def run_pieri_homotopies(mdim, pdim, qdeg, planes, *pts, **opt):
r"""
Computes the number of *pdim*-plane producing maps of degree *qdeg*
that meet *mdim*-planes at mdim*pdim + qdeq*(mdim+pdim) points.
For *qdeg* = 0, there are no interpolation points in *pts*.
"""
from phcpy.phcpy2c3 import py2c_schubert_pieri_count
from phcpy.phcpy2c3 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c3 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c3 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c3 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c3 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solution_string
if 'verbose' not in opt:
verbose = True # by default, the function is verbose
else:
verbose = opt['verbose']
root_count = py2c_schubert_pieri_count(mdim, pdim, qdeg)
if verbose:
print('Pieri root count for', (mdim, pdim, qdeg), 'is', root_count)
strplanes = planes_to_string(planes)
# print 'length of input data :', len(strplanes)
if(qdeg > 0):
strpts = points_to_string(pts[0])
# print 'the interpolation points :', strpts
else:
strpts = ''
# print 'calling py2c_pieri_homotopies ...'
py2c_solcon_clear_standard_solutions()
if verbose:
print('passing %d characters for (m, p, q) = (%d, %d, %d)' \
% (len(strplanes), mdim, pdim, qdeg))
py2c_schubert_pieri_homotopies(mdim, pdim, qdeg, \
len(strplanes), strplanes, strpts)
# print 'making the system ...'
pols = []
if(qdeg == 0):
for i in range(1, mdim*pdim+1):
pols.append(py2c_syscon_load_standard_polynomial(i))
else:
for i in range(1, mdim*pdim+qdeg*(mdim+pdim)+1):
pols.append(py2c_syscon_load_standard_polynomial(i))
if verbose:
print('the system :')
for poly in pols:
print(poly)
print('root count :', root_count)
nbsols = py2c_solcon_number_of_standard_solutions()
sols = []
for k in range(1, nbsols+1):
lns = py2c_solcon_length_standard_solution_string(k)
sol = py2c_solcon_write_standard_solution_string(k, lns)
sols.append(sol)
if verbose:
print('the solutions :')
for solution in sols:
print(solution)
return (pols, sols)
def standard_get_solution(verbose=False):
"""
Returns the current solution on the path, in double precision,
which starts at the solution set with standard_set_solution().
If verbose, then extra output is written.
"""
from phcpy.phcpy2c3 import py2c_padcon_get_standard_solution
from phcpy.phcpy2c3 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solution_string
py2c_padcon_get_standard_solution(1, int(verbose))
lns = py2c_solcon_length_standard_solution_string(1)
return py2c_solcon_write_standard_solution_string(1, lns)
def next_standard_solution():
"""
Returns the next solution on a path tracked with standard
double precision arithmetic, provided the functions
initialize_standard_tracker() and initialize_standard_solution()
have been executed properly.
"""
from phcpy.phcpy2c3 import py2c_next_standard_solution
from phcpy.phcpy2c3 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solution_string
py2c_next_standard_solution(1)
lns = py2c_solcon_length_standard_solution_string(1)
sol = py2c_solcon_write_standard_solution_string(1, lns)
return sol
def next_standard_solution():
r"""
Returns the next solution on a path tracked with standard
double precision arithmetic, provided the functions
**initialize_standard_tracker()** and **initialize_standard_solution()**
have been executed properly.
"""
from phcpy.phcpy2c3 import py2c_next_standard_solution
from phcpy.phcpy2c3 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c3 import py2c_solcon_write_standard_solution_string
py2c_next_standard_solution(1)
lns = py2c_solcon_length_standard_solution_string(1)
sol = py2c_solcon_write_standard_solution_string(1, lns)
return sol
