	MWRANK MAJOR CHANGES MADE (other than bug fixes)

NB This file has not been updated since 2006.  See git logs for all
more recent changes to eclib, including mwrank itself.

Oct 2006
========

28. [mwrank-2006-10-03] Minor: the lower bound code (#27 below) now
    works ok in normal precision.

Aug 2006
========

27. [mwrank-2006-08-23] Saturation more efficient using new lower
    height bounds (cf ANTS7 paper by JEC & SS).

Sept 2005
=========

24. Changed all exit() calls to abort() to enable better error
    catching in SAGE.

25. Better error message and abort() if attempting to round a floating
    point which does not fit into a long (on calculation of a and c
    n=bounds in mrank1.cc).

26. Curve input now catches syntax errors (and then aborts).

May 2005
========

22. Fourth arithmetic option NTL_ALL uses NTL library with
    multiprecision floating point arithmetic.

23. Released under GPL for the first time!

January 2005
==============

21. Points are now saturated after the 2-descent, using the method
    described in Siksek's and Prickett's theses.

September 2000
==============

20. Major improvement in handling of "large" quartics, after joint
    work with Stoll.

April 2000
==========

19. Bug fixes in mrank1.cc, caused wrong computation of selmer rank
    (when > rank).

May 1998
=========

18. Fixed various memory leaks.

April 1998
==========

17. Bug fixes to mrank1.cc: (a) added braces {...} to correct compiler
parsing resulting in "wrong type" messages, (b) correct computation of
Selmer rank when rank>0.  (Latter caused wrong Selmer rank of 2 for
curve 0,0,1,0,929]; thanks again to Fermigier.

Feb/March 1998
==============

15. Added autoconfigure to source distribution, thanks to Thomas
Papanikolaiou.  [Redesigned in 2005 mainly by WIlliam Stein]

16. Bug fix in flag initialization in mrank1.cc, to correctly handle
C2xC2 primes when one value of z is negative (failed on
[0,0,0,0,-50800]).  Thanks to Fermigier.

Nov 1997
========

8. Descent via 2-isogeny made much more efficient by better
book-keeping.

File(s) affected: mrank2.h/cc

9. Added second descent on to descent via 2-isogeny.  For hard cases
the multiprecision version is better here, but is also slower in
general so the released version is NOT multi.

File(s) affected: mrank2.h/cc

10. Improved bounds in quartic search.  This speeds things up well
when disc<0 (only relevant when no 2-torsion)

File(s) affected: mrank1.h/cc

11. Added version.h/cc so that program always displays its date of
compilation. 

File(s) affected: version.h/cc

12. Added options.h to give command-line option support.  See file
mwrank.options for details, or try "mwrank -h" for a summary.

File(s) affected: options.h, mwrank.options

13. Added so-called p-adic filtration to descent without isogeny,
making fuller use of sieving primes to use the explicit image of a
quartic in E(Qp)/2E(Qp) when this is C2 or C2xC2.

File(s) affected: mrank1.h/cc

14. Added PARI/GP output option "-o".  Also made mrank redundant as
"-c 0" (= default) turns off the infinte descent step, while "-c -1"
as before gives automatic computation of bound.

File(s) affected: options.h, mwrank.cc, mrank.cc

13 May 1996
===========

Important changes to mwrank since summer 1995 

See preprint "Classical Invariant Theory and 2-descent on elliptic
curves" [Journal of Symbolic Computation (Proceedings of the Second
Magma Conference, Milwaukee, May 1996), Jan/Feb 2001, pages 71-87] for
details of the theory behind these changes.

1. Transferring points from quartics to the curve:  Now uses one fixed
model for the curve E: y^2=x^3-27Ix-27J, and any rational point on a
quartic (yz)^2=g(x,z) with invariants I,J maps directly to a point on
E.  One can compute once and for all the isomorphism between E and the
original/minimal model to transfer these points back.  Result: simpler
code and no wasting time minimising many different models for E

File(s) affected: qc.h/cc

2. Sieving for quartics: now uses a 2-D sieve on (a,h) where h=8ac-b^2
instead of a 3-D sieve on (a,b,c), based on the seminvariant syzygy.
Given an (a,b,c) triple which passes the sieve, now compute the
seminvariant r and hence solve for d,e algebraically.  Result: simpler
code, less dependent on precision as no floating point arithmetic used
to solve for d,e.

File(s) affected: mrank1.h/cc

3. Testing equivalence of quartics:
(a) store with each quartic a hash value coding the number of roots
mod p for several primes p; equivalent quartics must have same hash
value, giving a quick necessary condition for equivalence.
(b) quartic equivalence testing now done algebraically, testing
whether  a third quartic has a root.  Vastly simpler code and much
more robust, not dependent on floating point precision.

File(s) affected: mequiv.h/cc

4. Using group structure to avoid/curtail searching for type 1
quartics.   When \Delta>0 the number of type 1 quartics is either 0 or
equal to the number of type 2s, according as there are no / are
rational points on the "egg" component of the real locus.   So one can
avoid searching for type 1s altogether if one knows in advance the
existence of such points, and in any case once a single type 1 quartic
is found one does not need to complete the search as one then knows
exactly how many tere are (assuming one has searched for type 2
quartics first).

File(s) affected: mrank1.h/cc

5. Searching for point on quartics: (a)add infinity to mod-p sieve, so
do not try denominators divisible by a prime p such that a is a
non-square mod p.  This eliminates many denominators very quickly.
(Suggested by J.  Gebel, Saarbruecken).  (b) For quartics of type
ax^4+cx^2+e, only search for x>0.  This saves half the time when there
are no points found, but does not necessarily save anything if a point
is found.

File(s) affected: msoluble.h/cc

7. (Theory still under construction! [See #20 above]) Avoid / curtail
search for quartics with "large" invariants (16I,64J), by careful
study of E(Q_2)/2E(Q_2).

7/8/95
======

1. Testing of equivalence of quartics 

(a) Uses a sieving idea of Samir Siksek's: each quartic is given a
code based on how many roots it has modulo 5 small (good) primes;
since equivalent quartics must have the same code this eliminates a
lot of equivalence tests.  For example, the 7 non-trivial quartics for
the famous curve [0,0,1,-7,6] all have different codes as can be seen
by running this curve with verbose=1.

(b) Uses an entirely algebraic equivalence test instead of using
floating point approximations to the roots, which regularly caused
problems with precision.  Now each pair of quartics determines a third
quartic with integer coefficients, which has an integer root iff the
original pair was equivalent.  This third quartic is NOT the "product"
of the first two in the Selmer group (it does not have the same
invariants), but is related to it.

2. From quartics to curves

This now uses a much simpler formula arising from the work used in
1(a) to give a point on the "IJ-curve" y^2=x^3-27Ix-J from a quartic
with invariants I,J and a rational point.   Previously each quartic
gave a new (isomorphic) curve with a point on it, and time was spent
reducing this to the standard model.

--------------------------------------------------------------------
