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)