def store_standard_system(polsys, **nbvar):
r"""
Stores the polynomials represented by the list of strings in *polsys* into
the container for systems with coefficients in standard double precision.
The number of variables is an optional argument given in *nbvar*.
If *nbvar* is omitted, then the system is assumed to be square.
Otherwise, suppose the number of variables equals 2 and pols is the list
of polynomials, then the call **store_standard_system(pols, nbvar=2)**
will store the polynomials in pols in the standard systems container.
"""
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
from phcpy.phcpy2c3 \
import py2c_syscon_initialize_number_of_standard_polynomials
from phcpy.phcpy2c3 import py2c_syscon_store_standard_polynomial
py2c_syscon_clear_standard_system()
dim = len(polsys)
fail = 0
py2c_syscon_initialize_number_of_standard_polynomials(dim)
for cnt in range(0, dim):
pol = polsys[cnt]
nchar = len(pol)
if (len(nbvar) == 0):
fail = py2c_syscon_store_standard_polynomial(
nchar, dim, cnt + 1, pol)
else:
nvr = list(nbvar.values())[0]
fail = py2c_syscon_store_standard_polynomial(
nchar, nvr, cnt + 1, pol)
if (fail != 0):
break
return fail
def store_standard_system(polsys, **nbvar):
r"""
Stores the polynomials represented by the list of strings in *polsys* into
the container for systems with coefficients in standard double precision.
The number of variables is an optional argument given in *nbvar*.
If *nbvar* is omitted, then the system is assumed to be square.
Otherwise, suppose the number of variables equals 2 and pols is the list
of polynomials, then the call **store_standard_system(pols, nbvar=2)**
will store the polynomials in pols in the standard systems container.
"""
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
from phcpy.phcpy2c3 \
import py2c_syscon_initialize_number_of_standard_polynomials
from phcpy.phcpy2c3 import py2c_syscon_store_standard_polynomial
py2c_syscon_clear_standard_system()
dim = len(polsys)
py2c_syscon_initialize_number_of_standard_polynomials(dim)
for cnt in range(0, dim):
pol = polsys[cnt]
nchar = len(pol)
if(len(nbvar) == 0):
fail = py2c_syscon_store_standard_polynomial(nchar, dim, cnt+1, pol)
else:
nvr = list(nbvar.values())[0]
fail = py2c_syscon_store_standard_polynomial(nchar, nvr, cnt+1, pol)
if(fail != 0):
break
return fail
def standard_start_diagonal_cascade(gamma=0, tasks=0):
r"""
Does the path tracking to start a diagonal cascade in standard double
precision. For this to work, the functions standard_diagonal_homotopy
and standard_diagonal_cascade_solutions must be executed successfully.
If *gamma* equals 0 on input, then a random gamma constant is generated,
otherwise, the given complex gamma will be used in the homotopy.
Multitasking is available, and activated by the *tasks* parameter.
Returns the target (system and its corresponding) solutions.
"""
from phcpy.phcpy2c3 import py2c_create_standard_homotopy
from phcpy.phcpy2c3 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c3 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
from phcpy.phcpy2c3 import py2c_copy_standard_target_solutions_to_container
from phcpy.phcpy2c3 import py2c_copy_standard_target_system_to_container
from phcpy.interface import load_standard_solutions
from phcpy.interface import load_standard_system
if(gamma == 0):
py2c_create_standard_homotopy()
else:
py2c_create_standard_homotopy_with_gamma(gamma.real, gamma.imag)
py2c_solve_by_standard_homotopy_continuation(tasks)
py2c_solcon_clear_standard_solutions()
py2c_syscon_clear_standard_system()
py2c_copy_standard_target_solutions_to_container()
# from phcpy.phcpy2c3 import py2c_write_standard_target_system
# print 'the standard target system :'
# py2c_write_standard_target_system()
py2c_copy_standard_target_system_to_container()
tsys = load_standard_system()
sols = load_standard_solutions()
return (tsys, sols)
def test_tableau():
"""
Tests on storing and loading of a tableau.
"""
from phcpy.phcpy2c3 import py2c_syscon_random_system
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
dim, nbrmon, deg, cff = 2, 4, 3, 0
py2c_syscon_random_system(dim, nbrmon, deg, cff)
pols = load_standard_system()
print('a random polynomial system :\n', pols)
neq, nvr, ptab = load_standard_tableau()
print('its tableau form :\n', ptab)
py2c_syscon_clear_standard_system()
store_standard_tableau(ptab)
storedpols = load_standard_system()
print('after clearing the container :\n', storedpols)
def test_standard_polyhedral_homotopy():
"""
Test on jumpstarting a polyhedral homotopy
in standard precision.
"""
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_Laurent_system
from phcpy.trackers import track
py2c_syscon_clear_standard_system()
py2c_syscon_clear_standard_Laurent_system()
qrt = random_trinomials()
mixvol = mixed_volume(qrt)
print('the mixed volume is', mixvol)
(rqs, rsols) = random_coefficient_system()
print('found %d solutions' % len(rsols))
newton_step(rqs, rsols)
print('tracking to target...')
pqr = permute_standard_system(qrt)
qsols = track(pqr, rqs, rsols)
newton_step(qrt, qsols)
def test_standard_polyhedral_homotopy():
"""
Test on jumpstarting a polyhedral homotopy
in standard precision.
"""
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_system
from phcpy.phcpy2c3 import py2c_syscon_clear_standard_Laurent_system
from phcpy.trackers import track
py2c_syscon_clear_standard_system()
py2c_syscon_clear_standard_Laurent_system()
qrt = random_trinomials()
mixvol = mixed_volume(qrt)
print('the mixed volume is', mixvol)
(rqs, rsols) = random_coefficient_system()
print('found %d solutions' % len(rsols))
newton_step(rqs, rsols)
print('tracking to target...')
pqr = permute_standard_system(qrt)
qsols = track(pqr, rqs, rsols)
newton_step(qrt, qsols)