def initialTerms(poly, positivesOnly=False):
"""
Return a list of (*gamma,c)* pairs giving the
first terms of each Puiseux solution of :py:data:`poly`.
"""
#hull = lowerHull(poly.support())
hull = ploty(poly.support(), 'hi')
if len(hull) == 1:
return []
slopes = []
for i in xrange(len(hull) - 1):
slopes.append(slp(hull[i], hull[i + 1]))
slope_vertices = {
} # dictionary with slope:[list of vertices on that edge]
for slope in slopes:
slope_vertices[slope] = []
slope_vertices[slopes[0]].append(hull[0][0])
oldSlope = slopes[0]
for i in xrange(1, len(hull)):
slope_vertices[oldSlope].append(hull[i][0])
if (i < len(hull) - 1) and slopes[i] != oldSlope:
oldSlope = slopes[i]
slope_vertices[oldSlope].append(hull[i][0])
slope_roots = {}
for slope in slope_vertices.keys():
if positivesOnly and slope >= 0: continue
deg = max(slope_vertices[slope])
toAdd = []
for i in xrange(deg + 1):
toAdd.append(0)
slope_roots[slope] = toAdd
for i in slope_vertices[slope]:
slope_roots[slope][i] = poly.internal[i].LC()
slope_roots[slope].reverse()
for key in slope_roots.keys():
while slope_roots[key][-1] == 0: #don't care about coeffs that are 0
slope_roots[key].pop()
toAdd = []
for x in np.roots(slope_roots[key]):
toAdd.append(complex(x))
slope_roots[key] = toAdd
toReturn = []
for slope in slope_roots.keys():
for coeff in slope_roots[slope]:
toReturn.append((-slope, coeff))
############################
# Removing duplicates
toReturn2 = []
for item in toReturn:
if item not in toReturn2:
toReturn2.append(item)
############################
return toReturn2
def initialTerms(poly,positivesOnly=False):
"""
Return a list of (*gamma,c)* pairs giving the
first terms of each Puiseux solution of :py:data:`poly`.
"""
#hull = lowerHull(poly.support())
hull = ploty(poly.support(),'hi')
if len(hull)==1:
return []
slopes = []
for i in xrange(len(hull)-1):
slopes.append(slp(hull[i],hull[i+1]))
slope_vertices = {} # dictionary with slope:[list of vertices on that edge]
for slope in slopes:
slope_vertices[slope] = []
slope_vertices[slopes[0]].append(hull[0][0])
oldSlope = slopes[0]
for i in xrange(1,len(hull)):
slope_vertices[oldSlope].append(hull[i][0])
if (i<len(hull)-1) and slopes[i]!=oldSlope:
oldSlope = slopes[i]
slope_vertices[oldSlope].append(hull[i][0])
slope_roots = {}
for slope in slope_vertices.keys():
if positivesOnly and slope>=0: continue
deg = max(slope_vertices[slope])
toAdd = []
for i in xrange(deg+1):
toAdd.append(0)
slope_roots[slope] = toAdd
for i in slope_vertices[slope]:
slope_roots[slope][i] = poly.internal[i].LC()
slope_roots[slope].reverse()
for key in slope_roots.keys():
while slope_roots[key][-1]==0: #don't care about coeffs that are 0
slope_roots[key].pop()
toAdd = []
for x in np.roots(slope_roots[key]):
toAdd.append(complex(x))
slope_roots[key] = toAdd
toReturn = []
for slope in slope_roots.keys():
for coeff in slope_roots[slope]:
toReturn.append((-slope,coeff))
############################
# Removing duplicates
toReturn2 = []
for item in toReturn:
if item not in toReturn2:
toReturn2.append(item)
############################
return toReturn2
def initialTerms(poly,positivesOnly=False):
"""
Return a list of (gamma,c) pairs giving the
first terms of each Puiseux solution of poly.
"""
hull = lowerHull(poly.support())
slopes = [slp(hull[i],hull[i+1]) for i in xrange(len(hull)-1)]
# dictionary with slope:[list of vertices on that edge]
slope_vertices = {slope:[] for slope in slopes}
slope_vertices[slopes[0]].append(hull[0][0])
oldSlope = slopes[0]
for i in xrange(1,len(hull)):
slope_vertices[oldSlope].append(hull[i][0])
if (i<len(hull)-1) and slopes[i]!=oldSlope:
oldSlope = slopes[i]
slope_vertices[oldSlope].append(hull[i][0])
slope_roots = {}
for slope in slope_vertices:
if positivesOnly and slope>=0: continue
deg = max(slope_vertices[slope])
slope_roots[slope] = [0 for i in xrange(deg+1)]
for i in slope_vertices[slope]:
slope_roots[slope][i] = poly.internal[i].LC()
slope_roots[slope].reverse()
for key in slope_roots:
while slope_roots[key][-1]==0: #don't care about coeffs that are 0
slope_roots[key].pop()
slope_roots[key]=[complex(x) for x in np.roots(slope_roots[key])]
toReturn = []
for slope in slope_roots:
for coeff in slope_roots[slope]:
toReturn.append((-slope,coeff))
#########################
# Removing duplicates
toReturn2 = []
for item in toReturn:
if item not in toReturn2:
toReturn2.append(item)
#########################
return toReturn2
def initialTerms(poly, positivesOnly=False):
"""
Return a list of (gamma,c) pairs giving the
first terms of each Puiseux solution of poly.
"""
hull = lowerHull(poly.support())
slopes = [slp(hull[i], hull[i + 1]) for i in xrange(len(hull) - 1)]
# dictionary with slope:[list of vertices on that edge]
slope_vertices = {slope: [] for slope in slopes}
slope_vertices[slopes[0]].append(hull[0][0])
oldSlope = slopes[0]
for i in xrange(1, len(hull)):
slope_vertices[oldSlope].append(hull[i][0])
if (i < len(hull) - 1) and slopes[i] != oldSlope:
oldSlope = slopes[i]
slope_vertices[oldSlope].append(hull[i][0])
slope_roots = {}
for slope in slope_vertices:
if positivesOnly and slope >= 0: continue
deg = max(slope_vertices[slope])
slope_roots[slope] = [0 for i in xrange(deg + 1)]
for i in slope_vertices[slope]:
slope_roots[slope][i] = poly.internal[i].LC()
slope_roots[slope].reverse()
for key in slope_roots:
while slope_roots[key][-1] == 0: #don't care about coeffs that are 0
slope_roots[key].pop()
slope_roots[key] = [complex(x) for x in np.roots(slope_roots[key])]
toReturn = []
for slope in slope_roots:
for coeff in slope_roots[slope]:
toReturn.append((-slope, coeff))
#########################
# Removing duplicates
toReturn2 = []
for item in toReturn:
if item not in toReturn2:
toReturn2.append(item)
#########################
return toReturn2