Customize printing of real numbers

[jasongrout]

From http://groups.google.com/group/sage-support/browse_thread/thread/06756df51d828bf4

we probably ought to make this easier to just print the 
first n digits after the decimal by default for RR numbers, or to not 
print out the trailing zeros.  I can't imagine telling my students, for 
example, that they need to do '%.3f'%num every time they come across a 
number, especially since they just want to display the equation, not 
format it as a string.

What do people think about this interface?

sage: RR.print_digits=3
sage: 3.09384
3.094
sage: RR.print_trailing_zeros=False
sage: RR.print_digits=None
sage: 3.09384
3.09384

Make it something like the RR.scientific_notation flag that is currently 
in use.

Additionally, and more flexibly, we could just have something like:

sage: RR.set_print_format('%.3f')
sage: RR(pi)
3.142

or more pythonically

sage: RR.print_format = '%.3f'
sage: RR(pi)
3.142

Edit: the patches below do not allow you to set a C format string or number of digits, but they do provide a framework for setting field-wide printing options, and wrap the current printing options Sage has implemented (plus a few minor extensions, I think).

CC: @robertwb @sagetrac-jkantor @williamstein @kcrisman @egourgoulhon

Component: numerical

Author: Jason Grout

Issue created by migration from https://trac.sagemath.org/ticket/7682

[jasongrout]

comment:1

Note that these extra zeros were introduced in the printing by the switch to pynac. They were eliminated a while ago in maxima by #4572.

[williamstein]

comment:2

I'm declaring a total feature freeze on sage-4.3.

[jasongrout]

comment:3

Here is a first cut of a print_options model for RealField that lets you specify default printing options for any RealField, all RealFields, and still lets you override the defaults when you actually print the numbers.

It mostly works. Docs need to be updated, deprecation warnings need to be added, and the interface for scientific notation needs to be revamped (no_sci and sci_not are confusing and inconsistent keyword choices!).

[jasongrout]

Author: Jason Grout

[jasongrout]

comment:6

I refreshed the patch which a much more comprehensive patch. This patch fixes all doctests in rings/*.pyx (running long doctests now). Documentation still needs to be updated, though, and some new doctests to test the new functionality.