I forgot to mention: this is a transfert from a sage-support message by
Emmanuel:
https://groups.google.com/d/msg/sage-support/5M50BRbHy2k/5jRYMnf7AQAJ
Le samedi 1 août 2020 12:19:45 UTC+2, Eric Gourgoulhon a écrit :
>
>
>
> Le samedi 1 août 2020 10:06:47 UTC+2, Emmanuel Charpentier a écrit :
>>
>> Consider :
>>
>> sage: f=function("f")
>> sage: m=var("m", domain="integer")
>> sage: assume(m>0)
>>
>> Sage follows the Maxima convention for multiple derivation d^n/dx^n f(x)
>> is diff(f(x),x,n) :
>>
>> sage: diff(sin(x),x,3)
>> -cos(x) # Okay....
>> sage: diff(sin(x),x,m)
>> 0 *## Huh ???*
>> sage: diff(f(x),x,3)
>> diff(f(x), x, x, x) # Okay, sort of
>> sage: diff(f(x),x,m)
>> 0 *## Huh ???*
>>
>> Note that Sage will silently return a mathematically false result when
>> the degree of derivation is symbolic.
>>
>> The problem doesn't seem to reside i Maxima, which returns results
>> consistent to its convention :
>>
>> sage: %maxima diff(sin(x),x,3)
>> -cos(x)
>> sage: %maxima diff(sin(x),x,m)
>> 'diff(sin(x),x,m)
>> sage: %maxima diff(f(x),x,3)
>> 'diff(f(x),x,3)
>> sage: %maxima diff(f(x),x,m)
>> 'diff(f(x),x,m)
>>
>> The problem is similar to the one seen in sympy *when incorrectly called
>> :*
>>
>> sage: import sympy
>> sage: sympy.diff(*[sympy.sympify(u) for u in [sin(x),x,3]])
>> -cos(x)
>> sage: sympy.diff(*[sympy.sympify(u) for u in [sin(x),x,m]])
>> 0 # Huh again...
>> sage: sympy.diff(*[sympy.sympify(u) for u in [sin(x),[x,m]]])
>> Derivative(sin(x), (x, m)) # Unfulfilling but correct...
>> sage: sympy.diff(*[sympy.sympify(u) for u in [f(x),[x,m]]])
>> Derivative(f(x), (x, m)) # Unfulfilling but correct...
>>
>> Note that sympy's alternative convention for multiple derivation gives
>> consistent results :
>>
>> sage: sympy.diff(*[sympy.sympify(u) for u in [sin(x),[x,m]]]).subs([(m,
>> 3)])
>> Derivative(sin(x), (x, 3))
>> sage: sympy.diff(*[sympy.sympify(u) for u in [sin(x),[x,m]]]).subs([(m,
>> 3)]).doit
>> ....: ()
>> -cos(x)
>> sage: sympy.diff(*[sympy.sympify(u) for u in [f(x),[x,m]]]).subs([(m, 3)])
>> Derivative(f(x), (x, 3))
>> sage: sympy.diff(*[sympy.sympify(u) for u in [f(x),[x,m]]]).subs([(m,
>> 3)]).doit()
>> ....:
>> Derivative(f(x), (x, 3))
>>
>> Sage doesn't accept Sympy's convention for multiple derivation :
>>
>> sage: diff(f(x), (x,3))
>>
>> ---------------------------------------------------------------------------
>> [ Snip ... ]
>>
>> TypeError: no canonical coercion from <class 'tuple'> to Symbolic Ring
>>
>> Therefore, Sage seems to interpret diff(<expression>, <variable>,
>> <numerical value>) as d/d<variable> <expression> and diff(<expression>,
>> <variable1>, <variable2>) as d/d<variable1> d/d<variable2> <expression>,
>> with no way to express d^<variable2>/d<variable1)^<variable2> <expression>.
>>
>> This is, IMNSHO, a serious mess. Which, as demonstrated above, *can silently
>> return
>> mathematically false results*.
>>
>> The problem is that I cannot see a way to fix this that doesn't break
>> backwards compatibility somehow.
>>
>> Help about the way to efficiently file a (probably critical) ticket
>> against this horror most welcome...
>>
>> PS : One can note that Mathematica expresses its result in the symbolic
>> case in a peculiar way :
>>
>> sage: mathematica.D(f(x),[x,m])
>> Derivative[m][F][x]
>>
>> One can also note that it may handle some special cases in a smarter way
>> than Sage/Maxima/Sympy :
>>
>> sage: mathematica.D(sin(x),[x,m])
>> Sin[(m*Pi)/2 + x]
>>
>> but this is another story...
>>
>>
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