Derivative D acts wrongly on symbolic integration

[golam-m-hossain]

In new symbolics, derivative operator does not know
how to act on symbolic integration.

sage: f(x) = function('f',x)
sage: g = integrate(f(x),x)
sage: g.diff(x)
D[0](integrate)(f(x), x)*D[0](f)(x) + D[1](integrate)(f(x), x)

Patches:

• Both patches should be applied in order (spkg is already included in sage-4.1.1).

Apart from solving this bug it introduces couple
of new features (by moving it into new symbolics' SFunction sub-class)

(1) Stricter syntax:

http://groups.google.com/group/sage-devel/browse_thread/thread/3e98841311653d7a

(2) Numerical approximation using .n() method

(3) Updated "integrate?" docstring

(4) Graceful handling of situations where integration is specified w.r.t. an expression

http://groups.google.com/group/sage-devel/browse_thread/thread/cd9f91338635ada9

(4) Behind the scene it provides a framework to hook up easily new integration algorithm written within sage.

Component: symbolics

Author: Burcin Erocal, Golam Mortuza Hossain

Reviewer: Tim Dumol, Karl-Dieter Crisman, Ross Kyprianou, Minh Van Nguyen

Merged: sage-4.3.3.alpha1

Issue created by migration from https://trac.sagemath.org/ticket/6465

[burcin]

support disabling chain rule for symbolic functions

[burcin]

comment:1

Attachment: trac_6465-chain_rule.patch.gz

attachment: trac_6465-chain_rule.patch adds support for disabling chain rule for symbolic functions. It depends on the new pynac package here:

http://sage.math.washington.edu/home/burcin/pynac/pynac-0.1.8.p2.spkg

[golam-m-hossain]

Description changed:

--- 
+++ 
@@ -7,3 +7,28 @@
 sage: g.diff(x)
 D[0](integrate)(f(x), x)*D[0](f)(x) + D[1](integrate)(f(x), x)
 ```
+
+**Patches**:
+
+* Both patches should be applied in order (spkg is already included in sage-4.1.1).
+
+Apart from solving this bug it introduces couple
+of new features (by moving it into new symbolics' SFunction sub-class)
+
+ (1) Stricter syntax:
+
+  http://groups.google.com/group/sage-devel/browse_thread/thread/3e98841311653d7a
+
+ (2) Numerical approximation using .n() method
+
+ (3) Updated "integrate?" docstring
+ 
+ (4) Graceful handling of situations where integration is specified w.r.t. an expression
+
+  http://groups.google.com/group/sage-devel/browse_thread/thread/cd9f91338635ada9
+
+
+
+ (4) Behind the scene it provides a framework to hook up easily new integration algorithm written within sage.
+
+

[golam-m-hossain]

Author: Burcin Erocal, Golam Mortuza Hossain

[golam-m-hossain]

Attachment: trac_6465-moves-integration-into-sfunction-subclass.patch.gz

Should be applied after the chain-rule patch

[kcrisman]

comment:3

There need to be deprecation warnings for things like

sage: integral(sin(x), pi, 2*pi)
sage: integral(sin(x)^3

[TimDumol]

comment:4

The sudden API change probably merits a deprecation warning, as kcrisman said. Also:

Doctest failure:

sage -t -long devel/sage/sage/libs/ginac/decl.pxi         
         [0.1 s]                                          
sage -t -long devel/sage/sage/misc/functional.py          
**********************************************************************
File "/opt/sage-bin/devel/sage-deriv/sage/misc/functional.py", line 412:
    sage: integral(exp(-x), (x, 1, oo))                                 
Expected:                                                               
    e^(-1)                                                              
Got:                                                                    
    gamma_incomplete(1, 1)                                              
**********************************************************************  
1 items had failures:                                                   
   1 of  15 in __main__.example_25                                      
***Test Failed*** 1 failures.                                           
For whitespace errors, see the file /opt/sage-bin/tmp/.doctest_functional.py
         [9.3 s]

[TimDumol]

Reviewer: Tim Dumol