Bug in printing symbolic derivative (PR#1697)

[murdoch@stats.uwo.ca]

A colleague pointed out the following error in D():

 f  <- expression(exp(-2*x*y))
 Dx <- D(f, 'x')
 Dy <- D(f,'y')
 Dxy <- D(Dx, 'y')
 Dyx <- D(Dy, 'x')

Then 

>  Dx    # this is right
-exp(-2 * x * y) * (2 * y)
>  Dy    # this is right
exp(-2 * x * y) * (-2 * x)
>  Dxy   # this is wrong in the sign of the second term!!!
-exp(-2 * x * y) * (-2 * x) * (2 * y) + exp(-2 * x * y) * 2
>  Dyx   # this is also wrong in the sign of the second term!!!
-exp(-2 * x * y) * 2 + exp(-2 * x * y) * (2 * y) * (-2 * x)

In both cases, the answer would be correct if the initial sign were
applied to the whole expression; is this just a case of not printing
some parentheses?  Let's experiment...

> x <- 1
> y <- 2
> eval(Dxy)
[1] 0.1098938  # this is right
> eval(Dyx)
[1] 0.1098938  # this is right
> -exp(-2 * x * y) * (-2 * x) * (2 * y) + exp(-2 * x * y) * 2 # this is how Dxy prints
[1] 0.1831564  # this is wrong!!
> -(exp(-2 * x * y) * (-2 * x) * (2 * y) + exp(-2 * x * y) * 2) # this is how it should print
[1] 0.1098938  # this is right

Looks like that's it...

Duncan Murdoch

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