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adding a little doc to FatGraph generating code #147

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58 changes: 40 additions & 18 deletions surface_dynamics/topology/fat_graph_exhaustive_generation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -19,13 +19,17 @@
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ

from .fat_graph import FatGraph, list_extrems
from .fat_graph import FatGraph


###########################
# Miscellaneous functions #
###########################

def minmax(l):
"""
Compute both the min and the max of a list.
"""
m = M = l[0]
for i in range(1, len(l)):
if l[i] < m:
Expand All @@ -36,6 +40,9 @@ def minmax(l):


def num_and_weighted_num(it):
"""
Compute both the number of terms and weighted sum of an iterable of pairs.
"""
from sage.rings.integer_ring import ZZ
from sage.rings.rational_field import QQ
s = QQ.zero()
Expand All @@ -62,7 +69,8 @@ def augment1(cm, aut_grp, g, callback):

This operation inserts two edges.

This augmentation function is sufficient to iterate through unicellular map.
This augmentation function is sufficient to iterate through
unicellular map.
"""
n = cm._n
fd = cm._fd
Expand Down Expand Up @@ -258,8 +266,8 @@ def augment3(cm, aut_grp, depth, min_degree, callback):
# callback to count elements (behaves somehow as a 2-tuple)
class CountAndWeightedCount:
def __init__(self):
self.count = ZZ(0)
self.weighted_count = QQ(0)
self.count = ZZ.zero()
self.weighted_count = QQ.zero()

def __repr__(self):
return "(%s, %s)" % (self.count, self.weighted_count)
Expand All @@ -279,19 +287,20 @@ def __getitem__(self, i):
raise IndexError("index out of range")

def __eq__(self, other):
if type(self) is not type(other):
if not isinstance(other, CountAndWeightedCount):
raise TypeError
return self.count == other.count and self.weighted_count == other.weighted_count

def __ne__(self, other):
if type(self) is not type(other):
if not isinstance(other, CountAndWeightedCount):
raise TypeError
return self.count != other.count or self.weighted_count != other.weighted_count

def __call__(self, cm, aut):
self.count += ZZ(1)
self.count += ZZ.one()
self.weighted_count += QQ((1, (1 if aut is None else aut.group_cardinality())))


# callback to list elements
class ListCallback:
def __init__(self, mutable=False):
Expand Down Expand Up @@ -323,6 +332,7 @@ def list(self):
/****************************************************************/
"""


class FatGraphsTrace:
"""
A class to trace the execution of the fat graphs generation.
Expand Down Expand Up @@ -480,6 +490,7 @@ def graphviz_tree(self, filename=None):
f.write(""" %s -> %s [color="%s"];\n""" % (s2, s3, col3))
yield cm3, a3


#################
# Main iterator #
#################
Expand Down Expand Up @@ -569,6 +580,7 @@ def run(self):
assert cm._n == 0, cm
augment3(cm, None, self._vmax - 2, max(1, self._vertex_min_degree), self)


##############
# Main class #
##############
Expand All @@ -577,6 +589,10 @@ class FatGraphs:
r"""
Isomorphism classes of fat graphs with topological constraints.

One can specify an exact value or lower and upper bounds for
several parameters. Not that lower bounds are inclusive and
upper bounds are exclusive, i.e. strict upper bounds.

EXAMPLES::

sage: from surface_dynamics import FatGraphs
Expand Down Expand Up @@ -718,7 +734,9 @@ class FatGraphs:
FatGraph('(0,4,1,3)(2,5)', '(0,4,2,1,3,5)'),
FatGraph('(0,4,3)(1,5,2)', '(0,2,4,1,3,5)')]
"""
def __init__(self, g=None, nf=None, ne=None, nv=None, vertex_min_degree=0, g_min=None, g_max=None, nf_min=None, nf_max=None, ne_min=None, ne_max=None, nv_min=None, nv_max=None):
def __init__(self, g=None, nf=None, ne=None, nv=None, vertex_min_degree=0,
g_min=None, g_max=None, nf_min=None, nf_max=None,
ne_min=None, ne_max=None, nv_min=None, nv_max=None):
r"""
INPUT:

Expand All @@ -731,6 +749,9 @@ def __init__(self, g=None, nf=None, ne=None, nv=None, vertex_min_degree=0, g_min
- ``nv``, ``nv_min``, ``nv_max`` - number of vertices

- ``vertex_min_degree`` - minimal degree of vertices (default to ``1``)

Note that all parameters for upper bounds will be interpreted
as strict upper bounds.
"""
self._gmin, self._gmax = self._get_interval(g, g_min, g_max, 0, 'g')
self._fmin, self._fmax = self._get_interval(nf, nf_min, nf_max, 1, 'nf')
Expand Down Expand Up @@ -800,20 +821,20 @@ def _adjust_bounds(self):
"""
# variable order: v, e, f, g
from sage.geometry.polyhedron.constructor import Polyhedron
eqns = [(-2, 1, -1, 1, 2)] # -2 + v - e + f + 2g = 0
ieqs = [(-self._vmin, 1, 0, 0, 0), # -vim + v >= 0
(-self._emin, 0, 1, 0, 0), # -emin + e >= 0
(-self._fmin, 0, 0, 1, 0), # -fmin + f >= 0
(-self._gmin, 0, 0, 0, 1), # -gmin + g >= 0
eqns = [(-2, 1, -1, 1, 2)] # -2 + v - e + f + 2g = 0
ieqs = [(-self._vmin, 1, 0, 0, 0), # -vim + v >= 0
(-self._emin, 0, 1, 0, 0), # -emin + e >= 0
(-self._fmin, 0, 0, 1, 0), # -fmin + f >= 0
(-self._gmin, 0, 0, 0, 1), # -gmin + g >= 0
(0, -self._vertex_min_degree, 2, 0, 0)] # -v_min_degree*v + 2e >= 0
if self._vmax is not None:
ieqs.append((self._vmax-1, -1, 0, 0, 0)) # v < vmax
ieqs.append((self._vmax-1, -1, 0, 0, 0)) # v < vmax
if self._emax is not None:
ieqs.append((self._emax-1, 0, -1, 0, 0)) # e < emax
ieqs.append((self._emax-1, 0, -1, 0, 0)) # e < emax
if self._fmax is not None:
ieqs.append((self._fmax-1, 0, 0, -1, 0)) # f < fmax
ieqs.append((self._fmax-1, 0, 0, -1, 0)) # f < fmax
if self._gmax is not None:
ieqs.append((self._gmax-1, 0, 0, 0, -1)) # g < gmax
ieqs.append((self._gmax-1, 0, 0, 0, -1)) # g < gmax
P = Polyhedron(ieqs=ieqs, eqns=eqns, ambient_dim=4, base_ring=QQ)
if P.is_empty():
self._vmin = self._vmax = 1
Expand All @@ -825,7 +846,7 @@ def _adjust_bounds(self):
if not P.is_compact():
raise ValueError('infinitely many fat graphs')

half = QQ((1,2))
half = QQ((1, 2))
self._vmin, self._vmax = minmax([v[0] for v in P.vertices_list()])
self._vmin = self._vmin.floor()
self._vmax = (self._vmax + half).ceil()
Expand Down Expand Up @@ -951,6 +972,7 @@ def list(self):
self.map_reduce(L)
return L.list()


###################
# Deprecated code #
###################
Expand Down
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