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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