def monomial_map_strings(dim, ind, nbvar):
r"""
Returns the list of strings representing the components of
the monomial map of dimension *dim*, with index *ind*, and
where the number of variables equals *nbvar*.
"""
from phcpy.phcpy2c3 import py2c_mapcon_coefficients_of_map
from phcpy.phcpy2c3 import py2c_mapcon_exponents_of_map
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
sym = py2c_syscon_string_of_symbols()
symvars = sym.split(' ')
# py2c_mapcon_write_maps may have inserted t-varables
thevars = symvars[-nbvar:]
# print '-> the variables', symvars, thevars
cff = py2c_mapcon_coefficients_of_map(dim, ind, nbvar)
# print '-> coefficients of map', ind, ':', cff
exp = py2c_mapcon_exponents_of_map(dim, ind, nbvar)
# print '-> exponents of map', ind, ':', exp
result = []
exp_ind = 0
for i in range(0, nbvar):
str_var = thevars[i]
if(cff[i] == 0):
str_var = str_var + ' - 0'
exp_ind = exp_ind + dim
else:
str_var = str_var + ' - ' + str(cff[i])
for j in range(0, dim):
pwr = exp[exp_ind]
if(pwr != 0):
str_var = str_var + '*' + 't' + str(j+1) + '**' + str(pwr)
exp_ind = exp_ind + 1
result.append(str_var)
return result
def monomial_map_strings(dim, ind, nbvar):
r"""
Returns the list of strings representing the components of
the monomial map of dimension *dim*, with index *ind*, and
where the number of variables equals *nbvar*.
"""
from phcpy.phcpy2c3 import py2c_mapcon_coefficients_of_map
from phcpy.phcpy2c3 import py2c_mapcon_exponents_of_map
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
sym = py2c_syscon_string_of_symbols()
symvars = sym.split(' ')
# py2c_mapcon_write_maps may have inserted t-varables
thevars = symvars[-nbvar:]
# print '-> the variables', symvars, thevars
cff = py2c_mapcon_coefficients_of_map(dim, ind, nbvar)
# print '-> coefficients of map', ind, ':', cff
exp = py2c_mapcon_exponents_of_map(dim, ind, nbvar)
# print '-> exponents of map', ind, ':', exp
result = []
exp_ind = 0
for i in range(0, nbvar):
str_var = thevars[i]
if (cff[i] == 0):
str_var = str_var + ' - 0'
exp_ind = exp_ind + dim
else:
str_var = str_var + ' - ' + str(cff[i])
for j in range(0, dim):
pwr = exp[exp_ind]
if (pwr != 0):
str_var = str_var + '*' + 't' + str(j +
1) + '**' + str(pwr)
exp_ind = exp_ind + 1
result.append(str_var)
return result
def replace_symbol(pol, idx):
"""
In the polynomial pol,
replaces the first symbol by the symbol at place idx.
"""
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
sbl = py2c_syscon_string_of_symbols()
var = sbl.split(' ')
result = pol.replace(var[0], var[idx - 1])
return result
def total_degree_start_system(pols):
"""
Returns the system and solutions of the total degree start system
for the polynomials represented by the strings in the list pols.
"""
from phcpy.phcpy2c3 import py2c_syscon_number_of_standard_polynomials
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
from phcpy.phcpy2c3 import py2c_syscon_degree_of_standard_polynomial
from phcpy.interface import store_standard_system
store_standard_system(pols)
dim = py2c_syscon_number_of_standard_polynomials()
svars = py2c_syscon_string_of_symbols()
nvars = svars.split(' ')
degrees = [py2c_syscon_degree_of_standard_polynomial(k+1) \
for k in range(dim)]
result = []
for ind in range(dim):
result.append(nvars[ind]+'^'+str(degrees[ind])+' - 1;')
return (result, solve(result))
def dobldobl_diagonal_homotopy(dim1, sys1, esols1, dim2, sys2, esols2):
r"""
Defines a diagonal homotopy to intersect the witness sets defined
by (*sys1*, *esols1*) and (*sys2*, *esols2*), respectively of dimensions
*dim1* and *dim2*. The systems *sys1* and *sys2* are assumed to be square
and with as many slack variables as the dimension of the solution sets.
The data is stored in double double precision.
"""
from phcpy.interface import store_dobldobl_system as storesys
from phcpy.interface import store_dobldobl_solutions as storesols
from phcpy.phcpy2c3 import py2c_copy_dobldobl_container_to_target_system
from phcpy.phcpy2c3 import py2c_copy_dobldobl_container_to_target_solutions
from phcpy.phcpy2c3 import py2c_copy_dobldobl_container_to_start_system
from phcpy.phcpy2c3 import py2c_copy_dobldobl_container_to_start_solutions
from phcpy.phcpy2c3 import py2c_dobldobl_diagonal_homotopy
from phcpy.phcpy2c3 import py2c_syscon_number_of_symbols
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
from phcpy.phcpy2c3 import py2c_diagonal_symbols_doubler
storesys(sys1)
symbols = py2c_syscon_string_of_symbols()
nbsymbs = py2c_syscon_number_of_symbols()
print('number of symbols :', nbsymbs)
print('names of variables :', symbols)
storesols(len(sys1), esols1)
if(dim1 >= dim2):
py2c_copy_dobldobl_container_to_target_system()
py2c_copy_dobldobl_container_to_target_solutions()
else:
py2c_copy_dobldobl_container_to_start_system()
py2c_copy_dobldobl_container_to_start_solutions()
storesys(sys2)
storesols(len(sys2), esols2)
if(dim1 >= dim2):
py2c_copy_dobldobl_container_to_start_system()
py2c_copy_dobldobl_container_to_start_solutions()
else:
py2c_copy_dobldobl_container_to_target_system()
py2c_copy_dobldobl_container_to_target_solutions()
if(dim1 >= dim2):
py2c_dobldobl_diagonal_homotopy(dim1, dim2)
else:
py2c_dobldobl_diagonal_homotopy(dim2, dim1)
py2c_diagonal_symbols_doubler(nbsymbs-dim1, dim1, len(symbols), symbols)
def total_degree_start_system(pols):
"""
Returns the system and solutions of the total degree start system
for the polynomials represented by the strings in the list pols.
"""
from phcpy.phcpy2c3 import py2c_syscon_number_of_standard_polynomials
from phcpy.phcpy2c3 import py2c_syscon_string_of_symbols
from phcpy.phcpy2c3 import py2c_syscon_degree_of_standard_polynomial
from phcpy.interface import store_standard_system
store_standard_system(pols)
dim = py2c_syscon_number_of_standard_polynomials()
svars = py2c_syscon_string_of_symbols()
nvars = svars.split(' ')
degrees = [py2c_syscon_degree_of_standard_polynomial(k+1) \
for k in range(dim)]
result = []
for ind in range(dim):
result.append(nvars[ind] + '^' + str(degrees[ind]) + ' - 1;')
return (result, solve(result))