def standard_pade_approximants(pols, sols, idx=1, numdeg=2, dendeg=2, \
nbr=4, verbose=True):
r"""
Computes Pade approximants based on the series in standard double
precision for the polynomials in *pols*, where the leading
coefficients of the series are the solutions in *sols*.
On entry are the following seven parameters:
*pols*: a list of string representations of polynomials,
*sols*: a list of solutions of the polynomials in *pols*,
*idx*: index of the series parameter, by default equals 1,
*numdeg*: the degree of the numerator,
*dendeg*: the degree of the denominator,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_solutions
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c3 \
import py2c_standard_Pade_approximant as Pade_approximants
from phcpy.phcpy2c3 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c3 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c3 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print("the polynomials :")
for pol in pols:
print(pol)
print("Number of variables :", nbsym)
store_standard_system(pols, nbvar=nbsym)
store_standard_solutions(nbsym, sols)
fail = Pade_approximants(idx, numdeg, dendeg, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print("An error occurred in the Pade constructor.")
else:
print("Computed %d Pade approximants." % size)
result = []
for k in range(1, size + 1):
py2c_syspool_copy_to_standard_container(k)
sersol = load_standard_system()
substsersol = substitute_symbol(sersol, idx)
result.append(make_fractions(substsersol))
py2c_syspool_standard_clear()
return result
def initialize_standard_solution(nvar, sol):
r"""
A standard double precision path tracker with a generator is
initialized with a start solution *sol* in a number of
variables equal to the value of *nvar*.
"""
from phcpy.phcpy2c3 import py2c_initialize_standard_solution
from phcpy.interface import store_standard_solutions
store_standard_solutions(nvar, [sol])
return py2c_initialize_standard_solution(1)
def initialize_standard_solution(nvar, sol):
"""
A standard double precision path tracker with a generator is
initialized with a start solution sol in a number of
variables equal to the value of nvar.
"""
from phcpy.phcpy2c2 import py2c_initialize_standard_solution
from phcpy.interface import store_standard_solutions
store_standard_solutions(nvar, [sol])
return py2c_initialize_standard_solution(1)
def newton_laurent_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the Laurent system.
For each solution, prints its last line of diagnostics.
Four levels of precision are supported:
d : standard double precision (1.1e-15 or 2^(-53)),
dd : double double precision (4.9e-32 or 2^(-104)),
qd : quad double precision (1.2e-63 or 2^(-209)).
mp : arbitrary precision, where the number of decimal places
in the working precision is determined by decimals.
"""
dim = number_of_symbols(system)
if (precision == 'd'):
from phcpy.interface import store_standard_laurent_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_laurent_system(system, nbvar=dim)
store_standard_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_standard_Newton_Laurent_step
py2c_standard_Newton_Laurent_step()
result = load_standard_solutions()
elif (precision == 'dd'):
from phcpy.interface import store_dobldobl_laurent_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_laurent_system(system, nbvar=dim)
store_dobldobl_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_dobldobl_Newton_Laurent_step
py2c_dobldobl_Newton_Laurent_step()
result = load_dobldobl_solutions()
elif (precision == 'qd'):
from phcpy.interface import store_quaddobl_laurent_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_laurent_system(system, nbvar=dim)
store_quaddobl_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_quaddobl_Newton_Laurent_step
py2c_quaddobl_Newton_Laurent_step()
result = load_quaddobl_solutions()
elif (precision == 'mp'):
from phcpy.interface import store_multprec_laurent_system
from phcpy.interface import store_multprec_solutions
from phcpy.interface import load_multprec_solutions
store_multprec_laurent_system(system, decimals, nbvar=dim)
store_multprec_solutions(dim, solutions)
from phcpy.phcpy2c3 import py2c_multprec_Newton_Laurent_step
py2c_multprec_Newton_Laurent_step(decimals)
result = load_multprec_solutions()
else:
print('wrong argument for precision')
return None
for sol in result:
strsol = sol.split('\n')
print(strsol[-1])
return result
def newton_laurent_step(system, solutions, precision='d', decimals=100):
"""
Applies one Newton step to the solutions of the Laurent system.
For each solution, prints its last line of diagnostics.
Four levels of precision are supported:
d : standard double precision (1.1e-15 or 2^(-53)),
dd : double double precision (4.9e-32 or 2^(-104)),
qd : quad double precision (1.2e-63 or 2^(-209)).
mp : arbitrary precision, where the number of decimal places
in the working precision is determined by decimals.
"""
if(precision == 'd'):
from phcpy.interface import store_standard_laurent_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_laurent_system(system)
store_standard_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_standard_Newton_Laurent_step
py2c_standard_Newton_Laurent_step()
result = load_standard_solutions()
elif(precision == 'dd'):
from phcpy.interface import store_dobldobl_laurent_system
from phcpy.interface import store_dobldobl_solutions
from phcpy.interface import load_dobldobl_solutions
store_dobldobl_laurent_system(system)
store_dobldobl_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_dobldobl_Newton_Laurent_step
py2c_dobldobl_Newton_Laurent_step()
result = load_dobldobl_solutions()
elif(precision == 'qd'):
from phcpy.interface import store_quaddobl_laurent_system
from phcpy.interface import store_quaddobl_solutions
from phcpy.interface import load_quaddobl_solutions
store_quaddobl_laurent_system(system)
store_quaddobl_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_quaddobl_Newton_Laurent_step
py2c_quaddobl_Newton_Laurent_step()
result = load_quaddobl_solutions()
elif(precision == 'mp'):
from phcpy.interface import store_multprec_laurent_system
from phcpy.interface import store_multprec_solutions
from phcpy.interface import load_multprec_solutions
store_multprec_laurent_system(system, decimals)
store_multprec_solutions(len(system), solutions)
from phcpy.phcpy2c3 import py2c_multprec_Newton_Laurent_step
py2c_multprec_Newton_Laurent_step(decimals)
result = load_multprec_solutions()
else:
print('wrong argument for precision')
return None
for sol in result:
strsol = sol.split('\n')
print(strsol[-1])
return result
def standard_set_solution(nvar, sol, verbose=False):
r"""
Sets the start solution in *sol* for the step-by-step run of
the series-Pade tracker, in standard double precision.
If verbose, then extra output is written.
The number of variables is in *nvar*.
"""
from phcpy.phcpy2c3 import py2c_padcon_initialize_standard_solution
from phcpy.interface import store_standard_solutions
store_standard_solutions(nvar, [sol])
return py2c_padcon_initialize_standard_solution(1, int(verbose))
def standard_newton_series(pols, sols, idx=1, maxdeg=4, nbr=4, verbose=True):
r"""
Computes series in standard double precision for the polynomials
in *pols*, where the leading coefficients are the solutions in *sols*.
On entry are the following five parameters:
*pols*: a list of string representations of polynomials,
*sols*: a list of solutions of the polynomials in *pols*,
*idx*: index of the series parameter, by default equals 1,
*maxdeg*: maximal degree of the series,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_solutions
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c2 import py2c_standard_Newton_series as newton
from phcpy.phcpy2c2 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c2 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c2 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print "the polynomials :"
for pol in pols:
print pol
print "Number of variables :", nbsym
store_standard_system(pols, nbvar=nbsym)
store_standard_solutions(nbsym, sols)
fail = newton(idx, maxdeg, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print "An error occurred in the execution of Newton's method."
else:
print "Computed %d series solutions." % size
result = []
for k in range(1, size+1):
py2c_syspool_copy_to_standard_container(k)
sersol = load_standard_system()
result.append(substitute_symbol(sersol, idx))
py2c_syspool_standard_clear()
return result
def standard_scale_solutions(nvar, sols, cffs):
"""
Scales the solutions in the list sols using the coefficients in cffs,
using standard double precision arithmetic.
The number of variables is given in the parameter nvar.
If the sols are the solution of the polynomials in the output of
standard_scale_system(pols), then the solutions on return will be
solutions of the original polynomials in the list pols.
"""
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.phcpy2c3 import py2c_scale_standard_solutions
store_standard_solutions(nvar, sols)
py2c_scale_standard_solutions(len(cffs), str(cffs))
return load_standard_solutions()
def standard_scale_solutions(nvar, sols, cffs):
"""
Scales the solutions in the list sols using the coefficients in cffs,
using standard double precision arithmetic.
The number of variables is given in the parameter nvar.
If the sols are the solution of the polynomials in the output of
standard_scale_system(pols), then the solutions on return will be
solutions of the original polynomials in the list pols.
"""
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.phcpy2c3 import py2c_scale_standard_solutions
store_standard_solutions(nvar, sols)
py2c_scale_standard_solutions(len(cffs), str(cffs))
return load_standard_solutions()
def standard_newton_series(pols, sols, idx=1, nbr=4, verbose=True):
r"""
Computes series in standard double precision for the polynomials
in *pols*, where the leading coefficients are the solutions in *sols*.
On entry are the following five parameters:
*pols*: a list of string representations of polynomials,
*sols*: a list of solutions of the polynomials in *pols*,
*idx*: index of the series parameter, by default equals 1,
*nbr*: number of steps with Newton's method,
*verbose*: whether to write intermediate output to screen or not.
On return is a list of lists of strings. Each lists of strings
represents the series solution for the variables in the list *pols*.
"""
from phcpy.solver import number_of_symbols
from phcpy.interface import store_standard_solutions
from phcpy.interface import store_standard_system, load_standard_system
from phcpy.phcpy2c2 import py2c_standard_Newton_series as newton
from phcpy.phcpy2c2 import py2c_syspool_standard_size as poolsize
from phcpy.phcpy2c2 import py2c_syspool_copy_to_standard_container
from phcpy.phcpy2c2 import py2c_syspool_standard_clear
nbsym = number_of_symbols(pols)
if verbose:
print "the polynomials :"
for pol in pols:
print pol
print "Number of variables :", nbsym
store_standard_system(pols, nbvar=nbsym)
store_standard_solutions(nbsym, sols)
fail = newton(idx, nbr, int(verbose))
size = (-1 if fail else poolsize())
if verbose:
if size == -1:
print "An error occurred in the execution of Newton's method."
else:
print "Computed %d series solutions." % size
result = []
for k in range(1, size+1):
py2c_syspool_copy_to_standard_container(k)
sersol = load_standard_system()
result.append(substitute_symbol(sersol, idx))
py2c_syspool_standard_clear()
return result
def ade_tuned_double_track(target, start, sols, pars, gamma=0, verbose=1):
r"""
Does path tracking with algorithm differentiation,
in standard double precision, with tuned parameters in pars.
On input are a target system, a start system with solutions.
The *target* is a list of strings representing the polynomials
of the target system (which has to be solved).
The *start* is a list of strings representing the polynomials
of the start system, with known solutions in *sols*.
The *sols* is a list of strings representing start solutions.
The *pars* is a tuple of 14 values for the path parameters.
On return are the string representations of the solutions
computed at the end of the paths.
If *gamma* on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of *gamma* are used.
"""
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_ade_manypaths_d_pars
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_system(target)
py2c_copy_standard_container_to_target_system()
store_standard_system(start)
py2c_copy_standard_container_to_start_system()
dim = len(start)
store_standard_solutions(dim, sols)
if(gamma == 0):
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2*pi)
gamma = exp(angle*complex(0, 1))
if(verbose > 0):
print('random gamma constant :', gamma)
if(verbose > 0):
print('the path parameters :\n', pars)
fail = py2c_ade_manypaths_d_pars(verbose, gamma.real, gamma.imag, \
pars[0], pars[1], pars[2], pars[3], pars[4], pars[5], pars[6], \
pars[7], pars[8], pars[9], pars[10], pars[11], pars[12], pars[13])
if(fail == 0):
if(verbose > 0):
print('Path tracking with AD was a success!')
else:
print('Path tracking with AD failed!')
return load_standard_solutions()
def standard_double_track(target, start, sols, gamma=0, tasks=0):
r"""
Does path tracking with standard double precision.
On input are a target system, a start system with solutions,
optionally: a (random) gamma constant and the number of tasks.
The *target* is a list of strings representing the polynomials
of the target system (which has to be solved).
The *start* is a list of strings representing the polynomials
of the start system, with known solutions in sols.
The *sols* is a list of strings representing start solutions.
By default, a random *gamma* constant is generated,
otherwise *gamma* must be a nonzero complex constant.
The number of tasks in the multithreading is defined by *tasks*.
The default zero value for *tasks* indicates no multithreading.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_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_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
# py2c_clear_standard_homotopy()
if(gamma == 0):
py2c_create_standard_homotopy()
else:
py2c_create_standard_homotopy_with_gamma(gamma.real, gamma.imag)
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
py2c_solve_by_standard_homotopy_continuation(tasks)
py2c_solcon_clear_standard_solutions()
py2c_copy_standard_target_solutions_to_container()
return load_standard_solutions()
def standard_deflate(system, solutions):
"""
The deflation method augments the given system with
derivatives to restore the quadratic convergence of
Newton's method at isolated singular solutions,
in standard double precision.
After application of deflation with default settings,
the new approximate solutions are returned.
"""
from phcpy.phcpy2c3 import py2c_standard_deflate
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_system(system)
store_standard_solutions(len(system), solutions)
py2c_standard_deflate()
result = load_standard_solutions()
return result
def ade_double_track(target, start, sols, gamma=0, verbose=1):
"""
Does path tracking with algorithm differentiation,
in standard double precision.
On input are a target system, a start system with solutions.
The target is a list of strings representing the polynomials
of the target system (which has to be solved).
The start is a list of strings representing the polynomials
of the start system, with known solutions in sols.
The sols is a list of strings representing start solutions.
On return are the string representations of the solutions
computed at the end of the paths.
If gamma on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of gamma are used.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_ade_manypaths_d
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_system(target)
py2c_copy_standard_container_to_target_system()
store_standard_system(start)
py2c_copy_standard_container_to_start_system()
dim = len(start)
store_standard_solutions(dim, sols)
if gamma == 0:
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2 * pi)
gamma = exp(angle * complex(0, 1))
if verbose > 0:
print "random gamma constant :", gamma
fail = py2c_ade_manypaths_d(verbose, gamma.real, gamma.imag)
if fail == 0:
if verbose > 0:
print "Path tracking with AD was a success!"
else:
print "Path tracking with AD failed!"
return load_standard_solutions()
def standard_double_track(target, start, sols, gamma=0, tasks=0):
"""
Does path tracking with standard double precision.
On input are a target system, a start system with solutions,
optionally: a (random) gamma constant and the number of tasks.
The target is a list of strings representing the polynomials
of the target system (which has to be solved).
The start is a list of strings representing the polynomials
of the start system, with known solutions in sols.
The sols is a list of strings representing start solutions.
By default, a random gamma constant is generated,
otherwise gamma must be a nonzero complex constant.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_standard_homotopy
from phcpy.phcpy2c2 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_solve_by_standard_homotopy_continuation
from phcpy.phcpy2c2 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c2 import py2c_copy_standard_target_solutions_to_container
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
# py2c_clear_standard_homotopy()
if(gamma == 0):
py2c_create_standard_homotopy()
else:
py2c_create_standard_homotopy_with_gamma(gamma.real, gamma.imag)
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
py2c_solve_by_standard_homotopy_continuation(tasks)
py2c_solcon_clear_standard_solutions()
py2c_copy_standard_target_solutions_to_container()
return load_standard_solutions()
def standard_deflate(system, solutions):
"""
The deflation method augments the given system with
derivatives to restore the quadratic convergence of
Newton's method at isolated singular solutions,
in standard double precision.
After application of deflation with default settings,
the new approximate solutions are returned.
"""
from phcpy.phcpy2c3 import py2c_standard_deflate
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
dim = number_of_symbols(system)
store_standard_system(system, nbvar=dim)
store_standard_solutions(dim, solutions)
py2c_standard_deflate()
result = load_standard_solutions()
return result
def ade_double_track(target, start, sols, gamma=0, verbose=1):
"""
Does path tracking with algorithm differentiation,
in standard double precision.
On input are a target system, a start system with solutions.
The target is a list of strings representing the polynomials
of the target system (which has to be solved).
The start is a list of strings representing the polynomials
of the start system, with known solutions in sols.
The sols is a list of strings representing start solutions.
On return are the string representations of the solutions
computed at the end of the paths.
If gamma on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of gamma are used.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_ade_manypaths_d
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_system(target)
py2c_copy_standard_container_to_target_system()
store_standard_system(start)
py2c_copy_standard_container_to_start_system()
dim = len(start)
store_standard_solutions(dim, sols)
if(gamma == 0):
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2*pi)
gamma = exp(angle*complex(0, 1))
if(verbose > 0):
print 'random gamma constant :', gamma
fail = py2c_ade_manypaths_d(verbose, gamma.real, gamma.imag)
if(fail == 0):
if(verbose > 0):
print 'Path tracking with AD was a success!'
else:
print 'Path tracking with AD failed!'
return load_standard_solutions()
def gpu_double_track(target, start, sols, gamma=0, verbose=1):
r"""
GPU accelerated path tracking with algorithm differentiation,
in standard double precision.
On input are a target system, a start system with solutions.
The *target* is a list of strings representing the polynomials
of the target system (which has to be solved).
The *start* is a list of strings representing the polynomials
of the start system, with known solutions in sols.
The *sols* is a list of strings representing start solutions.
On return are the string representations of the solutions
computed at the end of the paths.
If *gamma* on input equals zero, then a random complex number is generated,
otherwise the real and imaginary parts of *gamma* are used.
"""
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c3 import py2c_gpu_manypaths_d
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
store_standard_system(target)
py2c_copy_standard_container_to_target_system()
store_standard_system(start)
py2c_copy_standard_container_to_start_system()
dim = len(start)
store_standard_solutions(dim, sols)
if(gamma == 0):
from random import uniform
from cmath import exp, pi
angle = uniform(0, 2*pi)
gamma = exp(angle*complex(0, 1))
if(verbose > 0):
print('random gamma constant :', gamma)
fail = py2c_gpu_manypaths_d(2, verbose, gamma.real, gamma.imag)
if(fail == 0):
if(verbose > 0):
print('Path tracking on the GPU was a success!')
else:
print('Path tracking on the GPU failed!')
return load_standard_solutions()
def standard_track(target, start, sols, filename="", verbose=False):
"""
Wraps the tracker for Pade continuation in standard double precision.
On input are a target system, a start system with solutions,
optionally: a string *filename* and the *verbose* flag.
The *target* is a list of strings representing the polynomials
of the target system (which has to be solved).
The *start* is a list of strings representing the polynomials
of the start system, with known solutions in *sols*.
The *sols* is a list of strings representing start solutions.
On return are the string representations of the solutions
computed at the end of the paths.
"""
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_target_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_system
from phcpy.phcpy2c2 import py2c_copy_standard_container_to_start_solutions
from phcpy.phcpy2c2 import py2c_create_standard_homotopy_with_gamma
from phcpy.phcpy2c2 import py2c_clear_standard_homotopy
from phcpy.phcpy2c2 import py2c_clear_standard_operations_data
from phcpy.interface import store_standard_system
from phcpy.interface import store_standard_solutions
from phcpy.interface import load_standard_solutions
from phcpy.solver import number_of_symbols
from phcpy.phcpy2c2 import py2c_padcon_standard_track
dim = number_of_symbols(start)
store_standard_system(target, nbvar=dim)
py2c_copy_standard_container_to_target_system()
store_standard_system(start, nbvar=dim)
py2c_copy_standard_container_to_start_system()
store_standard_solutions(dim, sols)
py2c_copy_standard_container_to_start_solutions()
(regamma, imgamma) = get_homotopy_continuation_parameter(1)
py2c_create_standard_homotopy_with_gamma(regamma, imgamma)
nbc = len(filename)
fail = py2c_padcon_standard_track(nbc, filename, int(verbose))
# py2c_clear_standard_homotopy()
# py2c_clear_standard_operations_data()
return load_standard_solutions()
