def laurent_top_cascade(nvr, dim, pols, tol, \
nbtasks=0, prc='d', verbose=True):
r"""
Constructs an embedding of the Laurent polynomials in *pols*,
with the number of variables in *pols* equal to *nvr*,
where *dim* is the top dimension of the solution set.
Applies the blackbox solver to the embedded system.
The tolerance *tol* is used to split the solution list in the list
of generic points and the nonsolutions for use in the cascade.
Returns a tuple with three items:
1. the embedded system,
2. the solutions with zero last coordinate w.r.t. *tol*,
3. the solutions with nonzero last coordinate w.r.t. *tol*.
The three parameters are
1. *nbtasks* is the number of tasks, 0 if no multitasking;
2. the working precision *prc*, 'd' for double, 'dd' for double double,
or 'qd' for quad double;
3. if *verbose*, then some output is written to screen.
"""
from phcpy.sets import laurent_embed
from phcpy.solver import solve
topemb = laurent_embed(nvr, dim, pols)
if verbose:
print 'solving the embedded system at the top ...'
topsols = solve(topemb, verbose=verbose, tasks=nbtasks, precision=prc)
if verbose:
print 'number of solutions found :', len(topsols)
(sols0, sols1) = split_filter(topsols, dim, tol, verbose=verbose)
return (topemb, sols0, sols1)
def laurent_top_cascade(nvr, dim, pols, tol, \
nbtasks=0, prc='d', verbose=True):
r"""
Constructs an embedding of the Laurent polynomials in *pols*,
with the number of variables in *pols* equal to *nvr*,
where *dim* is the top dimension of the solution set.
Applies the blackbox solver to the embedded system.
The tolerance *tol* is used to split the solution list in the list
of generic points and the nonsolutions for use in the cascade.
Returns a tuple with three items:
1. the embedded system,
2. the solutions with zero last coordinate w.r.t. *tol*,
3. the solutions with nonzero last coordinate w.r.t. *tol*.
The three parameters are
1. *nbtasks* is the number of tasks, 0 if no multitasking;
2. the working precision *prc*, 'd' for double, 'dd' for double double,
or 'qd' for quad double;
3. if *verbose*, then some output is written to screen.
"""
from phcpy.sets import laurent_embed
from phcpy.solver import solve
topemb = laurent_embed(nvr, dim, pols)
if verbose:
print 'solving the embedded system at the top ...'
topsols = solve(topemb, verbose=verbose, tasks=nbtasks, precision=prc)
if verbose:
print 'number of solutions found :', len(topsols)
(sols0, sols1) = split_filter(topsols, dim, tol, verbose=verbose)
return (topemb, sols0, sols1)