hashes for derivatives of symbolic functions w.r.t. different variables are the same

[burcin]

From Alex Raichev on sage-support:

Hi all:

Upon upgrading to Sage 4.0, i can no longer make a dictionary with
derivatives as keys (see below).  Can someone please fix this?

Alex

----------------------------------------------------------------------
| Sage Version 4.0, Release Date: 2009-05-29                         |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: X= var('x,y')
sage: f= function('f',*X); f
f(x, y)
sage: for x in X:
....:     diff(f,x)
....:
D[0](f)(x, y)
D[1](f)(x, y)
sage: d= {}
sage: for x in X:
....:     d[diff(f,x)] = 1
....:
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call
last)

/Users/raichev/<ipython console> in <module>()

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression.__nonzero__ (sage/
symbolic/expression.cpp:7814)()

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression.test_relation
(sage/symbolic/expression.cpp:9187)()

/Applications/sage/local/lib/python2.5/site-packages/sage/rings/
complex_interval_field.pyc in __call__(self, x, im)
    286
    287             try:
--> 288                 return x._complex_mpfi_( self )  
    289             except AttributeError:
    290                 pass

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression.so in sage.symbolic.expression.Expression._complex_mpfi_
(sage/symbolic/expression.cpp:5484)()

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression_conversions.pyc in __call__(self, ex)
    212                 div = self.get_fake_div(ex)
    213                 return self.arithmetic(div, div.operator())
--> 214             return self.arithmetic(ex, operator)  
    215         elif operator in relation_operators:
    216             return self.relation(ex, operator)

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression_conversions.pyc in arithmetic(self, ex, operator)
   1424             return base ** expt
   1425         else:
-> 1426             return reduce(operator, map(self, operands))  
   1427
   1428     def composition(self, ex, operator):

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression_conversions.pyc in __call__(self, ex)
    216             return self.relation(ex, operator)
    217         elif isinstance(operator, FDerivativeOperator):
--> 218             return self.derivative(ex, operator)  
    219         else:
    220             return self.composition(ex, operator)

/Applications/sage/local/lib/python2.5/site-packages/sage/symbolic/
expression_conversions.pyc in derivative(self, ex, operator)
    344             NotImplementedError: derivative
    345         """
--> 346         raise NotImplementedError, "derivative"  
    347
    348     def arithmetic(self, ex, operator):

NotImplementedError: derivative

I suppose an immediate fix is to implement the derivative method in sage.symbolic.expression_conversions.Converter. I believe the right fix is to change pynac to pass on the parent for numerical approximation instead of just the precision. I'll work on making the necessary changes in pynac.

CC: @mwhansen

Component: symbolics

Author: Burcin Erocal

Reviewer: Golam Mortuza Hossain

Merged: Sage 4.1.1.rc1

Issue created by migration from https://trac.sagemath.org/ticket/6243

[burcin]

doctests for the fix

[burcin]

Author: Burcin Erocal

[burcin]

comment:1

Attachment: trac_6243-fderivative_hash.patch.gz

I have a fix for this in my local pynac tree. I took a shortcut and changed the fderivative hashes to include the parameters.

I'll make a new pynac package with fixes for some other bugs available soon.

[burcin]

comment:2

This now depends on the package linked from #6404.

Please follow the instructions on that ticket to apply & test.

[golam-m-hossain]

comment:3

I tested this out. Pynac changes seem fine to me. I encountered one issue though:

sage: d = {}
sage: d[x] = 1
sage: d
{x: 1}
sage: f(x) = function('f',x)
sage: d[diff(f(x),x)] = 2
sage: d.keys()
[D[0](f)(x), x]
sage: d.values()
[2, 1]
sage: d
!boom!

The origin of this !boom! lies in expression_conversions.py for fderivative
which is clearly NOT in purview of this patch. So I am going to give it a positive review
shortly.

[golam-m-hossain]

comment:4

Note: I am giving partial positive review because I tested this patch against my stable
sage-4.1. So if it applies cleanly on Sage-4.1.1.rc1 then that would be full positive from me.

[golam-m-hossain]

Reviewer: Golam Mortuza Hossain

[sagetrac-mvngu]

comment:6

I applied patches in the following order:

1. the spkg pynac-0.1.8.p2.spkg at Typeseting for conjugate() of symbolic function is inadequate #6404
2. trac_6404-conjugate_typesetting.patch
3. trac_6401-real_imag_typesetting.patch
4. trac_6377-exp_infinity.patch
5. trac_6243-fderivative_hash.patch
   All doctests pass in my merge tree. So I'm changing Typeseting for conjugate() of symbolic function is inadequate #6404, Typesettings of real() and imag() are broken #6401, exp(x) is broken at x=Infinity and x=-Infinity #6377 and hashes for derivatives of symbolic functions w.r.t. different variables are the same #6243 to positive review as per Golam's request.

[sagetrac-mvngu]

Merged: Sage 4.1.1.rc1