def test_track(silent=True, precision="d", decimals=80):
"""
Tests the path tracking on a small random system.
Two random trinomials are generated and random constants
are added to ensure there are no singular solutions
so we can use this generated system as a start system.
The target system has the same monomial structure as
the start system, but with random real coefficients.
Because all coefficients are random, the number of
paths tracked equals the mixed volume of the system.
"""
from phcpy.solver import random_trinomials, real_random_trinomials
from phcpy.solver import solve, mixed_volume, newton_step
pols = random_trinomials()
real_pols = real_random_trinomials(pols)
from random import uniform as u
qone = pols[0][:-1] + ("%+.17f" % u(-1, +1)) + ";"
qtwo = pols[1][:-1] + ("%+.17f" % u(-1, +1)) + ";"
rone = real_pols[0][:-1] + ("%+.17f" % u(-1, +1)) + ";"
rtwo = real_pols[1][:-1] + ("%+.17f" % u(-1, +1)) + ";"
start = [qone, qtwo]
target = [rone, rtwo]
start_sols = solve(start, silent)
sols = track(target, start, start_sols, precision, decimals)
mixvol = mixed_volume(target)
print "mixed volume of the target is", mixvol
print "number of solutions found :", len(sols)
newton_step(target, sols, precision, decimals)
def compute_degree():
"""
Prompts the user for the parameters m and L.
Computes the degree of the cyclic n-roots set,
for n = m**2*L.
"""
(m, L, n) = ask_inputs()
print 'The dimension n = %d**2*%d = %d.' % (m, L, n)
coords = component_monomials(m, L)
print 'monomial coordinates of a cyclic %d-roots component :' % n
for c in coords:
print c
dim = m-1
print 'dimension =', dim
pol = ''
for c in coords:
pol = pol + c
print pol
sys = []
for k in range(dim):
sys.append(pol + ';')
print sys
from phcpy.solver import mixed_volume
deg = mixed_volume(sys)
print 'the degree of cyclic %d-roots set : %d' % (n, deg)
def degree(m, L):
"""
Returns the degree of the cyclic n-roots solution set,
for n = m**2*L.
"""
coords = component_monomials(m, L)
dim = m - 1
pol = ''
for c in coords:
pol = pol + c
sys = []
for k in range(m - 1):
sys.append(pol + ';')
from phcpy.solver import mixed_volume
deg = mixed_volume(sys)
return deg
def degree(m, L):
"""
Returns the degree of the cyclic n-roots solution set,
for n = m**2*L.
"""
coords = component_monomials(m, L)
dim = m-1
pol = ''
for c in coords:
pol = pol + c
sys = []
for k in range(m-1):
sys.append(pol + ';')
from phcpy.solver import mixed_volume
deg = mixed_volume(sys)
return deg