def run_pieri_homotopies(mdim, pdim, qdeg, planes, *pts, **opt):
r"""
Computes the number of *pdim*-plane producing maps of degree q*deg*
that meet *mdim*-planes at mdim*pdim + qdeq*(mdim+pdim) points.
For *qdeg* = 0, there are no interpolation points in *pts*.
The last parameter in opt contains the value for 'verbose',
which is True by default.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_count
from phcpy.phcpy2c2 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c2 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c2 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 run_pieri_homotopies(mdim, pdim, qdeg, planes, *pts, **opt):
r"""
Computes the number of *pdim*-plane producing maps of degree q*deg*
that meet *mdim*-planes at mdim*pdim + qdeq*(mdim+pdim) points.
For *qdeg* = 0, there are no interpolation points in *pts*.
The last parameter in opt contains the value for 'verbose',
which is True by default.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_count
from phcpy.phcpy2c2 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c2 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_clear_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c2 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 run_pieri_homotopies(mdim, pdim, qdeg, planes, verbose=True, *pts):
r"""
Computes the number of *pdim*-plane producing maps of degree q*deg*
that meet *mdim*-planes at mdim*pdim + qdeq*(mdim+pdim) points.
For *qdeg* = 0, there are no interpolation points in *pts*.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_count
from phcpy.phcpy2c2 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c2 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c2 import py2c_solcon_write_standard_solution_string
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 ...'
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 run_pieri_homotopies(mdim, pdim, qdeg, planes, *pts):
"""
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.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_count
from phcpy.phcpy2c2 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c2 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c2 import py2c_solcon_write_standard_solution_string
root_count = py2c_schubert_pieri_count(mdim, pdim, qdeg)
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 ...'
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))
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)
print 'the solutions :'
for solution in sols:
print solution
return (pols, sols)
def run_pieri_homotopies(mdim, pdim, qdeg, planes, *pts):
"""
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.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_count
from phcpy.phcpy2c2 import py2c_schubert_pieri_homotopies
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
from phcpy.phcpy2c2 import py2c_solcon_number_of_standard_solutions
from phcpy.phcpy2c2 import py2c_solcon_length_standard_solution_string
from phcpy.phcpy2c2 import py2c_solcon_write_standard_solution_string
root_count = py2c_schubert_pieri_count(mdim, pdim, qdeg)
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 ...'
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))
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)
print 'the solutions :'
for solution in sols:
print solution
return (pols, sols)
def load_standard_system():
"""
Returns the polynomials stored in the system container
for standard double precision arithmetic.
"""
from phcpy.phcpy2c2 import py2c_syscon_number_of_standard_polynomials
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
dim = py2c_syscon_number_of_standard_polynomials()
result = []
for ind in range(1, dim + 1):
result.append(py2c_syscon_load_standard_polynomial(ind))
return result
def load_standard_system():
"""
Returns the polynomials stored in the system container
for standard double precision arithmetic.
"""
from phcpy.phcpy2c2 import py2c_syscon_number_of_standard_polynomials
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
dim = py2c_syscon_number_of_standard_polynomials()
result = []
for ind in range(1, dim+1):
result.append(py2c_syscon_load_standard_polynomial(ind))
return result
def make_pieri_system(mdim, pdim, qdeg, planes, is_real=False):
r"""
Makes the polynomial system defined by the *mdim*-planes
in the list *planes*.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_system
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
strplanes = planes_to_string(planes)
# print 'the string of planes :', strplanes
if is_real:
py2c_schubert_pieri_system(mdim, pdim, qdeg, len(strplanes), strplanes, 1)
else:
py2c_schubert_pieri_system(mdim, pdim, qdeg, len(strplanes), strplanes, 0)
result = []
if qdeg == 0:
for i in range(1, mdim * pdim + 1):
result.append(py2c_syscon_load_standard_polynomial(i))
return result
def make_pieri_system(mdim, pdim, qdeg, planes, is_real=False):
"""
Makes the polynomial system defined by the mdim-planes
in the list planes.
"""
from phcpy.phcpy2c2 import py2c_schubert_pieri_system
from phcpy.phcpy2c2 import py2c_syscon_load_standard_polynomial
strplanes = planes_to_string(planes)
# print 'the string of planes :', strplanes
if is_real:
py2c_schubert_pieri_system(mdim, pdim, qdeg, \
len(strplanes), strplanes, 1)
else:
py2c_schubert_pieri_system(mdim, pdim, qdeg, \
len(strplanes), strplanes, 0)
result = []
if (qdeg == 0):
for i in range(1, mdim * pdim + 1):
result.append(py2c_syscon_load_standard_polynomial(i))
return result
