mwrank interface improvements

[rlmill]

Ticket TODO list:

• src/qrank/mrank1.cc needs to be patched, as John described.

• Switch all uses of mwrank from the interface to the library.

• Make sure that all options to mwrank are properly used.

• Make sure that all output from mwrank is available.

• ...?

Component: elliptic curves

Author: Robert Miller

Reviewer: John Cremona

Merged: sage-4.3.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7575

[rlmill]

comment:1

With the patch trac_7575-heegner_index_example.patch applied on top of (sage-4.3 plus) #7576 and #7819, I get the following:

sage: E = EllipticCurve('123a1')
sage: E.prove_BSD(verbosity=2)
p = 2: true by 2-descent
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
...<SNIP>...
/Users/rlmill/sage-4.3/local/lib/python2.6/site-packages/sage/libs/mwrank/interface.pyc in gens(self)
    310         """
    311         self.saturate()
--> 312         return eval(self.__two_descent_data().getbasis().replace(":",","))
    313 
    314     def certain(self):

RuntimeError: 

[JohnCremona]

comment:2

In the original example (in this ticket's description), note that calling E.two_descent() produces output to the screen but returns nothing and stores nothing in E which was not there before. E.gens() by default uses mwrank_shell, which does not allow any passing of parameters (see the TODO block in the docstring), not because it cannot be done but because we have not implemented it. The non-default option mwrank_lib goes via creation of the associated mwrank_curve which also does not allow changing of the parameters.

What I suggest is that we use mwrank_lib by default; that we allow passing of all the parameters which the two_descent function of an mwrank elliptic curve allows from all higher level functions which call mwrank (e.g. gens()) and that we use the enquiry functions provided by mwrank to find out how successful it has been: it can give you a lower and upper bound for the rank, so all is well if they are equal and in any case can give you a number of gens equal to the lower bound. The only difficulty would be with caching rank and gens -- probably best not to do so at all unless we have certainly found them.

Does this all make sense? I think it would be much more helpful to have sample curves where things do not work well and sample code which does not go via a call to the (presumably complicated) function prove_BSD()!

[JohnCremona]

comment:3

Another thought: perhaps we should have a class to hold a list of all mwrank-options.

[rlmill]

comment:4

Here is another part where using the library would help:

sage: EllipticCurve([1, 1, 1, -9718914979, 370891890941633]).mwrank()
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (47, 0))

ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (362, 0))

---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)

/Users/rlmill/sage-4.3.1.rc1/devel/sage-main/<ipython console> in <module>()

/Users/rlmill/sage-4.3.1.rc1/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_rational_field.pyc in mwrank(self, options)
    484             from sage.interfaces.all import Mwrank
    485             mwrank = Mwrank(options=options)
--> 486         return mwrank(list(self.a_invariants()))
    487 
    488     def conductor(self, algorithm="pari"):

/Users/rlmill/sage-4.3.1.rc1/local/lib/python2.6/site-packages/sage/interfaces/mwrank.pyc in __call__(self, cmd)
     75 
     76     def __call__(self, cmd):
---> 77         return self.eval(str(cmd))
     78 
     79     def eval(self, *args, **kwds):

/Users/rlmill/sage-4.3.1.rc1/local/lib/python2.6/site-packages/sage/interfaces/mwrank.pyc in eval(self, *args, **kwds)
     95             # Doing _start again fixes that always. See trac #5157.
     96             self._start()
---> 97         return Expect.eval(self, *args, **kwds)
     98 
     99     def console(self):

/Users/rlmill/sage-4.3.1.rc1/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in eval(self, code, strip, synchronize, locals, **kwds)
    981         try:
    982             with gc_disabled():
--> 983                 return '\n'.join([self._eval_line(L, **kwds) for L in code.split('\n') if L != ''])
    984         except KeyboardInterrupt:
    985             # DO NOT CATCH KeyboardInterrupt, as it is being caught

/Users/rlmill/sage-4.3.1.rc1/local/lib/python2.6/site-packages/sage/interfaces/expect.pyc in _eval_line(self, line, allow_use_file, wait_for_prompt)
    666                         # we expect to get an EOF if we're quitting.
    667                         return ''
--> 668                     raise RuntimeError, "%s\n%s crashed executing %s"%(msg,self, line)
    669                 out = E.before
    670             else:

RuntimeError: End Of File (EOF) in read_nonblocking(). Empty string style platform.
<pexpect.spawn instance at 0xebec738>
version: 2.0 ($Revision: 1.151 $)
command: /Users/rlmill/sage-4.3.1.rc1/local/bin/mwrank
args: ['/Users/rlmill/sage-4.3.1.rc1/local/bin/mwrank']
patterns:
    Enter curve: 
buffer (last 100 chars): 
before (last 100 chars): up to 232549 (square a first...)
Attempt to round -9608958007.0937 to a long int fails, aborting!

after: <class 'pexpect.EOF'>
match: None
match_index: None
exitstatus: None
flag_eof: 1
pid: 90387
child_fd: 7
timeout: None
delimiter: <class 'pexpect.EOF'>
logfile: None
maxread: 10000
searchwindowsize: None
delaybeforesend: 0
Mwrank crashed executing [1, 1, 1, -9718914979, 370891890941633]

[JohnCremona]

comment:5

This behaviour is supposed to be caught by mwrank C++ code, so that this can be detected gracefully by using the ok() function.

As we are planning to replace the pexpect interface entirely this will be dealt with. (There is absolutely no reason to use the interactive interface when everything can be found from the library interface.)

[JohnCremona]

comment:6

Replying to @JohnCremona:

This behaviour is supposed to be caught by mwrank C++ code, so that this can be detected gracefully by using the ok() function.

On looking into it, I see that this will need a patch to the file src/qrank/mrank1.cc, since I just call abort() when I try to round to a long int and it overflows. Instead I need to catch that properly. (Pity C++ does not have the try/except functionality of python).

So this particular bug / behaviour needs to be flagged as "report upstream (done) and wait for a patch from upstream (on my todo list)".

As we are planning to replace the pexpect interface entirely this will be dealt with. (There is absolutely no reason to use the interactive interface when everything can be found from the library interface.)

[rlmill]

Description changed:

--- 
+++ 
@@ -1,26 +1,11 @@
-The documentation for `EllipticCurve.gens` says:
+Ticket TODO list:
 
-```
-HINT: If you would like to control the height bounds used in the
-2-descent, first call the two_descent function with those height
-bounds. However that function, while it displays a lot of output,
-returns no values.
-```
+* `src/qrank/mrank1.cc` needs to be patched, as John described.
 
-However, this doesn't work, because `EllipticCurve.gens` doesn't know about it:
+* Switch all uses of mwrank from the interface to the library.
 
-```
-sage: x,y=var('x,y')
-sage: E = EllipticCurve(y^2 + x*y + y == x^3 - 10525529*x - 21714803524)
-sage: E.two_descent(second_limit=11, verbose=False)
-sage: E.gens()
-*BOOM*
-```
+* Make sure that all options to mwrank are properly used.
 
-Despite:
+* Make sure that all output from mwrank is available.
 
-```
-sage: A = E.mwrank_curve()
-sage: A.gens()
-[[1737553736529419603224344006006032245457891558644991945121564365621L, -1605018042749306385493128932071874233128412498544999275367916849231954L, 2038538889602737161869943561394015059980551394212496529475951L]]
-```
+* ...?

[rlmill]

comment:7

The documentation for EllipticCurve.gens says:

HINT: If you would like to control the height bounds used in the
2-descent, first call the two_descent function with those height
bounds. However that function, while it displays a lot of output,
returns no values.

However, this doesn't work, because EllipticCurve.gens doesn't know about it:

sage: x,y=var('x,y')
sage: E = EllipticCurve(y^2 + x*y + y == x^3 - 10525529*x - 21714803524)
sage: E.two_descent(second_limit=11, verbose=False)
sage: E.gens()
*BOOM*

Despite:

sage: A = E.mwrank_curve()
sage: A.gens()
[[1737553736529419603224344006006032245457891558644991945121564365621L, -1605018042749306385493128932071874233128412498544999275367916849231954L, 2038538889602737161869943561394015059980551394212496529475951L]]