Typesetting partial derivatives in new symbolics

[golam-m-hossain]

New symbolics uses "D" format for derivatives instead of old "diff" format.

See the threads below for discussion on various related issues

[1] http://groups.google.com/group/sage-devel/browse_thread/thread/7479c3eeb96348a2

[2] http://groups.google.com/group/sage-devel/browse_thread/thread/2c8068f27c1fb642

Some patches attached to #5711 also has code for this.

CC: @jasongrout @sagetrac-mvngu @robertwb @eviatarbach @sagetrac-schymans @pjbruin @nbruin

Component: symbolics

Author: Burcin Erocal

Issue created by migration from https://trac.sagemath.org/ticket/6344

[burcin]

an attempt at implementing the MMA style, for testing only

[burcin]

Description changed:

--- 
+++ 
@@ -6,8 +6,6 @@
 
 **[2]**  http://groups.google.com/group/sage-devel/browse_thread/thread/2c8068f27c1fb642
 
-The purpose of this patch to decide the strategy: how to tackle the various issues while typesetting D derivative.
-
-Some part of the code from the patch #5711 should be taken out.
+Some patches attached to #5711 also has code for this.
  
 

[burcin]

comment:1

Attachment: trac_6344-mma_style_attempt.patch.gz

attachment: trac_6344-mma_style_attempt.patch implements an approximation to MMA style. It is just for testing, needs much more work for inclusion.

It doesn't look good in text only mode:

sage: f = function('f')
sage: f(x).derivative(x,3)
f^{(3)}(x)

[burcin]

comment:2

I uploaded a new patch at attachment: trac_6344-symbolic_derivative_print.patch.

The new patch keeps the text mode printing similar to the old one, but changes the printed parameters to indicate how many times each argument is differentiated. E.g., old output:

sage: var('x,y')
sage: f = function('f')
sage: f(x).derivative(x)
D[0](f)(x)
sage: f(x,x).derivative(x,2)
D[0, 0](f)(x, x) + 2*D[0, 1](f)(x, x) + D[1, 1](f)(x, x)

New output:

sage: f(x).derivative(x)
D[1](f)(x)
sage: f(x,x).derivative(x,2)
D[2, 0](f)(x, x) + 2*D[1, 1](f)(x, x) + D[0, 2](f)(x, x)

New latex output:

sage: latex(f(x).derivative(x))
f'\left(x\right)
sage: latex(f(x,x).derivative(x,2))
f^{(2,0)}\left(x, x\right) + 2 \, f^{(1,1)}\left(x, x\right) + f^{(0,2)}\left(x, x\right)

It would be better to add more documentation to explain the output, provide conversions to "textbook style" and fix other problems that pop up when printing derivatives:

sage: binomial(x,y).derivative(x)
<boom>
sage: latex(floor(x).derivative(x))
D[0]\left \lfloor x \right \rfloor
sage: latex(ceil(x).derivative(x))
D[0]\left \lceil x \right \rceil

However, I think we should settle on an output style ASAP, without letting too many releases go by.

Jason, Minh, can one (or both) of you review this?

[burcin]

Author: Burcin Erocal