1135 lines
56 KiB
Python
1135 lines
56 KiB
Python
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"""Compatibility interface between dense and sparse polys. """
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from sympy.polys.densearith import dup_add_term
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from sympy.polys.densearith import dmp_add_term
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from sympy.polys.densearith import dup_sub_term
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from sympy.polys.densearith import dmp_sub_term
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from sympy.polys.densearith import dup_mul_term
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from sympy.polys.densearith import dmp_mul_term
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from sympy.polys.densearith import dup_add_ground
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from sympy.polys.densearith import dmp_add_ground
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from sympy.polys.densearith import dup_sub_ground
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from sympy.polys.densearith import dmp_sub_ground
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from sympy.polys.densearith import dup_mul_ground
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from sympy.polys.densearith import dmp_mul_ground
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from sympy.polys.densearith import dup_quo_ground
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from sympy.polys.densearith import dmp_quo_ground
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from sympy.polys.densearith import dup_exquo_ground
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from sympy.polys.densearith import dmp_exquo_ground
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from sympy.polys.densearith import dup_lshift
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from sympy.polys.densearith import dup_rshift
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from sympy.polys.densearith import dup_abs
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from sympy.polys.densearith import dmp_abs
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from sympy.polys.densearith import dup_neg
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from sympy.polys.densearith import dmp_neg
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from sympy.polys.densearith import dup_add
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from sympy.polys.densearith import dmp_add
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from sympy.polys.densearith import dup_sub
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from sympy.polys.densearith import dmp_sub
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from sympy.polys.densearith import dup_add_mul
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from sympy.polys.densearith import dmp_add_mul
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from sympy.polys.densearith import dup_sub_mul
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from sympy.polys.densearith import dmp_sub_mul
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from sympy.polys.densearith import dup_mul
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from sympy.polys.densearith import dmp_mul
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from sympy.polys.densearith import dup_sqr
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from sympy.polys.densearith import dmp_sqr
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from sympy.polys.densearith import dup_pow
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from sympy.polys.densearith import dmp_pow
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from sympy.polys.densearith import dup_pdiv
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from sympy.polys.densearith import dup_prem
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from sympy.polys.densearith import dup_pquo
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from sympy.polys.densearith import dup_pexquo
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from sympy.polys.densearith import dmp_pdiv
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from sympy.polys.densearith import dmp_prem
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from sympy.polys.densearith import dmp_pquo
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from sympy.polys.densearith import dmp_pexquo
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from sympy.polys.densearith import dup_rr_div
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from sympy.polys.densearith import dmp_rr_div
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from sympy.polys.densearith import dup_ff_div
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from sympy.polys.densearith import dmp_ff_div
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from sympy.polys.densearith import dup_div
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from sympy.polys.densearith import dup_rem
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from sympy.polys.densearith import dup_quo
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from sympy.polys.densearith import dup_exquo
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from sympy.polys.densearith import dmp_div
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from sympy.polys.densearith import dmp_rem
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from sympy.polys.densearith import dmp_quo
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from sympy.polys.densearith import dmp_exquo
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from sympy.polys.densearith import dup_max_norm
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from sympy.polys.densearith import dmp_max_norm
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from sympy.polys.densearith import dup_l1_norm
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from sympy.polys.densearith import dmp_l1_norm
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from sympy.polys.densearith import dup_l2_norm_squared
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from sympy.polys.densearith import dmp_l2_norm_squared
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from sympy.polys.densearith import dup_expand
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from sympy.polys.densearith import dmp_expand
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from sympy.polys.densebasic import dup_LC
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from sympy.polys.densebasic import dmp_LC
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from sympy.polys.densebasic import dup_TC
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from sympy.polys.densebasic import dmp_TC
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from sympy.polys.densebasic import dmp_ground_LC
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from sympy.polys.densebasic import dmp_ground_TC
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from sympy.polys.densebasic import dup_degree
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from sympy.polys.densebasic import dmp_degree
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from sympy.polys.densebasic import dmp_degree_in
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from sympy.polys.densebasic import dmp_to_dict
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from sympy.polys.densetools import dup_integrate
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from sympy.polys.densetools import dmp_integrate
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from sympy.polys.densetools import dmp_integrate_in
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from sympy.polys.densetools import dup_diff
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from sympy.polys.densetools import dmp_diff
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from sympy.polys.densetools import dmp_diff_in
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from sympy.polys.densetools import dup_eval
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from sympy.polys.densetools import dmp_eval
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from sympy.polys.densetools import dmp_eval_in
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from sympy.polys.densetools import dmp_eval_tail
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from sympy.polys.densetools import dmp_diff_eval_in
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from sympy.polys.densetools import dup_trunc
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from sympy.polys.densetools import dmp_trunc
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from sympy.polys.densetools import dmp_ground_trunc
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from sympy.polys.densetools import dup_monic
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from sympy.polys.densetools import dmp_ground_monic
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from sympy.polys.densetools import dup_content
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from sympy.polys.densetools import dmp_ground_content
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from sympy.polys.densetools import dup_primitive
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from sympy.polys.densetools import dmp_ground_primitive
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from sympy.polys.densetools import dup_extract
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from sympy.polys.densetools import dmp_ground_extract
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from sympy.polys.densetools import dup_real_imag
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from sympy.polys.densetools import dup_mirror
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from sympy.polys.densetools import dup_scale
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from sympy.polys.densetools import dup_shift
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from sympy.polys.densetools import dup_transform
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from sympy.polys.densetools import dup_compose
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from sympy.polys.densetools import dmp_compose
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from sympy.polys.densetools import dup_decompose
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from sympy.polys.densetools import dmp_lift
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from sympy.polys.densetools import dup_sign_variations
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from sympy.polys.densetools import dup_clear_denoms
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from sympy.polys.densetools import dmp_clear_denoms
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from sympy.polys.densetools import dup_revert
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from sympy.polys.euclidtools import dup_half_gcdex
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from sympy.polys.euclidtools import dmp_half_gcdex
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from sympy.polys.euclidtools import dup_gcdex
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from sympy.polys.euclidtools import dmp_gcdex
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from sympy.polys.euclidtools import dup_invert
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from sympy.polys.euclidtools import dmp_invert
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from sympy.polys.euclidtools import dup_euclidean_prs
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from sympy.polys.euclidtools import dmp_euclidean_prs
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from sympy.polys.euclidtools import dup_primitive_prs
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from sympy.polys.euclidtools import dmp_primitive_prs
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from sympy.polys.euclidtools import dup_inner_subresultants
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from sympy.polys.euclidtools import dup_subresultants
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from sympy.polys.euclidtools import dup_prs_resultant
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from sympy.polys.euclidtools import dup_resultant
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from sympy.polys.euclidtools import dmp_inner_subresultants
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from sympy.polys.euclidtools import dmp_subresultants
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from sympy.polys.euclidtools import dmp_prs_resultant
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from sympy.polys.euclidtools import dmp_zz_modular_resultant
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from sympy.polys.euclidtools import dmp_zz_collins_resultant
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from sympy.polys.euclidtools import dmp_qq_collins_resultant
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from sympy.polys.euclidtools import dmp_resultant
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from sympy.polys.euclidtools import dup_discriminant
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from sympy.polys.euclidtools import dmp_discriminant
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from sympy.polys.euclidtools import dup_rr_prs_gcd
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from sympy.polys.euclidtools import dup_ff_prs_gcd
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from sympy.polys.euclidtools import dmp_rr_prs_gcd
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from sympy.polys.euclidtools import dmp_ff_prs_gcd
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from sympy.polys.euclidtools import dup_zz_heu_gcd
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from sympy.polys.euclidtools import dmp_zz_heu_gcd
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from sympy.polys.euclidtools import dup_qq_heu_gcd
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from sympy.polys.euclidtools import dmp_qq_heu_gcd
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from sympy.polys.euclidtools import dup_inner_gcd
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from sympy.polys.euclidtools import dmp_inner_gcd
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from sympy.polys.euclidtools import dup_gcd
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from sympy.polys.euclidtools import dmp_gcd
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from sympy.polys.euclidtools import dup_rr_lcm
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from sympy.polys.euclidtools import dup_ff_lcm
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from sympy.polys.euclidtools import dup_lcm
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from sympy.polys.euclidtools import dmp_rr_lcm
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from sympy.polys.euclidtools import dmp_ff_lcm
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from sympy.polys.euclidtools import dmp_lcm
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from sympy.polys.euclidtools import dmp_content
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from sympy.polys.euclidtools import dmp_primitive
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from sympy.polys.euclidtools import dup_cancel
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from sympy.polys.euclidtools import dmp_cancel
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from sympy.polys.factortools import dup_trial_division
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from sympy.polys.factortools import dmp_trial_division
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from sympy.polys.factortools import dup_zz_mignotte_bound
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from sympy.polys.factortools import dmp_zz_mignotte_bound
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from sympy.polys.factortools import dup_zz_hensel_step
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from sympy.polys.factortools import dup_zz_hensel_lift
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from sympy.polys.factortools import dup_zz_zassenhaus
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from sympy.polys.factortools import dup_zz_irreducible_p
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from sympy.polys.factortools import dup_cyclotomic_p
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from sympy.polys.factortools import dup_zz_cyclotomic_poly
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from sympy.polys.factortools import dup_zz_cyclotomic_factor
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from sympy.polys.factortools import dup_zz_factor_sqf
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from sympy.polys.factortools import dup_zz_factor
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from sympy.polys.factortools import dmp_zz_wang_non_divisors
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from sympy.polys.factortools import dmp_zz_wang_lead_coeffs
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from sympy.polys.factortools import dup_zz_diophantine
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from sympy.polys.factortools import dmp_zz_diophantine
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from sympy.polys.factortools import dmp_zz_wang_hensel_lifting
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from sympy.polys.factortools import dmp_zz_wang
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from sympy.polys.factortools import dmp_zz_factor
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from sympy.polys.factortools import dup_qq_i_factor
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from sympy.polys.factortools import dup_zz_i_factor
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from sympy.polys.factortools import dmp_qq_i_factor
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from sympy.polys.factortools import dmp_zz_i_factor
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from sympy.polys.factortools import dup_ext_factor
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from sympy.polys.factortools import dmp_ext_factor
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from sympy.polys.factortools import dup_gf_factor
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from sympy.polys.factortools import dmp_gf_factor
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from sympy.polys.factortools import dup_factor_list
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from sympy.polys.factortools import dup_factor_list_include
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from sympy.polys.factortools import dmp_factor_list
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from sympy.polys.factortools import dmp_factor_list_include
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from sympy.polys.factortools import dup_irreducible_p
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from sympy.polys.factortools import dmp_irreducible_p
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from sympy.polys.rootisolation import dup_sturm
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from sympy.polys.rootisolation import dup_root_upper_bound
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from sympy.polys.rootisolation import dup_root_lower_bound
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from sympy.polys.rootisolation import dup_step_refine_real_root
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from sympy.polys.rootisolation import dup_inner_refine_real_root
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from sympy.polys.rootisolation import dup_outer_refine_real_root
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from sympy.polys.rootisolation import dup_refine_real_root
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from sympy.polys.rootisolation import dup_inner_isolate_real_roots
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from sympy.polys.rootisolation import dup_inner_isolate_positive_roots
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from sympy.polys.rootisolation import dup_inner_isolate_negative_roots
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from sympy.polys.rootisolation import dup_isolate_real_roots_sqf
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from sympy.polys.rootisolation import dup_isolate_real_roots
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from sympy.polys.rootisolation import dup_isolate_real_roots_list
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from sympy.polys.rootisolation import dup_count_real_roots
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from sympy.polys.rootisolation import dup_count_complex_roots
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from sympy.polys.rootisolation import dup_isolate_complex_roots_sqf
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from sympy.polys.rootisolation import dup_isolate_all_roots_sqf
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from sympy.polys.rootisolation import dup_isolate_all_roots
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from sympy.polys.sqfreetools import (
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dup_sqf_p, dmp_sqf_p, dup_sqf_norm, dmp_sqf_norm, dup_gf_sqf_part, dmp_gf_sqf_part,
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dup_sqf_part, dmp_sqf_part, dup_gf_sqf_list, dmp_gf_sqf_list, dup_sqf_list,
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dup_sqf_list_include, dmp_sqf_list, dmp_sqf_list_include, dup_gff_list, dmp_gff_list)
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from sympy.polys.galoistools import (
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gf_degree, gf_LC, gf_TC, gf_strip, gf_from_dict,
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gf_to_dict, gf_from_int_poly, gf_to_int_poly, gf_neg, gf_add_ground, gf_sub_ground,
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gf_mul_ground, gf_quo_ground, gf_add, gf_sub, gf_mul, gf_sqr, gf_add_mul, gf_sub_mul,
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gf_expand, gf_div, gf_rem, gf_quo, gf_exquo, gf_lshift, gf_rshift, gf_pow, gf_pow_mod,
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gf_gcd, gf_lcm, gf_cofactors, gf_gcdex, gf_monic, gf_diff, gf_eval, gf_multi_eval,
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gf_compose, gf_compose_mod, gf_trace_map, gf_random, gf_irreducible, gf_irred_p_ben_or,
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gf_irred_p_rabin, gf_irreducible_p, gf_sqf_p, gf_sqf_part, gf_Qmatrix,
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gf_berlekamp, gf_ddf_zassenhaus, gf_edf_zassenhaus, gf_ddf_shoup, gf_edf_shoup,
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gf_zassenhaus, gf_shoup, gf_factor_sqf, gf_factor)
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from sympy.utilities import public
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@public
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class IPolys:
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symbols = None
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ngens = None
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domain = None
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order = None
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gens = None
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def drop(self, gen):
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pass
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def clone(self, symbols=None, domain=None, order=None):
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pass
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def to_ground(self):
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pass
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def ground_new(self, element):
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pass
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def domain_new(self, element):
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pass
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def from_dict(self, d):
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pass
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def wrap(self, element):
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from sympy.polys.rings import PolyElement
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if isinstance(element, PolyElement):
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if element.ring == self:
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return element
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else:
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raise NotImplementedError("domain conversions")
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else:
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return self.ground_new(element)
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def to_dense(self, element):
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return self.wrap(element).to_dense()
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def from_dense(self, element):
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return self.from_dict(dmp_to_dict(element, self.ngens-1, self.domain))
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def dup_add_term(self, f, c, i):
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return self.from_dense(dup_add_term(self.to_dense(f), c, i, self.domain))
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def dmp_add_term(self, f, c, i):
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|
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return self.from_dense(dmp_add_term(self.to_dense(f), self.wrap(c).drop(0).to_dense(), i, self.ngens-1, self.domain))
|
||
|
|
def dup_sub_term(self, f, c, i):
|
||
|
|
return self.from_dense(dup_sub_term(self.to_dense(f), c, i, self.domain))
|
||
|
|
def dmp_sub_term(self, f, c, i):
|
||
|
|
return self.from_dense(dmp_sub_term(self.to_dense(f), self.wrap(c).drop(0).to_dense(), i, self.ngens-1, self.domain))
|
||
|
|
def dup_mul_term(self, f, c, i):
|
||
|
|
return self.from_dense(dup_mul_term(self.to_dense(f), c, i, self.domain))
|
||
|
|
def dmp_mul_term(self, f, c, i):
|
||
|
|
return self.from_dense(dmp_mul_term(self.to_dense(f), self.wrap(c).drop(0).to_dense(), i, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_add_ground(self, f, c):
|
||
|
|
return self.from_dense(dup_add_ground(self.to_dense(f), c, self.domain))
|
||
|
|
def dmp_add_ground(self, f, c):
|
||
|
|
return self.from_dense(dmp_add_ground(self.to_dense(f), c, self.ngens-1, self.domain))
|
||
|
|
def dup_sub_ground(self, f, c):
|
||
|
|
return self.from_dense(dup_sub_ground(self.to_dense(f), c, self.domain))
|
||
|
|
def dmp_sub_ground(self, f, c):
|
||
|
|
return self.from_dense(dmp_sub_ground(self.to_dense(f), c, self.ngens-1, self.domain))
|
||
|
|
def dup_mul_ground(self, f, c):
|
||
|
|
return self.from_dense(dup_mul_ground(self.to_dense(f), c, self.domain))
|
||
|
|
def dmp_mul_ground(self, f, c):
|
||
|
|
return self.from_dense(dmp_mul_ground(self.to_dense(f), c, self.ngens-1, self.domain))
|
||
|
|
def dup_quo_ground(self, f, c):
|
||
|
|
return self.from_dense(dup_quo_ground(self.to_dense(f), c, self.domain))
|
||
|
|
def dmp_quo_ground(self, f, c):
|
||
|
|
return self.from_dense(dmp_quo_ground(self.to_dense(f), c, self.ngens-1, self.domain))
|
||
|
|
def dup_exquo_ground(self, f, c):
|
||
|
|
return self.from_dense(dup_exquo_ground(self.to_dense(f), c, self.domain))
|
||
|
|
def dmp_exquo_ground(self, f, c):
|
||
|
|
return self.from_dense(dmp_exquo_ground(self.to_dense(f), c, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_lshift(self, f, n):
|
||
|
|
return self.from_dense(dup_lshift(self.to_dense(f), n, self.domain))
|
||
|
|
def dup_rshift(self, f, n):
|
||
|
|
return self.from_dense(dup_rshift(self.to_dense(f), n, self.domain))
|
||
|
|
|
||
|
|
def dup_abs(self, f):
|
||
|
|
return self.from_dense(dup_abs(self.to_dense(f), self.domain))
|
||
|
|
def dmp_abs(self, f):
|
||
|
|
return self.from_dense(dmp_abs(self.to_dense(f), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_neg(self, f):
|
||
|
|
return self.from_dense(dup_neg(self.to_dense(f), self.domain))
|
||
|
|
def dmp_neg(self, f):
|
||
|
|
return self.from_dense(dmp_neg(self.to_dense(f), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_add(self, f, g):
|
||
|
|
return self.from_dense(dup_add(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dmp_add(self, f, g):
|
||
|
|
return self.from_dense(dmp_add(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_sub(self, f, g):
|
||
|
|
return self.from_dense(dup_sub(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dmp_sub(self, f, g):
|
||
|
|
return self.from_dense(dmp_sub(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_add_mul(self, f, g, h):
|
||
|
|
return self.from_dense(dup_add_mul(self.to_dense(f), self.to_dense(g), self.to_dense(h), self.domain))
|
||
|
|
def dmp_add_mul(self, f, g, h):
|
||
|
|
return self.from_dense(dmp_add_mul(self.to_dense(f), self.to_dense(g), self.to_dense(h), self.ngens-1, self.domain))
|
||
|
|
def dup_sub_mul(self, f, g, h):
|
||
|
|
return self.from_dense(dup_sub_mul(self.to_dense(f), self.to_dense(g), self.to_dense(h), self.domain))
|
||
|
|
def dmp_sub_mul(self, f, g, h):
|
||
|
|
return self.from_dense(dmp_sub_mul(self.to_dense(f), self.to_dense(g), self.to_dense(h), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_mul(self, f, g):
|
||
|
|
return self.from_dense(dup_mul(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dmp_mul(self, f, g):
|
||
|
|
return self.from_dense(dmp_mul(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_sqr(self, f):
|
||
|
|
return self.from_dense(dup_sqr(self.to_dense(f), self.domain))
|
||
|
|
def dmp_sqr(self, f):
|
||
|
|
return self.from_dense(dmp_sqr(self.to_dense(f), self.ngens-1, self.domain))
|
||
|
|
def dup_pow(self, f, n):
|
||
|
|
return self.from_dense(dup_pow(self.to_dense(f), n, self.domain))
|
||
|
|
def dmp_pow(self, f, n):
|
||
|
|
return self.from_dense(dmp_pow(self.to_dense(f), n, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_pdiv(self, f, g):
|
||
|
|
q, r = dup_pdiv(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dup_prem(self, f, g):
|
||
|
|
return self.from_dense(dup_prem(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dup_pquo(self, f, g):
|
||
|
|
return self.from_dense(dup_pquo(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dup_pexquo(self, f, g):
|
||
|
|
return self.from_dense(dup_pexquo(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
|
||
|
|
def dmp_pdiv(self, f, g):
|
||
|
|
q, r = dmp_pdiv(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dmp_prem(self, f, g):
|
||
|
|
return self.from_dense(dmp_prem(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
def dmp_pquo(self, f, g):
|
||
|
|
return self.from_dense(dmp_pquo(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
def dmp_pexquo(self, f, g):
|
||
|
|
return self.from_dense(dmp_pexquo(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_rr_div(self, f, g):
|
||
|
|
q, r = dup_rr_div(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dmp_rr_div(self, f, g):
|
||
|
|
q, r = dmp_rr_div(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dup_ff_div(self, f, g):
|
||
|
|
q, r = dup_ff_div(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dmp_ff_div(self, f, g):
|
||
|
|
q, r = dmp_ff_div(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
|
||
|
|
def dup_div(self, f, g):
|
||
|
|
q, r = dup_div(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dup_rem(self, f, g):
|
||
|
|
return self.from_dense(dup_rem(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dup_quo(self, f, g):
|
||
|
|
return self.from_dense(dup_quo(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dup_exquo(self, f, g):
|
||
|
|
return self.from_dense(dup_exquo(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
|
||
|
|
def dmp_div(self, f, g):
|
||
|
|
q, r = dmp_div(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(q), self.from_dense(r))
|
||
|
|
def dmp_rem(self, f, g):
|
||
|
|
return self.from_dense(dmp_rem(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
def dmp_quo(self, f, g):
|
||
|
|
return self.from_dense(dmp_quo(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
def dmp_exquo(self, f, g):
|
||
|
|
return self.from_dense(dmp_exquo(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_max_norm(self, f):
|
||
|
|
return dup_max_norm(self.to_dense(f), self.domain)
|
||
|
|
def dmp_max_norm(self, f):
|
||
|
|
return dmp_max_norm(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_l1_norm(self, f):
|
||
|
|
return dup_l1_norm(self.to_dense(f), self.domain)
|
||
|
|
def dmp_l1_norm(self, f):
|
||
|
|
return dmp_l1_norm(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_l2_norm_squared(self, f):
|
||
|
|
return dup_l2_norm_squared(self.to_dense(f), self.domain)
|
||
|
|
def dmp_l2_norm_squared(self, f):
|
||
|
|
return dmp_l2_norm_squared(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_expand(self, polys):
|
||
|
|
return self.from_dense(dup_expand(list(map(self.to_dense, polys)), self.domain))
|
||
|
|
def dmp_expand(self, polys):
|
||
|
|
return self.from_dense(dmp_expand(list(map(self.to_dense, polys)), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_LC(self, f):
|
||
|
|
return dup_LC(self.to_dense(f), self.domain)
|
||
|
|
def dmp_LC(self, f):
|
||
|
|
LC = dmp_LC(self.to_dense(f), self.domain)
|
||
|
|
if isinstance(LC, list):
|
||
|
|
return self[1:].from_dense(LC)
|
||
|
|
else:
|
||
|
|
return LC
|
||
|
|
def dup_TC(self, f):
|
||
|
|
return dup_TC(self.to_dense(f), self.domain)
|
||
|
|
def dmp_TC(self, f):
|
||
|
|
TC = dmp_TC(self.to_dense(f), self.domain)
|
||
|
|
if isinstance(TC, list):
|
||
|
|
return self[1:].from_dense(TC)
|
||
|
|
else:
|
||
|
|
return TC
|
||
|
|
|
||
|
|
def dmp_ground_LC(self, f):
|
||
|
|
return dmp_ground_LC(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
def dmp_ground_TC(self, f):
|
||
|
|
return dmp_ground_TC(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_degree(self, f):
|
||
|
|
return dup_degree(self.to_dense(f))
|
||
|
|
def dmp_degree(self, f):
|
||
|
|
return dmp_degree(self.to_dense(f), self.ngens-1)
|
||
|
|
def dmp_degree_in(self, f, j):
|
||
|
|
return dmp_degree_in(self.to_dense(f), j, self.ngens-1)
|
||
|
|
def dup_integrate(self, f, m):
|
||
|
|
return self.from_dense(dup_integrate(self.to_dense(f), m, self.domain))
|
||
|
|
def dmp_integrate(self, f, m):
|
||
|
|
return self.from_dense(dmp_integrate(self.to_dense(f), m, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_diff(self, f, m):
|
||
|
|
return self.from_dense(dup_diff(self.to_dense(f), m, self.domain))
|
||
|
|
def dmp_diff(self, f, m):
|
||
|
|
return self.from_dense(dmp_diff(self.to_dense(f), m, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dmp_diff_in(self, f, m, j):
|
||
|
|
return self.from_dense(dmp_diff_in(self.to_dense(f), m, j, self.ngens-1, self.domain))
|
||
|
|
def dmp_integrate_in(self, f, m, j):
|
||
|
|
return self.from_dense(dmp_integrate_in(self.to_dense(f), m, j, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_eval(self, f, a):
|
||
|
|
return dup_eval(self.to_dense(f), a, self.domain)
|
||
|
|
def dmp_eval(self, f, a):
|
||
|
|
result = dmp_eval(self.to_dense(f), a, self.ngens-1, self.domain)
|
||
|
|
return self[1:].from_dense(result)
|
||
|
|
|
||
|
|
def dmp_eval_in(self, f, a, j):
|
||
|
|
result = dmp_eval_in(self.to_dense(f), a, j, self.ngens-1, self.domain)
|
||
|
|
return self.drop(j).from_dense(result)
|
||
|
|
def dmp_diff_eval_in(self, f, m, a, j):
|
||
|
|
result = dmp_diff_eval_in(self.to_dense(f), m, a, j, self.ngens-1, self.domain)
|
||
|
|
return self.drop(j).from_dense(result)
|
||
|
|
|
||
|
|
def dmp_eval_tail(self, f, A):
|
||
|
|
result = dmp_eval_tail(self.to_dense(f), A, self.ngens-1, self.domain)
|
||
|
|
if isinstance(result, list):
|
||
|
|
return self[:-len(A)].from_dense(result)
|
||
|
|
else:
|
||
|
|
return result
|
||
|
|
|
||
|
|
def dup_trunc(self, f, p):
|
||
|
|
return self.from_dense(dup_trunc(self.to_dense(f), p, self.domain))
|
||
|
|
def dmp_trunc(self, f, g):
|
||
|
|
return self.from_dense(dmp_trunc(self.to_dense(f), self[1:].to_dense(g), self.ngens-1, self.domain))
|
||
|
|
def dmp_ground_trunc(self, f, p):
|
||
|
|
return self.from_dense(dmp_ground_trunc(self.to_dense(f), p, self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_monic(self, f):
|
||
|
|
return self.from_dense(dup_monic(self.to_dense(f), self.domain))
|
||
|
|
def dmp_ground_monic(self, f):
|
||
|
|
return self.from_dense(dmp_ground_monic(self.to_dense(f), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_extract(self, f, g):
|
||
|
|
c, F, G = dup_extract(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (c, self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_ground_extract(self, f, g):
|
||
|
|
c, F, G = dmp_ground_extract(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (c, self.from_dense(F), self.from_dense(G))
|
||
|
|
|
||
|
|
def dup_real_imag(self, f):
|
||
|
|
p, q = dup_real_imag(self.wrap(f).drop(1).to_dense(), self.domain)
|
||
|
|
return (self.from_dense(p), self.from_dense(q))
|
||
|
|
|
||
|
|
def dup_mirror(self, f):
|
||
|
|
return self.from_dense(dup_mirror(self.to_dense(f), self.domain))
|
||
|
|
def dup_scale(self, f, a):
|
||
|
|
return self.from_dense(dup_scale(self.to_dense(f), a, self.domain))
|
||
|
|
def dup_shift(self, f, a):
|
||
|
|
return self.from_dense(dup_shift(self.to_dense(f), a, self.domain))
|
||
|
|
def dup_transform(self, f, p, q):
|
||
|
|
return self.from_dense(dup_transform(self.to_dense(f), self.to_dense(p), self.to_dense(q), self.domain))
|
||
|
|
|
||
|
|
def dup_compose(self, f, g):
|
||
|
|
return self.from_dense(dup_compose(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dmp_compose(self, f, g):
|
||
|
|
return self.from_dense(dmp_compose(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_decompose(self, f):
|
||
|
|
components = dup_decompose(self.to_dense(f), self.domain)
|
||
|
|
return list(map(self.from_dense, components))
|
||
|
|
|
||
|
|
def dmp_lift(self, f):
|
||
|
|
result = dmp_lift(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return self.to_ground().from_dense(result)
|
||
|
|
|
||
|
|
def dup_sign_variations(self, f):
|
||
|
|
return dup_sign_variations(self.to_dense(f), self.domain)
|
||
|
|
|
||
|
|
def dup_clear_denoms(self, f, convert=False):
|
||
|
|
c, F = dup_clear_denoms(self.to_dense(f), self.domain, convert=convert)
|
||
|
|
if convert:
|
||
|
|
ring = self.clone(domain=self.domain.get_ring())
|
||
|
|
else:
|
||
|
|
ring = self
|
||
|
|
return (c, ring.from_dense(F))
|
||
|
|
def dmp_clear_denoms(self, f, convert=False):
|
||
|
|
c, F = dmp_clear_denoms(self.to_dense(f), self.ngens-1, self.domain, convert=convert)
|
||
|
|
if convert:
|
||
|
|
ring = self.clone(domain=self.domain.get_ring())
|
||
|
|
else:
|
||
|
|
ring = self
|
||
|
|
return (c, ring.from_dense(F))
|
||
|
|
|
||
|
|
def dup_revert(self, f, n):
|
||
|
|
return self.from_dense(dup_revert(self.to_dense(f), n, self.domain))
|
||
|
|
|
||
|
|
def dup_half_gcdex(self, f, g):
|
||
|
|
s, h = dup_half_gcdex(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(s), self.from_dense(h))
|
||
|
|
def dmp_half_gcdex(self, f, g):
|
||
|
|
s, h = dmp_half_gcdex(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(s), self.from_dense(h))
|
||
|
|
def dup_gcdex(self, f, g):
|
||
|
|
s, t, h = dup_gcdex(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(s), self.from_dense(t), self.from_dense(h))
|
||
|
|
def dmp_gcdex(self, f, g):
|
||
|
|
s, t, h = dmp_gcdex(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(s), self.from_dense(t), self.from_dense(h))
|
||
|
|
|
||
|
|
def dup_invert(self, f, g):
|
||
|
|
return self.from_dense(dup_invert(self.to_dense(f), self.to_dense(g), self.domain))
|
||
|
|
def dmp_invert(self, f, g):
|
||
|
|
return self.from_dense(dmp_invert(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_euclidean_prs(self, f, g):
|
||
|
|
prs = dup_euclidean_prs(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
def dmp_euclidean_prs(self, f, g):
|
||
|
|
prs = dmp_euclidean_prs(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
def dup_primitive_prs(self, f, g):
|
||
|
|
prs = dup_primitive_prs(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
def dmp_primitive_prs(self, f, g):
|
||
|
|
prs = dmp_primitive_prs(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
|
||
|
|
def dup_inner_subresultants(self, f, g):
|
||
|
|
prs, sres = dup_inner_subresultants(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (list(map(self.from_dense, prs)), sres)
|
||
|
|
def dmp_inner_subresultants(self, f, g):
|
||
|
|
prs, sres = dmp_inner_subresultants(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (list(map(self.from_dense, prs)), sres)
|
||
|
|
|
||
|
|
def dup_subresultants(self, f, g):
|
||
|
|
prs = dup_subresultants(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
def dmp_subresultants(self, f, g):
|
||
|
|
prs = dmp_subresultants(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return list(map(self.from_dense, prs))
|
||
|
|
|
||
|
|
def dup_prs_resultant(self, f, g):
|
||
|
|
res, prs = dup_prs_resultant(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (res, list(map(self.from_dense, prs)))
|
||
|
|
def dmp_prs_resultant(self, f, g):
|
||
|
|
res, prs = dmp_prs_resultant(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self[1:].from_dense(res), list(map(self.from_dense, prs)))
|
||
|
|
|
||
|
|
def dmp_zz_modular_resultant(self, f, g, p):
|
||
|
|
res = dmp_zz_modular_resultant(self.to_dense(f), self.to_dense(g), self.domain_new(p), self.ngens-1, self.domain)
|
||
|
|
return self[1:].from_dense(res)
|
||
|
|
def dmp_zz_collins_resultant(self, f, g):
|
||
|
|
res = dmp_zz_collins_resultant(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self[1:].from_dense(res)
|
||
|
|
def dmp_qq_collins_resultant(self, f, g):
|
||
|
|
res = dmp_qq_collins_resultant(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self[1:].from_dense(res)
|
||
|
|
|
||
|
|
def dup_resultant(self, f, g): #, includePRS=False):
|
||
|
|
return dup_resultant(self.to_dense(f), self.to_dense(g), self.domain) #, includePRS=includePRS)
|
||
|
|
def dmp_resultant(self, f, g): #, includePRS=False):
|
||
|
|
res = dmp_resultant(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain) #, includePRS=includePRS)
|
||
|
|
if isinstance(res, list):
|
||
|
|
return self[1:].from_dense(res)
|
||
|
|
else:
|
||
|
|
return res
|
||
|
|
|
||
|
|
def dup_discriminant(self, f):
|
||
|
|
return dup_discriminant(self.to_dense(f), self.domain)
|
||
|
|
def dmp_discriminant(self, f):
|
||
|
|
disc = dmp_discriminant(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
if isinstance(disc, list):
|
||
|
|
return self[1:].from_dense(disc)
|
||
|
|
else:
|
||
|
|
return disc
|
||
|
|
|
||
|
|
def dup_rr_prs_gcd(self, f, g):
|
||
|
|
H, F, G = dup_rr_prs_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dup_ff_prs_gcd(self, f, g):
|
||
|
|
H, F, G = dup_ff_prs_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_rr_prs_gcd(self, f, g):
|
||
|
|
H, F, G = dmp_rr_prs_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_ff_prs_gcd(self, f, g):
|
||
|
|
H, F, G = dmp_ff_prs_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dup_zz_heu_gcd(self, f, g):
|
||
|
|
H, F, G = dup_zz_heu_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_zz_heu_gcd(self, f, g):
|
||
|
|
H, F, G = dmp_zz_heu_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dup_qq_heu_gcd(self, f, g):
|
||
|
|
H, F, G = dup_qq_heu_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_qq_heu_gcd(self, f, g):
|
||
|
|
H, F, G = dmp_qq_heu_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dup_inner_gcd(self, f, g):
|
||
|
|
H, F, G = dup_inner_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_inner_gcd(self, f, g):
|
||
|
|
H, F, G = dmp_inner_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return (self.from_dense(H), self.from_dense(F), self.from_dense(G))
|
||
|
|
def dup_gcd(self, f, g):
|
||
|
|
H = dup_gcd(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dmp_gcd(self, f, g):
|
||
|
|
H = dmp_gcd(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dup_rr_lcm(self, f, g):
|
||
|
|
H = dup_rr_lcm(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dup_ff_lcm(self, f, g):
|
||
|
|
H = dup_ff_lcm(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dup_lcm(self, f, g):
|
||
|
|
H = dup_lcm(self.to_dense(f), self.to_dense(g), self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dmp_rr_lcm(self, f, g):
|
||
|
|
H = dmp_rr_lcm(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dmp_ff_lcm(self, f, g):
|
||
|
|
H = dmp_ff_lcm(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
def dmp_lcm(self, f, g):
|
||
|
|
H = dmp_lcm(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain)
|
||
|
|
return self.from_dense(H)
|
||
|
|
|
||
|
|
def dup_content(self, f):
|
||
|
|
cont = dup_content(self.to_dense(f), self.domain)
|
||
|
|
return cont
|
||
|
|
def dup_primitive(self, f):
|
||
|
|
cont, prim = dup_primitive(self.to_dense(f), self.domain)
|
||
|
|
return cont, self.from_dense(prim)
|
||
|
|
|
||
|
|
def dmp_content(self, f):
|
||
|
|
cont = dmp_content(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
if isinstance(cont, list):
|
||
|
|
return self[1:].from_dense(cont)
|
||
|
|
else:
|
||
|
|
return cont
|
||
|
|
def dmp_primitive(self, f):
|
||
|
|
cont, prim = dmp_primitive(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
if isinstance(cont, list):
|
||
|
|
return (self[1:].from_dense(cont), self.from_dense(prim))
|
||
|
|
else:
|
||
|
|
return (cont, self.from_dense(prim))
|
||
|
|
|
||
|
|
def dmp_ground_content(self, f):
|
||
|
|
cont = dmp_ground_content(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return cont
|
||
|
|
def dmp_ground_primitive(self, f):
|
||
|
|
cont, prim = dmp_ground_primitive(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (cont, self.from_dense(prim))
|
||
|
|
|
||
|
|
def dup_cancel(self, f, g, include=True):
|
||
|
|
result = dup_cancel(self.to_dense(f), self.to_dense(g), self.domain, include=include)
|
||
|
|
if not include:
|
||
|
|
cf, cg, F, G = result
|
||
|
|
return (cf, cg, self.from_dense(F), self.from_dense(G))
|
||
|
|
else:
|
||
|
|
F, G = result
|
||
|
|
return (self.from_dense(F), self.from_dense(G))
|
||
|
|
def dmp_cancel(self, f, g, include=True):
|
||
|
|
result = dmp_cancel(self.to_dense(f), self.to_dense(g), self.ngens-1, self.domain, include=include)
|
||
|
|
if not include:
|
||
|
|
cf, cg, F, G = result
|
||
|
|
return (cf, cg, self.from_dense(F), self.from_dense(G))
|
||
|
|
else:
|
||
|
|
F, G = result
|
||
|
|
return (self.from_dense(F), self.from_dense(G))
|
||
|
|
|
||
|
|
def dup_trial_division(self, f, factors):
|
||
|
|
factors = dup_trial_division(self.to_dense(f), list(map(self.to_dense, factors)), self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
def dmp_trial_division(self, f, factors):
|
||
|
|
factors = dmp_trial_division(self.to_dense(f), list(map(self.to_dense, factors)), self.ngens-1, self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dup_zz_mignotte_bound(self, f):
|
||
|
|
return dup_zz_mignotte_bound(self.to_dense(f), self.domain)
|
||
|
|
def dmp_zz_mignotte_bound(self, f):
|
||
|
|
return dmp_zz_mignotte_bound(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_zz_hensel_step(self, m, f, g, h, s, t):
|
||
|
|
D = self.to_dense
|
||
|
|
G, H, S, T = dup_zz_hensel_step(m, D(f), D(g), D(h), D(s), D(t), self.domain)
|
||
|
|
return (self.from_dense(G), self.from_dense(H), self.from_dense(S), self.from_dense(T))
|
||
|
|
def dup_zz_hensel_lift(self, p, f, f_list, l):
|
||
|
|
D = self.to_dense
|
||
|
|
polys = dup_zz_hensel_lift(p, D(f), list(map(D, f_list)), l, self.domain)
|
||
|
|
return list(map(self.from_dense, polys))
|
||
|
|
|
||
|
|
def dup_zz_zassenhaus(self, f):
|
||
|
|
factors = dup_zz_zassenhaus(self.to_dense(f), self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dup_zz_irreducible_p(self, f):
|
||
|
|
return dup_zz_irreducible_p(self.to_dense(f), self.domain)
|
||
|
|
def dup_cyclotomic_p(self, f, irreducible=False):
|
||
|
|
return dup_cyclotomic_p(self.to_dense(f), self.domain, irreducible=irreducible)
|
||
|
|
def dup_zz_cyclotomic_poly(self, n):
|
||
|
|
F = dup_zz_cyclotomic_poly(n, self.domain)
|
||
|
|
return self.from_dense(F)
|
||
|
|
def dup_zz_cyclotomic_factor(self, f):
|
||
|
|
result = dup_zz_cyclotomic_factor(self.to_dense(f), self.domain)
|
||
|
|
if result is None:
|
||
|
|
return result
|
||
|
|
else:
|
||
|
|
return list(map(self.from_dense, result))
|
||
|
|
|
||
|
|
# E: List[ZZ], cs: ZZ, ct: ZZ
|
||
|
|
def dmp_zz_wang_non_divisors(self, E, cs, ct):
|
||
|
|
return dmp_zz_wang_non_divisors(E, cs, ct, self.domain)
|
||
|
|
|
||
|
|
# f: Poly, T: List[(Poly, int)], ct: ZZ, A: List[ZZ]
|
||
|
|
#def dmp_zz_wang_test_points(f, T, ct, A):
|
||
|
|
# dmp_zz_wang_test_points(self.to_dense(f), T, ct, A, self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
# f: Poly, T: List[(Poly, int)], cs: ZZ, E: List[ZZ], H: List[Poly], A: List[ZZ]
|
||
|
|
def dmp_zz_wang_lead_coeffs(self, f, T, cs, E, H, A):
|
||
|
|
mv = self[1:]
|
||
|
|
T = [ (mv.to_dense(t), k) for t, k in T ]
|
||
|
|
uv = self[:1]
|
||
|
|
H = list(map(uv.to_dense, H))
|
||
|
|
f, HH, CC = dmp_zz_wang_lead_coeffs(self.to_dense(f), T, cs, E, H, A, self.ngens-1, self.domain)
|
||
|
|
return self.from_dense(f), list(map(uv.from_dense, HH)), list(map(mv.from_dense, CC))
|
||
|
|
|
||
|
|
# f: List[Poly], m: int, p: ZZ
|
||
|
|
def dup_zz_diophantine(self, F, m, p):
|
||
|
|
result = dup_zz_diophantine(list(map(self.to_dense, F)), m, p, self.domain)
|
||
|
|
return list(map(self.from_dense, result))
|
||
|
|
|
||
|
|
# f: List[Poly], c: List[Poly], A: List[ZZ], d: int, p: ZZ
|
||
|
|
def dmp_zz_diophantine(self, F, c, A, d, p):
|
||
|
|
result = dmp_zz_diophantine(list(map(self.to_dense, F)), self.to_dense(c), A, d, p, self.ngens-1, self.domain)
|
||
|
|
return list(map(self.from_dense, result))
|
||
|
|
|
||
|
|
# f: Poly, H: List[Poly], LC: List[Poly], A: List[ZZ], p: ZZ
|
||
|
|
def dmp_zz_wang_hensel_lifting(self, f, H, LC, A, p):
|
||
|
|
uv = self[:1]
|
||
|
|
mv = self[1:]
|
||
|
|
H = list(map(uv.to_dense, H))
|
||
|
|
LC = list(map(mv.to_dense, LC))
|
||
|
|
result = dmp_zz_wang_hensel_lifting(self.to_dense(f), H, LC, A, p, self.ngens-1, self.domain)
|
||
|
|
return list(map(self.from_dense, result))
|
||
|
|
|
||
|
|
def dmp_zz_wang(self, f, mod=None, seed=None):
|
||
|
|
factors = dmp_zz_wang(self.to_dense(f), self.ngens-1, self.domain, mod=mod, seed=seed)
|
||
|
|
return [ self.from_dense(g) for g in factors ]
|
||
|
|
|
||
|
|
def dup_zz_factor_sqf(self, f):
|
||
|
|
coeff, factors = dup_zz_factor_sqf(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ self.from_dense(g) for g in factors ])
|
||
|
|
|
||
|
|
def dup_zz_factor(self, f):
|
||
|
|
coeff, factors = dup_zz_factor(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_zz_factor(self, f):
|
||
|
|
coeff, factors = dmp_zz_factor(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_qq_i_factor(self, f):
|
||
|
|
coeff, factors = dup_qq_i_factor(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_qq_i_factor(self, f):
|
||
|
|
coeff, factors = dmp_qq_i_factor(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_zz_i_factor(self, f):
|
||
|
|
coeff, factors = dup_zz_i_factor(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_zz_i_factor(self, f):
|
||
|
|
coeff, factors = dmp_zz_i_factor(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_ext_factor(self, f):
|
||
|
|
coeff, factors = dup_ext_factor(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_ext_factor(self, f):
|
||
|
|
coeff, factors = dmp_ext_factor(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_gf_factor(self, f):
|
||
|
|
coeff, factors = dup_gf_factor(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_gf_factor(self, f):
|
||
|
|
coeff, factors = dmp_gf_factor(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_factor_list(self, f):
|
||
|
|
coeff, factors = dup_factor_list(self.to_dense(f), self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dup_factor_list_include(self, f):
|
||
|
|
factors = dup_factor_list_include(self.to_dense(f), self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dmp_factor_list(self, f):
|
||
|
|
coeff, factors = dmp_factor_list(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_factor_list_include(self, f):
|
||
|
|
factors = dmp_factor_list_include(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dup_irreducible_p(self, f):
|
||
|
|
return dup_irreducible_p(self.to_dense(f), self.domain)
|
||
|
|
def dmp_irreducible_p(self, f):
|
||
|
|
return dmp_irreducible_p(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_sturm(self, f):
|
||
|
|
seq = dup_sturm(self.to_dense(f), self.domain)
|
||
|
|
return list(map(self.from_dense, seq))
|
||
|
|
|
||
|
|
def dup_sqf_p(self, f):
|
||
|
|
return dup_sqf_p(self.to_dense(f), self.domain)
|
||
|
|
def dmp_sqf_p(self, f):
|
||
|
|
return dmp_sqf_p(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
|
||
|
|
def dup_sqf_norm(self, f):
|
||
|
|
s, F, R = dup_sqf_norm(self.to_dense(f), self.domain)
|
||
|
|
return (s, self.from_dense(F), self.to_ground().from_dense(R))
|
||
|
|
def dmp_sqf_norm(self, f):
|
||
|
|
s, F, R = dmp_sqf_norm(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return (s, self.from_dense(F), self.to_ground().from_dense(R))
|
||
|
|
|
||
|
|
def dup_gf_sqf_part(self, f):
|
||
|
|
return self.from_dense(dup_gf_sqf_part(self.to_dense(f), self.domain))
|
||
|
|
def dmp_gf_sqf_part(self, f):
|
||
|
|
return self.from_dense(dmp_gf_sqf_part(self.to_dense(f), self.domain))
|
||
|
|
def dup_sqf_part(self, f):
|
||
|
|
return self.from_dense(dup_sqf_part(self.to_dense(f), self.domain))
|
||
|
|
def dmp_sqf_part(self, f):
|
||
|
|
return self.from_dense(dmp_sqf_part(self.to_dense(f), self.ngens-1, self.domain))
|
||
|
|
|
||
|
|
def dup_gf_sqf_list(self, f, all=False):
|
||
|
|
coeff, factors = dup_gf_sqf_list(self.to_dense(f), self.domain, all=all)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_gf_sqf_list(self, f, all=False):
|
||
|
|
coeff, factors = dmp_gf_sqf_list(self.to_dense(f), self.ngens-1, self.domain, all=all)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
|
||
|
|
def dup_sqf_list(self, f, all=False):
|
||
|
|
coeff, factors = dup_sqf_list(self.to_dense(f), self.domain, all=all)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dup_sqf_list_include(self, f, all=False):
|
||
|
|
factors = dup_sqf_list_include(self.to_dense(f), self.domain, all=all)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
def dmp_sqf_list(self, f, all=False):
|
||
|
|
coeff, factors = dmp_sqf_list(self.to_dense(f), self.ngens-1, self.domain, all=all)
|
||
|
|
return (coeff, [ (self.from_dense(g), k) for g, k in factors ])
|
||
|
|
def dmp_sqf_list_include(self, f, all=False):
|
||
|
|
factors = dmp_sqf_list_include(self.to_dense(f), self.ngens-1, self.domain, all=all)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dup_gff_list(self, f):
|
||
|
|
factors = dup_gff_list(self.to_dense(f), self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
def dmp_gff_list(self, f):
|
||
|
|
factors = dmp_gff_list(self.to_dense(f), self.ngens-1, self.domain)
|
||
|
|
return [ (self.from_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def dup_root_upper_bound(self, f):
|
||
|
|
return dup_root_upper_bound(self.to_dense(f), self.domain)
|
||
|
|
def dup_root_lower_bound(self, f):
|
||
|
|
return dup_root_lower_bound(self.to_dense(f), self.domain)
|
||
|
|
|
||
|
|
def dup_step_refine_real_root(self, f, M, fast=False):
|
||
|
|
return dup_step_refine_real_root(self.to_dense(f), M, self.domain, fast=fast)
|
||
|
|
def dup_inner_refine_real_root(self, f, M, eps=None, steps=None, disjoint=None, fast=False, mobius=False):
|
||
|
|
return dup_inner_refine_real_root(self.to_dense(f), M, self.domain, eps=eps, steps=steps, disjoint=disjoint, fast=fast, mobius=mobius)
|
||
|
|
def dup_outer_refine_real_root(self, f, s, t, eps=None, steps=None, disjoint=None, fast=False):
|
||
|
|
return dup_outer_refine_real_root(self.to_dense(f), s, t, self.domain, eps=eps, steps=steps, disjoint=disjoint, fast=fast)
|
||
|
|
def dup_refine_real_root(self, f, s, t, eps=None, steps=None, disjoint=None, fast=False):
|
||
|
|
return dup_refine_real_root(self.to_dense(f), s, t, self.domain, eps=eps, steps=steps, disjoint=disjoint, fast=fast)
|
||
|
|
def dup_inner_isolate_real_roots(self, f, eps=None, fast=False):
|
||
|
|
return dup_inner_isolate_real_roots(self.to_dense(f), self.domain, eps=eps, fast=fast)
|
||
|
|
def dup_inner_isolate_positive_roots(self, f, eps=None, inf=None, sup=None, fast=False, mobius=False):
|
||
|
|
return dup_inner_isolate_positive_roots(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, fast=fast, mobius=mobius)
|
||
|
|
def dup_inner_isolate_negative_roots(self, f, inf=None, sup=None, eps=None, fast=False, mobius=False):
|
||
|
|
return dup_inner_isolate_negative_roots(self.to_dense(f), self.domain, inf=inf, sup=sup, eps=eps, fast=fast, mobius=mobius)
|
||
|
|
def dup_isolate_real_roots_sqf(self, f, eps=None, inf=None, sup=None, fast=False, blackbox=False):
|
||
|
|
return dup_isolate_real_roots_sqf(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, fast=fast, blackbox=blackbox)
|
||
|
|
def dup_isolate_real_roots(self, f, eps=None, inf=None, sup=None, basis=False, fast=False):
|
||
|
|
return dup_isolate_real_roots(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, basis=basis, fast=fast)
|
||
|
|
def dup_isolate_real_roots_list(self, polys, eps=None, inf=None, sup=None, strict=False, basis=False, fast=False):
|
||
|
|
return dup_isolate_real_roots_list(list(map(self.to_dense, polys)), self.domain, eps=eps, inf=inf, sup=sup, strict=strict, basis=basis, fast=fast)
|
||
|
|
def dup_count_real_roots(self, f, inf=None, sup=None):
|
||
|
|
return dup_count_real_roots(self.to_dense(f), self.domain, inf=inf, sup=sup)
|
||
|
|
def dup_count_complex_roots(self, f, inf=None, sup=None, exclude=None):
|
||
|
|
return dup_count_complex_roots(self.to_dense(f), self.domain, inf=inf, sup=sup, exclude=exclude)
|
||
|
|
def dup_isolate_complex_roots_sqf(self, f, eps=None, inf=None, sup=None, blackbox=False):
|
||
|
|
return dup_isolate_complex_roots_sqf(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, blackbox=blackbox)
|
||
|
|
def dup_isolate_all_roots_sqf(self, f, eps=None, inf=None, sup=None, fast=False, blackbox=False):
|
||
|
|
return dup_isolate_all_roots_sqf(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, fast=fast, blackbox=blackbox)
|
||
|
|
def dup_isolate_all_roots(self, f, eps=None, inf=None, sup=None, fast=False):
|
||
|
|
return dup_isolate_all_roots(self.to_dense(f), self.domain, eps=eps, inf=inf, sup=sup, fast=fast)
|
||
|
|
|
||
|
|
def fateman_poly_F_1(self):
|
||
|
|
from sympy.polys.specialpolys import dmp_fateman_poly_F_1
|
||
|
|
return tuple(map(self.from_dense, dmp_fateman_poly_F_1(self.ngens-1, self.domain)))
|
||
|
|
def fateman_poly_F_2(self):
|
||
|
|
from sympy.polys.specialpolys import dmp_fateman_poly_F_2
|
||
|
|
return tuple(map(self.from_dense, dmp_fateman_poly_F_2(self.ngens-1, self.domain)))
|
||
|
|
def fateman_poly_F_3(self):
|
||
|
|
from sympy.polys.specialpolys import dmp_fateman_poly_F_3
|
||
|
|
return tuple(map(self.from_dense, dmp_fateman_poly_F_3(self.ngens-1, self.domain)))
|
||
|
|
|
||
|
|
def to_gf_dense(self, element):
|
||
|
|
return gf_strip([ self.domain.dom.convert(c, self.domain) for c in self.wrap(element).to_dense() ])
|
||
|
|
|
||
|
|
def from_gf_dense(self, element):
|
||
|
|
return self.from_dict(dmp_to_dict(element, self.ngens-1, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_degree(self, f):
|
||
|
|
return gf_degree(self.to_gf_dense(f))
|
||
|
|
|
||
|
|
def gf_LC(self, f):
|
||
|
|
return gf_LC(self.to_gf_dense(f), self.domain.dom)
|
||
|
|
def gf_TC(self, f):
|
||
|
|
return gf_TC(self.to_gf_dense(f), self.domain.dom)
|
||
|
|
|
||
|
|
def gf_strip(self, f):
|
||
|
|
return self.from_gf_dense(gf_strip(self.to_gf_dense(f)))
|
||
|
|
def gf_trunc(self, f):
|
||
|
|
return self.from_gf_dense(gf_strip(self.to_gf_dense(f), self.domain.mod))
|
||
|
|
def gf_normal(self, f):
|
||
|
|
return self.from_gf_dense(gf_strip(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_from_dict(self, f):
|
||
|
|
return self.from_gf_dense(gf_from_dict(f, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_to_dict(self, f, symmetric=True):
|
||
|
|
return gf_to_dict(self.to_gf_dense(f), self.domain.mod, symmetric=symmetric)
|
||
|
|
|
||
|
|
def gf_from_int_poly(self, f):
|
||
|
|
return self.from_gf_dense(gf_from_int_poly(f, self.domain.mod))
|
||
|
|
def gf_to_int_poly(self, f, symmetric=True):
|
||
|
|
return gf_to_int_poly(self.to_gf_dense(f), self.domain.mod, symmetric=symmetric)
|
||
|
|
|
||
|
|
def gf_neg(self, f):
|
||
|
|
return self.from_gf_dense(gf_neg(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_add_ground(self, f, a):
|
||
|
|
return self.from_gf_dense(gf_add_ground(self.to_gf_dense(f), a, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_sub_ground(self, f, a):
|
||
|
|
return self.from_gf_dense(gf_sub_ground(self.to_gf_dense(f), a, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_mul_ground(self, f, a):
|
||
|
|
return self.from_gf_dense(gf_mul_ground(self.to_gf_dense(f), a, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_quo_ground(self, f, a):
|
||
|
|
return self.from_gf_dense(gf_quo_ground(self.to_gf_dense(f), a, self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_add(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_add(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_sub(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_sub(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_mul(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_mul(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_sqr(self, f):
|
||
|
|
return self.from_gf_dense(gf_sqr(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_add_mul(self, f, g, h):
|
||
|
|
return self.from_gf_dense(gf_add_mul(self.to_gf_dense(f), self.to_gf_dense(g), self.to_gf_dense(h), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_sub_mul(self, f, g, h):
|
||
|
|
return self.from_gf_dense(gf_sub_mul(self.to_gf_dense(f), self.to_gf_dense(g), self.to_gf_dense(h), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_expand(self, F):
|
||
|
|
return self.from_gf_dense(gf_expand(list(map(self.to_gf_dense, F)), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_div(self, f, g):
|
||
|
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q, r = gf_div(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom)
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||
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|
return self.from_gf_dense(q), self.from_gf_dense(r)
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||
|
|
def gf_rem(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_rem(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_quo(self, f, g):
|
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|
|
return self.from_gf_dense(gf_quo(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_exquo(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_exquo(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_lshift(self, f, n):
|
||
|
|
return self.from_gf_dense(gf_lshift(self.to_gf_dense(f), n, self.domain.dom))
|
||
|
|
def gf_rshift(self, f, n):
|
||
|
|
return self.from_gf_dense(gf_rshift(self.to_gf_dense(f), n, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_pow(self, f, n):
|
||
|
|
return self.from_gf_dense(gf_pow(self.to_gf_dense(f), n, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_pow_mod(self, f, n, g):
|
||
|
|
return self.from_gf_dense(gf_pow_mod(self.to_gf_dense(f), n, self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_cofactors(self, f, g):
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||
|
|
h, cff, cfg = gf_cofactors(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom)
|
||
|
|
return self.from_gf_dense(h), self.from_gf_dense(cff), self.from_gf_dense(cfg)
|
||
|
|
def gf_gcd(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_gcd(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_lcm(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_lcm(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_gcdex(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_gcdex(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_monic(self, f):
|
||
|
|
return self.from_gf_dense(gf_monic(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_diff(self, f):
|
||
|
|
return self.from_gf_dense(gf_diff(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_eval(self, f, a):
|
||
|
|
return gf_eval(self.to_gf_dense(f), a, self.domain.mod, self.domain.dom)
|
||
|
|
def gf_multi_eval(self, f, A):
|
||
|
|
return gf_multi_eval(self.to_gf_dense(f), A, self.domain.mod, self.domain.dom)
|
||
|
|
|
||
|
|
def gf_compose(self, f, g):
|
||
|
|
return self.from_gf_dense(gf_compose(self.to_gf_dense(f), self.to_gf_dense(g), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_compose_mod(self, g, h, f):
|
||
|
|
return self.from_gf_dense(gf_compose_mod(self.to_gf_dense(g), self.to_gf_dense(h), self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_trace_map(self, a, b, c, n, f):
|
||
|
|
a = self.to_gf_dense(a)
|
||
|
|
b = self.to_gf_dense(b)
|
||
|
|
c = self.to_gf_dense(c)
|
||
|
|
f = self.to_gf_dense(f)
|
||
|
|
U, V = gf_trace_map(a, b, c, n, f, self.domain.mod, self.domain.dom)
|
||
|
|
return self.from_gf_dense(U), self.from_gf_dense(V)
|
||
|
|
|
||
|
|
def gf_random(self, n):
|
||
|
|
return self.from_gf_dense(gf_random(n, self.domain.mod, self.domain.dom))
|
||
|
|
def gf_irreducible(self, n):
|
||
|
|
return self.from_gf_dense(gf_irreducible(n, self.domain.mod, self.domain.dom))
|
||
|
|
|
||
|
|
def gf_irred_p_ben_or(self, f):
|
||
|
|
return gf_irred_p_ben_or(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
def gf_irred_p_rabin(self, f):
|
||
|
|
return gf_irred_p_rabin(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
def gf_irreducible_p(self, f):
|
||
|
|
return gf_irreducible_p(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
def gf_sqf_p(self, f):
|
||
|
|
return gf_sqf_p(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
|
||
|
|
def gf_sqf_part(self, f):
|
||
|
|
return self.from_gf_dense(gf_sqf_part(self.to_gf_dense(f), self.domain.mod, self.domain.dom))
|
||
|
|
def gf_sqf_list(self, f, all=False):
|
||
|
|
coeff, factors = gf_sqf_part(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return coeff, [ (self.from_gf_dense(g), k) for g, k in factors ]
|
||
|
|
|
||
|
|
def gf_Qmatrix(self, f):
|
||
|
|
return gf_Qmatrix(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
def gf_berlekamp(self, f):
|
||
|
|
factors = gf_berlekamp(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
|
||
|
|
def gf_ddf_zassenhaus(self, f):
|
||
|
|
factors = gf_ddf_zassenhaus(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ (self.from_gf_dense(g), k) for g, k in factors ]
|
||
|
|
def gf_edf_zassenhaus(self, f, n):
|
||
|
|
factors = gf_edf_zassenhaus(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
|
||
|
|
def gf_ddf_shoup(self, f):
|
||
|
|
factors = gf_ddf_shoup(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ (self.from_gf_dense(g), k) for g, k in factors ]
|
||
|
|
def gf_edf_shoup(self, f, n):
|
||
|
|
factors = gf_edf_shoup(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
|
||
|
|
def gf_zassenhaus(self, f):
|
||
|
|
factors = gf_zassenhaus(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
def gf_shoup(self, f):
|
||
|
|
factors = gf_shoup(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
|
||
|
|
def gf_factor_sqf(self, f, method=None):
|
||
|
|
coeff, factors = gf_factor_sqf(self.to_gf_dense(f), self.domain.mod, self.domain.dom, method=method)
|
||
|
|
return coeff, [ self.from_gf_dense(g) for g in factors ]
|
||
|
|
def gf_factor(self, f):
|
||
|
|
coeff, factors = gf_factor(self.to_gf_dense(f), self.domain.mod, self.domain.dom)
|
||
|
|
return coeff, [ (self.from_gf_dense(g), k) for g, k in factors ]
|