Hi Martin Thanks for the explanations. I really don't want to be nit-picking, however, you hit the nail:
> Maybe the confusion comes from the difference between D and f_1: > f_1(a,b) is the *result* of D(f(a,b), a). > D is a FriCAS function, whereas f_1(a,b) is an expression. F(x,y)==D(y*sin(x),x) -> InputForm (* y (cos x)) That is, the information that y*cos(x) comes from a derivative is lost (although not really because F(y,y)::INFORM -> (+ (sin y) (* y (cos y))) (before your patch). So why not expecting F(u,v)==D(f(u,v),u) as f_1(u,v)? Then F(u,u)=f_1(u,u) naturally. On the other hand when using macro (==>): F(x,y) ==> D(y*sin(x),x) it's clear to me that we have a substitution F(x,x)->D(x*sin(x),x). But you are right of course, one may/should see it as you mentioned: > D is a FriCAS function, whereas f_1(a,b) is an expression. Again, thanks for the trouble! Kurt On Tuesday, 19 February 2019 07:28:07 UTC+1, Martin R wrote: > > Dear Kurt! > > As far as I can see, eval, D, == and := are behaving exactly as > specified. With > > f(x,y) == D(f(x,y),x) > > the symbol "f" is a FriCAS function, and NOT a function in the usual > mathematical sense! > In particular, f(a,b) returns the expression (in the pre-calculus sense) > > f_1(a,b), > > first derivative of with respect to the first argument, evaluated at a and > b. > Note that it is somewhat sloppy to write f_x(a,b) in calculus, because it > is > unclear what x refers to. > > Therefore, eval(f(a,b), b=a) must return f_1(a,a). > > On the other hand, f(a,a) should return the expression D(f(a,a), a), which > is the derivative of f(a,a) with respect to a. > > Maybe the confusion comes from the difference between D and f_1: > > f_1(a,b) is the *result* of D(f(a,b), a). > > D is a FriCAS function, whereas f_1(a,b) is an expression. > > Martin > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/03c24daf-bf28-449e-abf4-68ae249d8b1e%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
