def testsolvebutton():
"""
Solves the cyclic 5-roots problems
and launches the solve button.
"""
from phcpy.families import cyclic
cyc5 = cyclic(5)
launchsolver(cyc5)
def testsolvebutton():
"""
Solves the cyclic 5-roots problem
and launches the solve button.
"""
from phcpy.families import cyclic
cyc5 = cyclic(5)
launchsolver(cyc5)
def testscroller():
"""
Solves the cyclic 5-roots problems
and launches the scroller.
"""
from phcpy.families import cyclic
from phcpy.solver import solve
cyc5 = cyclic(5)
sols = solve(cyc5, silent=True)
scrollsols(sols)
def testscroller():
"""
Solves the cyclic 5-roots problems
and launches the scroller.
"""
from phcpy.families import cyclic
from phcpy.solver import solve
cyc5 = cyclic(5)
sols = solve(cyc5, silent=True)
scrollsols(sols)
def testcoordinateplot():
"""
Solves the cyclic 5-roots problem,
prompts the user for an index of a coordinate,
and launches the plotcoordinate function.
"""
from phcpy.families import cyclic
from phcpy.solver import solve
print('solving the cyclic 5-roots problem ...')
cyc5 = cyclic(5)
sols = solve(cyc5, silent=True)
idx = int(input('Give an index : '))
plotcoordinate(sols, idx)
def testcoordinateplot():
"""
Solves the cyclic 5-roots problem,
prompts the user for an index of a coordinate,
and launches the plotcoordinate function.
"""
from phcpy.families import cyclic
from phcpy.solver import solve
print 'solving the cyclic 5-roots problem ...'
cyc5 = cyclic(5)
sols = solve(cyc5, silent=True)
idx = int(input('Give an index : '))
plotcoordinate(sols, idx)
def embedpoint(dim, point, addslack=True):
"""
Embeds the point in a witness set representation
for a cyclic n-roots solution set of dimension dim.
If addslack, then slack variables will be added
to square the embedded system.
"""
from phcpy.families import cyclic
nvr = len(point)
sys = cyclic(nvr)
emb = embedsys(dim, sys, addslack)
for p in point:
print p
for k in range(dim):
hyp = hyperplane(dim, point, addslack)
emb.append(hyp)
return emb
def embedpoint(dim, point, addslack=True):
"""
Embeds the point in a witness set representation
for a cyclic n-roots solution set of dimension dim.
If addslack, then slack variables will be added
to square the embedded system.
"""
from phcpy.families import cyclic
nvr = len(point)
sys = cyclic(nvr)
emb = embedsys(dim, sys, addslack)
for p in point:
print p
for k in range(dim):
hyp = hyperplane(dim, point, addslack)
emb.append(hyp)
return emb
def evaluate(point):
"""
Evaluates the point in the cyclic n-roots problem,
where n = len(point).
"""
from phcpy.families import cyclic
n = len(point)
f = cyclic(n)
d = globals()
for k in range(n):
var = 'x' + str(k)
d[var] = point[k]
for k in range(n):
var = 'x' + str(k)
print var, '=', d[var]
result = []
for r in f:
result.append(eval(r[0:-1]))
return result
def evaluate(point):
"""
Evaluates the point in the cyclic n-roots problem,
where n = len(point).
"""
from phcpy.families import cyclic
n = len(point)
f = cyclic(n)
d = globals()
for k in range(n):
var = 'x' + str(k)
d[var] = point[k]
for k in range(n):
var = 'x' + str(k)
print var, '=', d[var]
result = []
for r in f:
result.append(eval(r[0:-1]))
return result
""" Demonstration of the multitasked blackbox solver. Run this at the command line as time python d1.py. """ from phcpy.families import cyclic from phcpy.solver import solve c7 = cyclic(7) s = solve(c7, tasks=4) print 'number of solutions :', len(s)
"""
Illustration of the witness set computation of the cyclic 4-roots system.
"""
from phcpy.families import cyclic
c4 = cyclic(4)
from phcpy.sets import embed
c4e1 = embed(4, 1, c4)
print 'the embedded cyclic 4-roots problem :'
for pol in c4e1:
print pol
from phcpy.solver import solve
sols = solve(c4e1)
print 'computed', len(sols), 'solutions'
from phcpy.solutions import filter_zero_coordinates as filter
genpts = filter(sols, 'zz1', 1.0e-8, 'select')
print 'generic points :'
for sol in genpts:
print sol
from phcpy.sets import membertest
sdpoint = [-1, 0, -1, 0, 1, 0, 1, 0]
print 'testing in standard double precision ...'
print membertest(c4e1, genpts, 1, sdpoint, verbose=True, precision='d')
raw_input('*** hit enter to continue ***')
print 'testing in double double precision ...'
ddpoint = [-1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]
print membertest(c4e1, genpts, 1, ddpoint, verbose=True, precision='dd')
raw_input('*** hit enter to continue ***')
print 'testing in quad double precision ...'
ddpoint = [-1, 0, 0, 0, 0, 0, 0, 0, \
-1, 0, 0, 0, 0, 0, 0, 0, \
1, 0, 0, 0, 0, 0, 0, 0, \