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ports/math/sage/files/patch-src_sage_libs_eclib_mwrank.pyx
Thierry Thomas 886efe447a Fix build, with patch from John Cremona. 
Reported by:	pkg-fallout
2021-03-17 16:58:21 +00:00

418 lines
16 KiB
Cython
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--- src/sage/libs/eclib/mwrank.pyx.orig 2021-03-16 21:40:43 UTC
+++ src/sage/libs/eclib/mwrank.pyx
@@ -28,6 +28,7 @@ from cysignals.signals cimport sig_on, sig_off
from sage.cpython.string cimport char_to_str, str_to_bytes
from sage.cpython.string import FS_ENCODING
from sage.libs.eclib cimport bigint, Curvedata, mw, two_descent
+from sage.rings.all import Integer
cdef extern from "wrap.cpp":
### misc functions ###
@@ -55,8 +56,8 @@ cdef extern from "wrap.cpp":
char* mw_getbasis(mw* m)
double mw_regulator(mw* m)
int mw_rank(mw* m)
- int mw_saturate(mw* m, bigint* index, char** unsat,
- long sat_bd, int odd_primes_only)
+ int mw_saturate(mw* m, long* index, char** unsat,
+ long sat_bd, long sat_low_bd)
void mw_search(mw* m, char* h_lim, int moduli_option, int verb)
### two_descent ###
@@ -67,9 +68,8 @@ cdef extern from "wrap.cpp":
long two_descent_get_rank(two_descent* t)
long two_descent_get_rank_bound(two_descent* t)
long two_descent_get_selmer_rank(two_descent* t)
- void two_descent_saturate(two_descent* t, long sat_bd)
+ void two_descent_saturate(two_descent* t, long sat_bd, long sat_low_bd)
-
cdef object string_sigoff(char* s):
sig_off()
# Makes a python string and deletes what is pointed to by s.
@@ -445,7 +445,6 @@ cdef class _Curvedata: # cython class wrapping eclib
-1269581104000000
"""
sig_on()
- from sage.rings.all import Integer
return Integer(string_sigoff(Curvedata_getdiscr(self.x)))
def conductor(self):
@@ -467,7 +466,6 @@ cdef class _Curvedata: # cython class wrapping eclib
126958110400
"""
sig_on()
- from sage.rings.all import Integer
return Integer(string_sigoff(Curvedata_conductor(self.x)))
def isogeny_class(self, verbose=False):
@@ -503,6 +501,36 @@ cdef class _Curvedata: # cython class wrapping eclib
############# _mw #################
+def parse_point_list(s):
+ r"""
+ Parse a string representing a list of points.
+
+ INPUT:
+
+ - ``s`` (string) -- string representation of a list of points, for
+ example '[]', '[[1:2:3]]', or '[[1:2:3],[4:5:6]]'.
+
+ OUTPUT:
+
+ (list) a list of triples of integers, for example [], [[1,2,3]], [[1,2,3],[4,5,6]].
+
+ EXAMPLES::
+
+ sage: from sage.libs.eclib.mwrank import parse_point_list
+ sage: parse_point_list('[]')
+ []
+ sage: parse_point_list('[[1:2:3]]')
+ [[1, 2, 3]]
+ sage: parse_point_list('[[1:2:3],[4:5:6]]')
+ [[1, 2, 3], [4, 5, 6]]
+
+ """
+ s = s.replace(":", ",").replace(" ", "")
+ if s == '[]':
+ return []
+ pts = s[2:-2].split('],[')
+ return [[Integer(x) for x in pt.split(",")] for pt in pts]
+
cdef class _mw:
"""
Cython class wrapping eclib's mw class.
@@ -561,72 +589,37 @@ cdef class _mw:
sage: EQ.search(1)
P1 = [0:1:0] is torsion point, order 1
P1 = [-3:0:1] is generator number 1
- ...
- P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion)
-
- The previous command produces the following output::
-
- P1 = [0:1:0] is torsion point, order 1
- P1 = [-3:0:1] is generator number 1
- saturating up to 20...Checking 2-saturation
- Points have successfully been 2-saturated (max q used = 7)
- Checking 3-saturation
- Points have successfully been 3-saturated (max q used = 7)
- Checking 5-saturation
- Points have successfully been 5-saturated (max q used = 23)
- Checking 7-saturation
- Points have successfully been 7-saturated (max q used = 41)
- Checking 11-saturation
- Points have successfully been 11-saturated (max q used = 17)
- Checking 13-saturation
- Points have successfully been 13-saturated (max q used = 43)
- Checking 17-saturation
- Points have successfully been 17-saturated (max q used = 31)
- Checking 19-saturation
- Points have successfully been 19-saturated (max q used = 37)
+ saturating up to 20...Saturation index bound (for points of good reduction) = 3
+ Reducing saturation bound from given value 20 to computed index bound 3
+ Checking saturation at [ 2 3 ]
+ Checking 2-saturation
+ Points were proved 2-saturated (max q used = 7)
+ Checking 3-saturation
+ Points were proved 3-saturated (max q used = 7)
done
P2 = [-2:3:1] is generator number 2
- saturating up to 20...Checking 2-saturation
+ saturating up to 20...Saturation index bound (for points of good reduction) = 4
+ Reducing saturation bound from given value 20 to computed index bound 4
+ Checking saturation at [ 2 3 ]
+ Checking 2-saturation
possible kernel vector = [1,1]
This point may be in 2E(Q): [14:-52:1]
- ...and it is!
+ ...and it is!
Replacing old generator #1 with new generator [1:-1:1]
+ Reducing index bound from 4 to 2
Points have successfully been 2-saturated (max q used = 7)
Index gain = 2^1
- Checking 3-saturation
- Points have successfully been 3-saturated (max q used = 13)
- Checking 5-saturation
- Points have successfully been 5-saturated (max q used = 67)
- Checking 7-saturation
- Points have successfully been 7-saturated (max q used = 53)
- Checking 11-saturation
- Points have successfully been 11-saturated (max q used = 73)
- Checking 13-saturation
- Points have successfully been 13-saturated (max q used = 103)
- Checking 17-saturation
- Points have successfully been 17-saturated (max q used = 113)
- Checking 19-saturation
- Points have successfully been 19-saturated (max q used = 47)
- done (index = 2).
+ done, index = 2.
Gained index 2, new generators = [ [1:-1:1] [-2:3:1] ]
P3 = [-14:25:8] is generator number 3
- saturating up to 20...Checking 2-saturation
- Points have successfully been 2-saturated (max q used = 11)
- Checking 3-saturation
- Points have successfully been 3-saturated (max q used = 13)
- Checking 5-saturation
- Points have successfully been 5-saturated (max q used = 71)
- Checking 7-saturation
- Points have successfully been 7-saturated (max q used = 101)
- Checking 11-saturation
- Points have successfully been 11-saturated (max q used = 127)
- Checking 13-saturation
- Points have successfully been 13-saturated (max q used = 151)
- Checking 17-saturation
- Points have successfully been 17-saturated (max q used = 139)
- Checking 19-saturation
- Points have successfully been 19-saturated (max q used = 179)
- done (index = 1).
+ saturating up to 20...Saturation index bound (for points of good reduction) = 3
+ Reducing saturation bound from given value 20 to computed index bound 3
+ Checking saturation at [ 2 3 ]
+ Checking 2-saturation
+ Points were proved 2-saturated (max q used = 11)
+ Checking 3-saturation
+ Points were proved 3-saturated (max q used = 13)
+ done, index = 1.
P4 = [-1:3:1] = -1*P1 + -1*P2 + -1*P3 (mod torsion)
P4 = [0:2:1] = 2*P1 + 0*P2 + 1*P3 (mod torsion)
P4 = [2:13:8] = -3*P1 + 1*P2 + -1*P3 (mod torsion)
@@ -687,7 +680,7 @@ cdef class _mw:
sig_on()
return string_sigoff(mw_getbasis(self.x))
- def process(self, point, sat=0):
+ def process(self, point, saturation_bound=0):
"""
Processes the given point, adding it to the mw group.
@@ -697,10 +690,12 @@ cdef class _mw:
An ``ArithmeticError`` is raised if the point is not on the
curve.
- - ``sat`` (int, default 0) --saturate at primes up to ``sat``.
- No saturation is done if ``sat=0``. (Note that it is more
- efficient to add several points at once and then saturate
- just once at the end).
+ - ``saturation_bound`` (int, default 0) --saturate at primes up to ``saturation_bound``.
+ No saturation is done if ``saturation_bound=0``. If ``saturation_bound=-1`` then
+ saturation is done at all primes, by computing a bound on
+ the saturation index. Note that it is more efficient to add
+ several points at once and then saturate just once at the
+ end.
.. NOTE::
@@ -746,7 +741,7 @@ cdef class _mw:
cdef _bigint x,y,z
sig_on()
x,y,z = _bigint(point[0]), _bigint(point[1]), _bigint(point[2])
- r = mw_process(self.curve, self.x, x.x, y.x, z.x, sat)
+ r = mw_process(self.curve, self.x, x.x, y.x, z.x, saturation_bound)
sig_off()
if r != 0:
raise ArithmeticError("point (=%s) not on curve." % point)
@@ -757,8 +752,8 @@ cdef class _mw:
OUTPUT:
- (string) String representation of the points in the basis of
- the mw group.
+ (list) list of integer triples giving the projective
+ coordinates of the points in the basis.
EXAMPLES::
@@ -768,13 +763,13 @@ cdef class _mw:
sage: EQ = _mw(E)
sage: EQ.search(3)
sage: EQ.getbasis()
- '[[0:-1:1], [-1:1:1]]'
+ [[0, -1, 1], [-1, 1, 1]]
sage: EQ.rank()
2
"""
sig_on()
s = string_sigoff(mw_getbasis(self.x))
- return s
+ return parse_point_list(s)
def regulator(self):
"""
@@ -797,7 +792,7 @@ cdef class _mw:
sage: EQ = _mw(E)
sage: EQ.search(3)
sage: EQ.getbasis()
- '[[0:-1:1], [-1:1:1]]'
+ [[0, -1, 1], [-1, 1, 1]]
sage: EQ.rank()
2
sage: EQ.regulator()
@@ -824,40 +819,55 @@ cdef class _mw:
sage: EQ = _mw(E)
sage: EQ.search(3)
sage: EQ.getbasis()
- '[[0:-1:1], [-1:1:1]]'
+ [[0, -1, 1], [-1, 1, 1]]
sage: EQ.rank()
2
"""
sig_on()
r = mw_rank(self.x)
sig_off()
- from sage.rings.all import Integer
return Integer(r)
- def saturate(self, int sat_bd=-1, int odd_primes_only=0):
+ def saturate(self, int sat_bd=-1, int sat_low_bd=2):
"""
Saturates the current subgroup of the mw group.
INPUT:
- - ``sat_bnd`` (int, default -1) -- bound on primes at which to
- saturate. If -1 (default), compute a bound for the primes
- which may not be saturated, and use that.
+ - ``sat_bnd`` (int, default -1) -- upper bound on primes at
+ which to saturate. If -1 (default), compute a bound for the
+ primes which may not be saturated, and use that. Otherwise,
+ the bound used is the minumum of the value of ``sat_bnd``
+ and the computed bound.
- - ``odd_primes_only`` (bool, default ``False``) -- only do
- saturation at odd primes. (If the points have been found
- via 2-descent they should already be 2-saturated.)
+ - ``sat_low_bd`` (int, default 2) -- only do saturation at
+ prime not less than this. For exampe, if the points have
+ been found via 2-descent they should already be 2-saturated,
+ and ``sat_low_bd=3`` is appropriate.
OUTPUT:
(tuple) (success flag, index, list) The success flag will be 1
unless something failed (usually an indication that the points
- were not saturated but the precision is not high enough to
- divide out successfully). The index is the index of the mw
- group before saturation in the mw group after. The list is a
- string representation of the primes at which saturation was
- not proved or achieved.
+ were not saturated but eclib was not able to divide out
+ successfully). The index is the index of the mw group before
+ saturation in the mw group after. The list is a string
+ representation of the primes at which saturation was not
+ proved or achieved.
+ .. NOTE::
+
+ ``eclib`` will compute a bound on the saturation index. If
+ the computed saturation bound is very large and ``sat_bnd`` is
+ -1, ``eclib`` may output a warning, but will still attempt to
+ saturate up to the computed bound. If a positive value of
+ ``sat_bnd`` is given which is greater than the computed bound,
+ `p`-saturation will only be carried out for primes up to the
+ compated bound. Setting ``sat_low_bnd`` to a value greater
+ than 2 allows for saturation to be done incrementally, or for
+ exactly one prime `p` by setting both ``sat_bd`` and
+ ``sat_low_bd`` to `p`.
+
EXAMPLES::
sage: from sage.libs.eclib.mwrank import _Curvedata
@@ -872,34 +882,23 @@ cdef class _mw:
sage: EQ
[[-1:1:1]]
- If we set the saturation bound at 2, then saturation will fail::
+ If we set the saturation bound at 2, then saturation will not
+ enlarge the basis, but the success flag is still 1 (True)
+ since we did not ask to check 3-saturation::
sage: EQ = _mw(E)
sage: EQ.process([494, -5720, 6859]) # 3 times another point
sage: EQ.saturate(sat_bd=2)
- Saturation index bound = 10
- WARNING: saturation at primes p > 2 will not be done;
- points may be unsaturated at primes between 2 and index bound
- Failed to saturate MW basis at primes [ ]
- (0, 1, '[ ]')
+ (1, 1, '[ ]')
sage: EQ
[[494:-5720:6859]]
- The following output is also seen in the preceding example::
-
- Saturation index bound = 10
- WARNING: saturation at primes p > 2 will not be done;
- points may be unsaturated at primes between 2 and index bound
- Failed to saturate MW basis at primes [ ]
-
-
"""
- cdef _bigint index
+ cdef long index
cdef char* s
cdef int ok
sig_on()
- index = _bigint()
- ok = mw_saturate(self.x, index.x, &s, sat_bd, odd_primes_only)
+ ok = mw_saturate(self.x, &index, &s, sat_bd, sat_low_bd)
unsat = string_sigoff(s)
return ok, index, unsat
@@ -1094,7 +1093,6 @@ cdef class _two_descent:
sig_on()
r = two_descent_get_rank(self.x)
sig_off()
- from sage.rings.all import Integer
return Integer(r)
def getrankbound(self):
@@ -1128,7 +1126,6 @@ cdef class _two_descent:
sig_on()
r = two_descent_get_rank_bound(self.x)
sig_off()
- from sage.rings.all import Integer
return Integer(r)
def getselmer(self):
@@ -1161,7 +1158,6 @@ cdef class _two_descent:
sig_on()
r = two_descent_get_selmer_rank(self.x)
sig_off()
- from sage.rings.all import Integer
return Integer(r)
def ok(self):
@@ -1222,10 +1218,21 @@ cdef class _two_descent:
"""
return two_descent_get_certain(self.x)
- def saturate(self, saturation_bound=0):
+ def saturate(self, saturation_bound=0, lower=3):
"""
Carries out saturation of the points found by a 2-descent.
+ INPUT:
+
+ - ``saturation_bound`` (int) -- an upper bound on the primes
+ `p` at which `p`-saturation will be carried out, or -1, in
+ which case ``eclib`` will compute an upper bound on the
+ saturation index.
+
+ - ``lower`` (int, default 3) -- do no `p`-saturation for `p`
+ less than this. The default is 3 since the points found
+ during 2-descent will be 2-saturated.
+
OUTPUT:
None.
@@ -1257,7 +1264,7 @@ cdef class _two_descent:
'[[1:-1:1], [-2:3:1], [-14:25:8]]'
"""
sig_on()
- two_descent_saturate(self.x, saturation_bound)
+ two_descent_saturate(self.x, saturation_bound, 3)
sig_off()
def getbasis(self):
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