Hi,

I put up a preliminary todo list for the switch to pynac here:

http://wiki.sagemath.org/symbolics/switch_todo

I made the list by changing the default of the "var" command to create
pynac variables, and running the doctests. Looking at the results I
realised that I should have made other changes, such as export the new
symbolic ring (NSR) to the command line as SR. These are listed in the
first section of that page.

Next section gives a list of methods which the pynac symbolic
expressions (sage.symbolic.expression.Expression) need to implement.
The last section is miscellaneous stuff I didn't want to classify
further.

Some time next week, I will put a clean version of the switchover
patch, along with a new pynac package and some fixes to the sage
library so others can reproduce the results above.


After looking through the errors caused by the switch, I have a few
questions:

- Syntax for derivative and integrate functions:

Current symbolics allows this:

sage: (x^2).integrate()
x^3/3

I propose to make the integration variable explicit, by deprecating
this use, and encouraging the use of this:

sage: (x^2).integrate(x)
x^3/3

Note that the MMA syntax for Integrate also asks for the variable
explicitly.

Same goes for .derivative(), current symbolics works without specifying
a variable. While this usage might be ok in a univariate polynomial
ring, where the variable is known already, I think it's better to ask
the user to explicitly state the variable. 


- What do we do with the old tests? 

In the sage/calculus/ directory there are files which contain only
tests. What shall I do with these? Copy them to sage/symbolics/test,
change the old ones to use old symbolics variables to test the old
code, and make the new copies test the new code?


Or, what do you think should happen to the old code? How long are we
going to keep it around?


Comments?


Cheers,
Burcin

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