FiSGO.OrderSearch

Module implementing order search functions.

Functions

absolute_bound_filter	Given a list of simple groups, returns only those whose order is less than or equal to a given bound.
add_lists	Adds two lists of integers of the same length pointwise.
candidate_from_power	Given a positive integer 'max_power' and a prime number 'prime', the function calculates which is the largest number n such that prime^max_power divides n!.
candidates_2E	Returns a list of all exceptional Steinberg \({}^2E_6(q^2)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_3D	Returns a list of all exceptional Steinberg \({}^3D_4(q^3)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_AA	Returns a list of all simple alternating groups \(\mathrm{A}_n\) whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_CA	Returns a list of all classical Chevalley \(A_n(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_CB	Returns a list of all classical Chevalley \(B_n(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_CC	Returns a list of all classical Chevalley \(C_n(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_CD	Returns a list of all classical Chevalley \(D_n(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_E6	Returns a list of all exceptional Chevalley \(E_6(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_E7	Returns a list of all exceptional Chevalley \(E_7(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_E8	Returns a list of all exceptional Chevalley \(E_8(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_F4	Returns a list of all exceptional Chevalley \(F_4(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_G2	Returns a list of all exceptional Chevalley \(G_2(q)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_RF	Returns a list of all Ree \({}^2F_4(2^{2n+1})\) groups, simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_RG	Returns a list of all Ree \({}^2G_2(3^{2n+1})\) groups, simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_SA	Returns a list of all classical Steinberg \({}^2A_n(q^2)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_SD	Returns a list of all classical Steinberg \({}^2D_n(q^2)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_SP	Returns a list of all sporadic simple groups whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_SZ	Returns a list of all Suzuki \({}^2B_2(2^{2n+1})\) groups, simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.
candidates_TT	Returns the Tits group \({}^2F_4(2)'\) if its order divides prime_bounds and is less than or equal to abs_bound.
candidates_exceptional_chevalley	Generic function with the procedure to find exceptional Chevalley groups whose order divides prime_bounds and is less than or equal to abs_bound.
check_candidate	Given a simple group code and a bound, determines if the group order divides the given bound.
clear_duplicates	Given a list of simple group objects or a list of simple group codes, returns a new list clear of duplicates.
div_scanned	Given two tuples originating from PrimesHandler.prime_scanner with the same upper_bound, returns the division of both decompositions.
order_search_logger	Decorator for logging candidate search functions.
powers_sequence	The function returns the exponent corresponding to the maximum power of 'prime' that divides prime*n.
prime_bound_compatiblity	Given the partial factorization of a number and a bound to the factorized part, the function checks if the given factorization satisfies the bound.
prod_scanned	Given two tuples originating from PrimesHandler.prime_scanner with the same upper_bound (or same length), returns the product of both decompositions.
simple_group_by_order	Returns a list of all simple groups whose order divides prime_bounds and is less than or equal to abs_bound.
smallest_factorial_from_bound	Given a positive integer 'bound' it returns the largest integer n such that n! <= bound.
substract_lists	Substracts two lists of integers with the same length pointwise.