| | |
- build_groebner_basis_doc_string()
- change_order_heuristic(d)
- clean_polys(I)
- clean_polys_pre(I)
- contained_vars(...)
- contained_vars( (BooleSet)arg1) -> BooleSet :
C++ signature :
polybori::BooleSet contained_vars(polybori::BooleSet)
- count_double(...)
- count_double( (BooleSet)arg1) -> float :
C++ signature :
double count_double(polybori::BooleSet)
- easy_linear_factors(...)
- easy_linear_factors( (Polynomial)arg1) -> BoolePolynomialVector :
C++ signature :
std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> > easy_linear_factors(polybori::BoolePolynomial)
- easy_linear_polynomials_pre(I)
- eliminate_identical_variables_pre(I, prot)
- filter_newstyle_options(func, **options)
- filter_oldstyle_options(**options)
- fix_deg_bound_post(I, state)
- gauss_on_linear_pre(I, prot)
- gb_with_pre_post_option(option, pre=None, post=None, if_not_option=(), default=False)
- get_options_from_function(f)
- groebner_basis(I, **kwds)
- Computes a Groebner basis of a given ideal I, w.r.t options.
Options are:
easy_linear_polynomials : True
prot : False
interpolation_gb : False
modified_linear_algebra : True
convert_with_fglm_from_ring : None
gauss_on_linear : True
incremental : False
preprocessor : None
preprocess_only : False
ll_constants : True
convert_with_fglm_to_ring : None
result_to_list : True
heuristic : True
clean_and_restart_algorithm : False
llfirst : False
other_ordering_first : False
clean_arguments : True
implementation : 'Python'
invert : False
redsb : True
fix_deg_bound : True
eliminate_identical_variables : True
draw_matrices : False
full_prot : False
fglm_bound : 40000
minsb : True
deg_bound : False
llfirstonthefly : False
unique_ideal_generator : False
Turn off heuristic by setting heuristic=False
Additional options come from the actual buchberger implementation.
In case of our standard Python implementation these are the following:
faugere : False
linear_algebra_in_last_block : True
selection_size : 1000
recursion : False
ll : False
over_deg_bound : 0
step_factor : 1.0
lazy : True
max_growth : 2.0
exchange : True
red_tail_deg_growth : True
matrix_prefix : 'mat'
max_generators : None
red_tail : True
noro : False
implications : False
- if_then_else(...)
- if_then_else( (object)arg1, (BooleSet)arg2, (BooleSet)arg3) -> BooleSet :
if-then else operator
C++ signature :
polybori::BooleSet if_then_else(int,polybori::BooleSet,polybori::BooleSet)
if_then_else( (Variable)arg1, (BooleSet)arg2, (BooleSet)arg3) -> BooleSet :
if-then else operator
C++ signature :
polybori::BooleSet if_then_else(polybori::BooleVariable,polybori::BooleSet,polybori::BooleSet)
- incremental_pre(I, prot, kwds)
- interpolate(...)
- interpolate( (BooleSet)arg1, (BooleSet)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial interpolate(polybori::BooleSet,polybori::BooleSet)
- interpolate_smallest_lex(...)
- interpolate_smallest_lex( (BooleSet)arg1, (BooleSet)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial interpolate_smallest_lex(polybori::BooleSet,polybori::BooleSet)
- interpolation_gb_heuristic(d)
- invert_all(I)
- invert_all_post(I, state)
- invert_all_pre(I)
- linear_algebra_heuristic(d)
- ll_constants_post(I, state)
- ll_constants_pre(I)
- ll_heuristic(d)
- ll_is_good(I)
- ll_red_nf_noredsb(...)
- ll_red_nf_noredsb( (Polynomial)arg1, (BooleSet)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial ll_red_nf_noredsb(polybori::BoolePolynomial,polybori::BooleSet)
- ll_red_nf_noredsb_single_recursive_call(...)
- ll_red_nf_noredsb_single_recursive_call( (Polynomial)arg1, (BooleSet)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial ll_red_nf_noredsb_single_recursive_call(polybori::BoolePolynomial,polybori::BooleSet)
- ll_red_nf_redsb(...)
- ll_red_nf_redsb( (Polynomial)arg1, (BooleSet)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial ll_red_nf_redsb(polybori::BoolePolynomial,polybori::BooleSet)
- llfirst_post(I, state, prot, kwds)
- llfirst_pre(I, prot)
- llfirstonthefly_pre(I, prot)
- map_every_x_to_x_plus_one(...)
- map_every_x_to_x_plus_one( (Polynomial)arg1) -> Polynomial :
C++ signature :
polybori::BoolePolynomial map_every_x_to_x_plus_one(polybori::BoolePolynomial)
- mapping(...)
- mapping( (Polynomial)arg1, (Monomial)arg2, (Monomial)arg3) -> Polynomial :
C++ signature :
polybori::BoolePolynomial mapping(polybori::BoolePolynomial,polybori::BooleMonomial,polybori::BooleMonomial)
- minsb_post(I, state)
- mod_mon_set(...)
- mod_mon_set( (BooleSet)arg1, (BooleSet)arg2) -> BooleSet :
C++ signature :
polybori::BooleSet mod_mon_set(polybori::BooleSet,polybori::BooleSet)
mod_mon_set( (BooleSet)arg1, (BooleSet)arg2) -> BooleSet :
C++ signature :
polybori::BooleSet mod_mon_set(polybori::BooleSet,polybori::BooleSet)
- mod_var_set(...)
- mod_var_set( (BooleSet)arg1, (BooleSet)arg2) -> BooleSet :
C++ signature :
polybori::BooleSet mod_var_set(polybori::BooleSet,polybori::BooleSet)
- mult_fast_sim_C(...)
- mult_fast_sim_C( (BoolePolynomialVector)arg1, (Ring)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial mult_fast_sim_C(std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> >,polybori::BoolePolyRing)
- nf3(...)
- nf3( (ReductionStrategy)arg1, (Polynomial)arg2, (Monomial)arg3) -> Polynomial :
C++ signature :
polybori::BoolePolynomial nf3(polybori::groebner::ReductionStrategy,polybori::BoolePolynomial,polybori::BooleMonomial)
- other_ordering_pre(I, option_set, kwds)
- >>> from polybori.blocks import declare_ring
>>> r = declare_ring(['x0', 'x1', 'x2', 'x3', 'x4'], globals())
>>> id = [x1*x3 + x1 + x2*x3 + x3 + x4, x0*x3 + x0 + x1*x2 + x2 + 1, x1*x3 + x1*x4 + x3*x4 + x4 + 1, x0*x2 + x0*x4 + x1 + x3 + x4]
>>> groebner_basis(id)
[1]
- owns_one_constant(I)
- Determines whether I contains the constant one polynomial.
- parallel_reduce(...)
- parallel_reduce( (BoolePolynomialVector)arg1, (GroebnerStrategy)arg2, (object)arg3, (float)arg4) -> BoolePolynomialVector :
C++ signature :
std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> > parallel_reduce(std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> >,polybori::groebner::GroebnerStrategy {lvalue},int,double)
- random_set(...)
- random_set( (Monomial)arg1, (int)arg2) -> BooleSet :
C++ signature :
polybori::BooleSet random_set(polybori::BooleMonomial,unsigned int)
- recursively_insert(...)
- recursively_insert( (CCuddNavigator)arg1, (object)arg2, (BooleSet)arg3) -> BooleSet :
C++ signature :
polybori::BooleSet recursively_insert(polybori::CCuddNavigator,int,polybori::BooleSet)
- redsb_post(I, state)
- result_to_list_post(I, state)
- set_random_seed(...)
- set_random_seed( (int)arg1) -> None :
C++ signature :
void set_random_seed(unsigned int)
- spoly(...)
- spoly( (Polynomial)arg1, (Polynomial)arg2) -> Polynomial :
Compute s-Polynomial between two Polynomials
C++ signature :
polybori::BoolePolynomial spoly(polybori::BoolePolynomial,polybori::BoolePolynomial)
- substitute_variables(...)
- substitute_variables( (Ring)arg1, (BoolePolynomialVector)arg2, (Polynomial)arg3) -> Polynomial :
C++ signature :
polybori::BoolePolynomial substitute_variables(polybori::BoolePolyRing,std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> >,polybori::BoolePolynomial)
- test_iterate_lex(...)
- test_iterate_lex( (Polynomial)arg1) -> int :
C++ signature :
unsigned long test_iterate_lex(polybori::BoolePolynomial {lvalue})
- test_iterate_lex_reversed(...)
- test_iterate_lex_reversed( (Polynomial)arg1) -> int :
C++ signature :
unsigned long test_iterate_lex_reversed(polybori::BoolePolynomial {lvalue})
- test_iterate_ordered(...)
- test_iterate_ordered( (Polynomial)arg1) -> int :
C++ signature :
unsigned long test_iterate_ordered(polybori::BoolePolynomial {lvalue})
- test_iterate_reference_ordered(...)
- test_iterate_reference_ordered( (Polynomial)arg1) -> int :
C++ signature :
unsigned long test_iterate_reference_ordered(polybori::BoolePolynomial {lvalue})
- testvalidstrat(...)
- testvalidstrat( (GroebnerStrategy)arg1) -> None :
C++ signature :
void testvalidstrat(polybori::groebner::GroebnerStrategy)
- time(...)
- time() -> floating point number
Return the current time in seconds since the Epoch.
Fractions of a second may be present if the system clock provides them.
- top_index(...)
- top_index( (BooleSet)arg1) -> int :
C++ signature :
int top_index(polybori::BooleSet)
- translate_indices(...)
- translate_indices( (Polynomial)arg1, (IntVector)arg2) -> Polynomial :
C++ signature :
polybori::BoolePolynomial translate_indices(polybori::BoolePolynomial,std::vector<int, std::allocator<int> >)
- trivial_heuristic(d)
- variety_lex_groebner_basis(...)
- variety_lex_groebner_basis( (BooleSet)arg1, (Monomial)arg2) -> BoolePolynomialVector :
C++ signature :
std::vector<polybori::BoolePolynomial, std::allocator<polybori::BoolePolynomial> > variety_lex_groebner_basis(polybori::BooleSet,polybori::BooleMonomial)
- variety_lex_leading_terms(...)
- variety_lex_leading_terms( (BooleSet)arg1, (Monomial)arg2) -> BooleSet :
C++ signature :
polybori::BooleSet variety_lex_leading_terms(polybori::BooleSet,polybori::BooleMonomial)
- variety_size_from_gb(I)
- >>> r=Ring(100)
>>> x = r.variable
>>> variety_size_from_gb([])
1
>>> variety_size_from_gb([Polynomial(0, r)])
1
>>> variety_size_from_gb([Polynomial(1, r)])
0.0
>>> variety_size_from_gb([x(1)])
1.0
>>> variety_size_from_gb([x(1), x(2)])
1.0
>>> variety_size_from_gb([x(1), x(2)*x(3)])
3.0
>>> variety_size_from_gb([x(1), x(1)*x(4), x(2)*x(3)])
6.0
>>> variety_size_from_gb([x(1)*x(2), x(2)*x(3)])
5.0
>>> mons = [Monomial([r.variable(i) for i in xrange(100) if i!=j]) for j in xrange(100)]
>>> variety_size_from_gb(mons)
1.2676506002282294e+30
- want_interpolation_gb(G)
- warn(...)
- Issue a warning, or maybe ignore it or raise an exception.
- with_heuristic(heuristic_function)
|