#4801 Bogus derivatives when arguments match variable names in DEFGRAD

[David Scherfgen]

Look how the partial derivatives of atan2 are defined:

(defgrad %atan2 ($x $y)
  #$$y/(y^2+x^2)$
  #$$-(x/(y^2+x^2))$)

Now when we differentiate an atan2 expression that uses exactly these arguments x and y, but in reverse order, we get bogus answers:

/* Wrong with arguments named y and x: */

(%i1)   diff(atan2(y,x),x);
(%o1)   -(1/(2*x))

(%i2)   diff(atan2(y,x),y);
(%o2)   1/(2*x)

/* Correct when renaming arguments: */

(%i3)   diff(atan2(yy,xx),xx);
(%o3)   -(yy/(yy^2+xx^2))

(%i4)   diff(atan2(yy,xx),yy);
(%o4)   xx/(yy^2+xx^2)

[Raymond Toy]

Oops. The derivatives should use $x and $y. defgrad should probably do more error checking. Maybe make sure every variable in the derivatives start with a $?

[David Scherfgen]

I think the problem is that variables are substituted sequentially using substitutel instead of in parallel using $psubstitute. I'm on it.

[David Scherfgen]

Fixed by commit [7bda3f] by using $psubstitute.