def solve4circles(syst, verbose=True):
"""
Given in syst is a list of polynomial systems.
Returns a list of tuples. Each tuple in the list of return
consists of the coordinates of the center and the radius of
a circle touching the three given circles.
"""
from phcpy.solver import solve
from phcpy.solutions import strsol2dict, is_real
(circle, eqscnt) = (0, 0)
result = []
for eqs in syst:
eqscnt = eqscnt + 1
if verbose:
print('solving system', eqscnt, ':')
for pol in eqs:
print(pol)
sols = solve(eqs, silent=True)
if verbose:
print('system', eqscnt, 'has', len(sols), 'solutions')
for sol in sols:
if is_real(sol, 1.0e-8):
soldic = strsol2dict(sol)
if soldic['r'].real > 0:
circle = circle + 1
ctr = (soldic['x'].real, soldic['y'].real)
rad = soldic['r'].real
result.append((ctr, rad))
if verbose:
print('solution circle', circle)
print('center =', ctr)
print('radius =', rad)
return result
def findEmbeddings_dist(syst, interval):
global prevSystem
global usePrev
global prevSolutions
# i = 0
y1_left, y1_right, y4_left, y4_right = interval
# print fileNamePref
while True:
if prevSystem and usePrev:
sols = track(syst, prevSystem, prevSolutions, tasks=tasks_num)
else:
sols = solve(syst, verbose=0, tasks=tasks_num)
result_real = []
for sol in sols:
soldic = strsol2dict(sol)
if is_real(sol, tolerance) and soldic['y1'].real>=y1_left and soldic['y1'].real<=y1_right and soldic['y4'].real>=y4_left and soldic['y4'].real<=y4_right:
result_real.append(soldic)
num_real = len(result_real)
if num_real%2==0 and len(sols)==numAll:
prevSystem = syst
prevSolutions = sols
return num_real
def straight_line(verbose=True):
"""
This function solves an instance where the five precision
points lie on a line. The coordinates are taken from Problem 7
of the paper by A.P. Morgan and C.W. Wampler.
Returns a list of solution dictionaries for the real solutions.
"""
from phcpy.solutions import strsol2dict, is_real
pt0 = Matrix([[ 0.50], [ 1.06]])
pt1 = Matrix([[-0.83], [-0.27]])
pt2 = Matrix([[-0.34], [ 0.22]])
pt3 = Matrix([[-0.13], [ 0.43]])
pt4 = Matrix([[ 0.22], [ 0.78]])
piv = Matrix([[1], [0]])
equ = polynomials(pt0,pt1,pt2,pt3,pt4,piv)
if verbose:
print 'the polynomial system :'
for pol in equ:
print pol
from phcpy.solver import solve
sols = solve(equ)
if verbose:
print 'the solutions :'
for sol in sols:
print sol
print 'computed', len(sols), 'solutions'
result = []
for sol in sols:
if is_real(sol, 1.0e-8):
soldic = strsol2dict(sol)
result.append(soldic)
return result
def findEmbeddings(syst):
global prevSystem
global usePrev
global prevSolutions
i = 0
while True:
if prevSystem and usePrev:
sols = track(syst, prevSystem, prevSolutions, tasks=tasks_num)
else:
sols = solve(syst, verbose=0, tasks=tasks_num)
result_real = []
for sol in sols:
soldic = strsol2dict(sol)
if is_real(sol, tolerance):
result_real.append(soldic)
num_real = len(result_real)
if num_real%4==0 and len(sols)==numAll:
prevSystem = syst
prevSolutions = sols
return num_real
elif numAllowedMissing and len(sols)==numAll:
print 'The number of real embeddings was not divisible by 4. ',
return num_real
elif numAllowedMissing and len(sols)>=numAll-numAllowedMissing:
print 'Continuing although there were '+str(numAll-len(sols))+' solutions missing. ',
return num_real
else:
usePrev = False
i += 1
# print 'PHC failed, trying again: '+str(i)
if i>=3:
print 'PHC failed 3 times',
return -1