def _sollya_annotate(self, center, rad, polys):
import sagesollya as sollya
logger = logging.getLogger(__name__ + ".sollya")
logger.info("calling annotatefunction() on %s derivatives", len(polys))
center = QQ(center)
sollya_fun = self._sollya_object
# sollya keeps all annotations, let's not bother with selecting
# the best one
for ord, pol0 in enumerate(polys):
pol = ZZ(ord).factorial() * pol0
sollya_pol = sum(
[c.center() * sollya.x**k for k, c in enumerate(pol)])
dom = RIF(center - rad,
center + rad) # XXX: dangerous when inexact
err_pol = pol.map_coefficients(lambda c: c - c.squash())
err = RIF(err_pol(RBF.zero().add_error(rad)))
with sollya.settings(display=sollya.dyadic):
logger = logging.getLogger(__name__ + ".sollya.annotate")
logger.debug("annotatefunction(%s, %s, %s, %s, %s);",
sollya_fun, sollya_pol, sollya.SollyaObject(dom),
sollya.SollyaObject(err),
sollya.SollyaObject(center))
sollya.annotatefunction(sollya_fun, sollya_pol, dom, err, center)
sollya_fun = sollya.diff(sollya_fun)
logger.info("...done")
def _disk(self, pt):
assert pt.is_real()
# Since approximation disks satisfy 2·rad ≤ dist(center, sing), any
# approximation disk containing pt must have rad ≤ dist(pt, sing)
max_rad = pt.dist_to_sing().min(self.max_rad)
# What we want is the largest such disk containing pt
expo = ZZ(max_rad.log(2).upper().ceil()) - 1 # rad = 2^expo
logger.log(logging.DEBUG - 2, "max_rad = %s, expo = %s", max_rad, expo)
while True:
approx_pt = pt.approx_abs_real(-expo)
mantissa = (approx_pt.squash() >> expo).floor()
if ZZ(mantissa) % 2 == 0:
mantissa += 1
center = mantissa << expo
dist = Point(center, pt.dop).dist_to_sing()
rad = RBF.one() << expo
logger.log(
logging.DEBUG - 2,
"candidate disk: approx_pt = %s, mantissa = %s, "
"center = %s, dist = %s, rad = %s", approx_pt, mantissa,
center, dist, rad)
if safe_ge(dist >> 1, rad):
break
expo -= 1
logger.debug("disk for %s: center=%s, rad=%s", pt, center, rad)
# pt may be a ball with nonzero radius: check that it is contained in
# our candidate disk
log = RBF.zero() if 0 in approx_pt else approx_pt.abs().log(2)
F = RealBallField(ZZ((expo - log).max(0).upper().ceil()) + 10)
dist_to_center = (F(approx_pt) - F(center)).abs()
if not safe_le(dist_to_center, rad):
assert not safe_gt((approx_pt.squash() - center).squash(), rad)
logger.info("check that |%s - %s| < %s failed", approx_pt, center,
rad)
return None, None
# exactify center so that subsequent computations are not limited by the
# precision of its parent
center = QQ(center)
return center, rad