Macsyma is right, I think. Line (c1) is wrong.
The user has named the 3 arguments to the function "a", all the same.
That is an error.
The three POSITIONS must have different names. e.g.
depends(a,[b1,b2,b3]);
depends (b1,b); depends(b2,b), depend(b3,b)...
then diff(a,b) would be da/db1*db1/db + ...
There is a uncomfortable issue that traditional mathematics
does not have a notation for "partial derivative with respect
to argument number n". Each computer algebra system has
a different solution, here.
Alexander Vidybida wrote:
>On Mon, Feb 09, 2004 at 08:02:45AM -0500, Dan Stanger wrote:
>
>
>>c1 depends(a,[b,b,b]);
>>d1 [a(b, b, b)]
>>c2 diff(a,b)
>>3 * (da/db)
>>
>>Shoudn't it be da/db?
>>
>>
>>
>
>It seems it should be neither 3*(da/db) nor da/db.
>
>If one needs to declare a function "a" which depends on a single
>variable "b", it is not correct to write a(b,b,b), or a(b,b).
>Correct declaration would be a(b). In order to exclude *declarations*
>like a(b,b,b) it would be helpful to use setify([b,b,b]):
>
>(C2) depends(a,setify([b,b,b]));
>(D2) [a(b)]
>
>*Expressions* like a(b,b,b) may appear if one has a function in a 3-d
>space, a(x,y,z) and put x:b,y:b,z:b. In this case a(b,b,b) will be
>the value of function a(x,y,z) in the point (b,b,b), which cannot be
>subjected to diff., because derivation needs the function to be known not
>only in the point (b,b,b), but also in slightly deviating points.
>The direction of the deviation must be specified explicitly.
>This can be done by defining another function of a single variable ep:
>a1(ep):=a(b+alf*ep,b+bet*ep,b+gam*ep). Here vector (alf,bet,gam) specifies
>direction in which one takes the derivative. It is expected that alf^2+
>bet^2+gam^2=1. Finally, in order to get derivative of function a(x,y,z)
>in the point (b,b,b) along the direction (alf,bet,gam) one needs to take
>diff(a1,ep) and put ep:0 in the result.
>--
>Alexander
>
>
>
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