> sage: maxima("subst([a=(%pi>3), b=(%pi<4)], a and b)")
>> %pi>3and%pi<4
>> sage: maxima("subst([a=(%pi>3), b=(%pi<4)], a and b)").sage()
>> ---------------------------------------------------------------------------
>> SyntaxError Traceback (most recent call last)
>>
>> [ Snip... ]
>>
>> TypeError: unable to make sense of Maxima expression 'pi>3andpi<4' in Sage
>>
>> Maxima’s logical operators are not recognized as such and are “pasted”
>> along their arguments.
>>
>> What should be done would be to get them parsed, and translated a Sages
>> logical function calls. An alternative would be to create “symbolic logical
>> operators” at least for the classes relevant asossible Maxima returns, but,
>> as far as I know, this is not possible in Python.
>>
>> In both cases, this requires recognizing and treating specially Maxima
>> logical operators. The code of the current Maxima interfaces stymied me : I
>> have been unable to identify the relevant parts. Traceing test
>> expressions failed, since the cricial parts probably written in Cython,
>> aren’t accessible to pdb.
>>
>> Any hint or criticism well received.
>>
>>
>
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