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Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z  ddӐl!m"Z" e"G ddՄ dՃZ#dS )z8Compatibility interface between dense and sparse polys.     )dup_add_term)dmp_add_term)dup_sub_term)dmp_sub_term)dup_mul_term)dmp_mul_term)dup_add_ground)dmp_add_ground)dup_sub_ground)dmp_sub_ground)dup_mul_ground)dmp_mul_ground)dup_quo_ground)dmp_quo_ground)dup_exquo_ground)dmp_exquo_ground)
dup_lshift)
dup_rshift)dup_abs)dmp_abs)dup_neg)dmp_neg)dup_add)dmp_add)dup_sub)dmp_sub)dup_add_mul)dmp_add_mul)dup_sub_mul)dmp_sub_mul)dup_mul)dmp_mul)dup_sqr)dmp_sqr)dup_pow)dmp_pow)dup_pdiv)dup_prem)dup_pquo)
dup_pexquo)dmp_pdiv)dmp_prem)dmp_pquo)
dmp_pexquo)
dup_rr_div)
dmp_rr_div)
dup_ff_div)
dmp_ff_div)dup_div)dup_rem)dup_quo)	dup_exquo)dmp_div)dmp_rem)dmp_quo)	dmp_exquo)dup_max_norm)dmp_max_norm)dup_l1_norm)dmp_l1_norm)dup_l2_norm_squared)dmp_l2_norm_squared)
dup_expand)
dmp_expand)dup_LC)dmp_LC)dup_TC)dmp_TC)dmp_ground_LC)dmp_ground_TC)
dup_degree)
dmp_degree)dmp_degree_in)dmp_to_dict)dup_integrate)dmp_integrate)dmp_integrate_in)dup_diff)dmp_diff)dmp_diff_in)dup_eval)dmp_eval)dmp_eval_in)dmp_eval_tail)dmp_diff_eval_in)	dup_trunc)	dmp_trunc)dmp_ground_trunc)	dup_monic)dmp_ground_monic)dup_content)dmp_ground_content)dup_primitive)dmp_ground_primitive)dup_extract)dmp_ground_extract)dup_real_imag)
dup_mirror)	dup_scale)	dup_shift)	dmp_shift)dup_transform)dup_compose)dmp_compose)dup_decompose)dmp_lift)dup_sign_variations)dup_clear_denoms)dmp_clear_denoms)
dup_revert)dup_half_gcdex)dmp_half_gcdex)	dup_gcdex)	dmp_gcdex)
dup_invert)
dmp_invert)dup_euclidean_prs)dmp_euclidean_prs)dup_primitive_prs)dmp_primitive_prs)dup_inner_subresultants)dup_subresultants)dup_prs_resultant)dup_resultant)dmp_inner_subresultants)dmp_subresultants)dmp_prs_resultant)dmp_zz_modular_resultant)dmp_zz_collins_resultant)dmp_qq_collins_resultant)dmp_resultant)dup_discriminant)dmp_discriminant)dup_rr_prs_gcd)dup_ff_prs_gcd)dmp_rr_prs_gcd)dmp_ff_prs_gcd)dup_zz_heu_gcd)dmp_zz_heu_gcd)dup_qq_heu_gcd)dmp_qq_heu_gcd)dup_inner_gcd)dmp_inner_gcd)dup_gcd)dmp_gcd)
dup_rr_lcm)
dup_ff_lcm)dup_lcm)
dmp_rr_lcm)
dmp_ff_lcm)dmp_lcm)dmp_content)dmp_primitive)
dup_cancel)
dmp_cancel)dup_trial_division)dmp_trial_division)dup_zz_mignotte_bound)dmp_zz_mignotte_bound)dup_zz_hensel_step)dup_zz_hensel_lift)dup_zz_zassenhaus)dup_zz_irreducible_p)dup_cyclotomic_p)dup_zz_cyclotomic_poly)dup_zz_cyclotomic_factor)dup_zz_factor_sqf)dup_zz_factor)dmp_zz_wang_non_divisors)dmp_zz_wang_lead_coeffs)dup_zz_diophantine)dmp_zz_diophantine)dmp_zz_wang_hensel_lifting)dmp_zz_wang)dmp_zz_factor)dup_qq_i_factor)dup_zz_i_factor)dmp_qq_i_factor)dmp_zz_i_factor)dup_ext_factor)dmp_ext_factor)dup_gf_factor)dmp_gf_factor)dup_factor_list)dup_factor_list_include)dmp_factor_list)dmp_factor_list_include)dup_irreducible_p)dmp_irreducible_p)	dup_sturm)dup_root_upper_bound)dup_root_lower_bound)dup_step_refine_real_root)dup_inner_refine_real_root)dup_outer_refine_real_root)dup_refine_real_root)dup_inner_isolate_real_roots) dup_inner_isolate_positive_roots) dup_inner_isolate_negative_roots)dup_isolate_real_roots_sqf)dup_isolate_real_roots)dup_isolate_real_roots_list)dup_count_real_roots)dup_count_complex_roots)dup_isolate_complex_roots_sqf)dup_isolate_all_roots_sqf)dup_isolate_all_roots)	dup_sqf_p	dmp_sqf_pdmp_normdup_sqf_normdmp_sqf_normdup_gf_sqf_partdmp_gf_sqf_partdup_sqf_partdmp_sqf_partdup_gf_sqf_listdmp_gf_sqf_listdup_sqf_listdup_sqf_list_includedmp_sqf_listdmp_sqf_list_includedup_gff_listdmp_gff_list)8	gf_degreegf_LCgf_TCgf_stripgf_from_dict
gf_to_dictgf_from_int_polygf_to_int_polygf_neggf_add_groundgf_sub_groundgf_mul_groundgf_quo_groundgf_addgf_subgf_mulgf_sqr
gf_add_mul
gf_sub_mul	gf_expandgf_divgf_remgf_quogf_exquo	gf_lshift	gf_rshiftgf_pow
gf_pow_modgf_gcdgf_lcmgf_cofactorsgf_gcdexgf_monicgf_diffgf_evalgf_multi_eval
gf_composegf_compose_modgf_trace_map	gf_randomgf_irreduciblegf_irred_p_ben_orgf_irred_p_rabingf_irreducible_pgf_sqf_pgf_sqf_part
gf_Qmatrixgf_berlekampgf_ddf_zassenhausgf_edf_zassenhausgf_ddf_shoupgf_edf_shoupgf_zassenhausgf_shoupgf_factor_sqf	gf_factor)publicc                   @   s  e Zd ZdZdZdZdZdZdd ZdTddZ	dd Z
dd	 Zd
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d
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ground_new   s    zIPolys.ground_newc                 C   s   d S r  r  r(  r  r  r   
domain_new   s    zIPolys.domain_newc                 C   s   d S r  r  )r  dr  r  r   	from_dict   s    zIPolys.from_dictc                 C   s<   ddl m} t||r.|j| kr$|S tdn
| |S d S )Nr   )PolyElementzdomain conversions)Zsympy.polys.ringsr.  
isinstanceringNotImplementedErrorr*  )r  r)  r.  r  r  r   wrap  s    


zIPolys.wrapc                 C   s   |  | S r  )r2  to_denser(  r  r  r   r3    s    zIPolys.to_densec                 C   s   |  t|| jd | jS N   )r-  rK   ngensr#  r(  r  r  r   
from_dense  s    zIPolys.from_densec                 C   s   |  t| |||| jS r  )r7  r   r3  r#  r  fcir  r  r   r     s    zIPolys.dup_add_termc                 C   s4   |  t| || |d || jd | jS Nr   r5  )r7  r   r3  r2  r!  r6  r#  r8  r  r  r   r     s    zIPolys.dmp_add_termc                 C   s   |  t| |||| jS r  )r7  r   r3  r#  r8  r  r  r   r     s    zIPolys.dup_sub_termc                 C   s4   |  t| || |d || jd | jS r<  )r7  r   r3  r2  r!  r6  r#  r8  r  r  r   r     s    zIPolys.dmp_sub_termc                 C   s   |  t| |||| jS r  )r7  r   r3  r#  r8  r  r  r   r     s    zIPolys.dup_mul_termc                 C   s4   |  t| || |d || jd | jS r<  )r7  r   r3  r2  r!  r6  r#  r8  r  r  r   r     s    zIPolys.dmp_mul_termc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r  r9  r:  r  r  r   r     s    zIPolys.dup_add_groundc                 C   s"   |  t| ||| jd | jS r4  )r7  r	   r3  r6  r#  r=  r  r  r   r	      s    zIPolys.dmp_add_groundc                 C   s   |  t| ||| jS r  )r7  r
   r3  r#  r=  r  r  r   r
   "  s    zIPolys.dup_sub_groundc                 C   s"   |  t| ||| jd | jS r4  )r7  r   r3  r6  r#  r=  r  r  r   r   $  s    zIPolys.dmp_sub_groundc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r=  r  r  r   r   &  s    zIPolys.dup_mul_groundc                 C   s"   |  t| ||| jd | jS r4  )r7  r   r3  r6  r#  r=  r  r  r   r   (  s    zIPolys.dmp_mul_groundc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r=  r  r  r   r   *  s    zIPolys.dup_quo_groundc                 C   s"   |  t| ||| jd | jS r4  )r7  r   r3  r6  r#  r=  r  r  r   r   ,  s    zIPolys.dmp_quo_groundc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r=  r  r  r   r   .  s    zIPolys.dup_exquo_groundc                 C   s"   |  t| ||| jd | jS r4  )r7  r   r3  r6  r#  r=  r  r  r   r   0  s    zIPolys.dmp_exquo_groundc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r  r9  nr  r  r   r   3  s    zIPolys.dup_lshiftc                 C   s   |  t| ||| jS r  )r7  r   r3  r#  r>  r  r  r   r   5  s    zIPolys.dup_rshiftc                 C   s   |  t| || jS r  )r7  r   r3  r#  r  r9  r  r  r   r   8  s    zIPolys.dup_absc                 C   s    |  t| || jd | jS r4  )r7  r   r3  r6  r#  r@  r  r  r   r   :  s    zIPolys.dmp_absc                 C   s   |  t| || jS r  )r7  r   r3  r#  r@  r  r  r   r   =  s    zIPolys.dup_negc                 C   s    |  t| || jd | jS r4  )r7  r   r3  r6  r#  r@  r  r  r   r   ?  s    zIPolys.dmp_negc                 C   s    |  t| || || jS r  )r7  r   r3  r#  r  r9  gr  r  r   r   B  s    zIPolys.dup_addc                 C   s(   |  t| || || jd | jS r4  )r7  r   r3  r6  r#  rA  r  r  r   r   D  s    zIPolys.dmp_addc                 C   s    |  t| || || jS r  )r7  r   r3  r#  rA  r  r  r   r   G  s    zIPolys.dup_subc                 C   s(   |  t| || || jd | jS r4  )r7  r   r3  r6  r#  rA  r  r  r   r   I  s    zIPolys.dmp_subc                 C   s(   |  t| || || || jS r  )r7  r   r3  r#  r  r9  rB  hr  r  r   r   L  s    zIPolys.dup_add_mulc                 C   s0   |  t| || || || jd | jS r4  )r7  r   r3  r6  r#  rC  r  r  r   r   N  s    zIPolys.dmp_add_mulc                 C   s(   |  t| || || || jS r  )r7  r   r3  r#  rC  r  r  r   r   P  s    zIPolys.dup_sub_mulc                 C   s0   |  t| || || || jd | jS r4  )r7  r   r3  r6  r#  rC  r  r  r   r   R  s    zIPolys.dmp_sub_mulc                 C   s    |  t| || || jS r  )r7  r    r3  r#  rA  r  r  r   r    U  s    zIPolys.dup_mulc                 C   s(   |  t| || || jd | jS r4  )r7  r!   r3  r6  r#  rA  r  r  r   r!   W  s    zIPolys.dmp_mulc                 C   s   |  t| || jS r  )r7  r"   r3  r#  r@  r  r  r   r"   Z  s    zIPolys.dup_sqrc                 C   s    |  t| || jd | jS r4  )r7  r#   r3  r6  r#  r@  r  r  r   r#   \  s    zIPolys.dmp_sqrc                 C   s   |  t| ||| jS r  )r7  r$   r3  r#  r>  r  r  r   r$   ^  s    zIPolys.dup_powc                 C   s"   |  t| ||| jd | jS r4  )r7  r%   r3  r6  r#  r>  r  r  r   r%   `  s    zIPolys.dmp_powc                 C   s2   t | || || j\}}| || |fS r  )r&   r3  r#  r7  r  r9  rB  qrr  r  r   r&   c  s    zIPolys.dup_pdivc                 C   s    |  t| || || jS r  )r7  r'   r3  r#  rA  r  r  r   r'   f  s    zIPolys.dup_premc                 C   s    |  t| || || jS r  )r7  r(   r3  r#  rA  r  r  r   r(   h  s    zIPolys.dup_pquoc                 C   s    |  t| || || jS r  )r7  r)   r3  r#  rA  r  r  r   r)   j  s    zIPolys.dup_pexquoc                 C   s:   t | || || jd | j\}}| || |fS r4  )r*   r3  r6  r#  r7  rE  r  r  r   r*   m  s    &zIPolys.dmp_pdivc                 C   s(   |  t| || || jd | jS r4  )r7  r+   r3  r6  r#  rA  r  r  r   r+   p  s    zIPolys.dmp_premc                 C   s(   |  t| || || jd | jS r4  )r7  r,   r3  r6  r#  rA  r  r  r   r,   r  s    zIPolys.dmp_pquoc                 C   s(   |  t| || || jd | jS r4  )r7  r-   r3  r6  r#  rA  r  r  r   r-   t  s    zIPolys.dmp_pexquoc                 C   s2   t | || || j\}}| || |fS r  )r.   r3  r#  r7  rE  r  r  r   r.   w  s    zIPolys.dup_rr_divc                 C   s:   t | || || jd | j\}}| || |fS r4  )r/   r3  r6  r#  r7  rE  r  r  r   r/   z  s    &zIPolys.dmp_rr_divc                 C   s2   t | || || j\}}| || |fS r  )r0   r3  r#  r7  rE  r  r  r   r0   }  s    zIPolys.dup_ff_divc                 C   s:   t | || || jd | j\}}| || |fS r4  )r1   r3  r6  r#  r7  rE  r  r  r   r1     s    &zIPolys.dmp_ff_divc                 C   s2   t | || || j\}}| || |fS r  )r2   r3  r#  r7  rE  r  r  r   r2     s    zIPolys.dup_divc                 C   s    |  t| || || jS r  )r7  r3   r3  r#  rA  r  r  r   r3     s    zIPolys.dup_remc                 C   s    |  t| || || jS r  )r7  r4   r3  r#  rA  r  r  r   r4     s    zIPolys.dup_quoc                 C   s    |  t| || || jS r  )r7  r5   r3  r#  rA  r  r  r   r5     s    zIPolys.dup_exquoc                 C   s:   t | || || jd | j\}}| || |fS r4  )r6   r3  r6  r#  r7  rE  r  r  r   r6     s    &zIPolys.dmp_divc                 C   s(   |  t| || || jd | jS r4  )r7  r7   r3  r6  r#  rA  r  r  r   r7     s    zIPolys.dmp_remc                 C   s(   |  t| || || jd | jS r4  )r7  r8   r3  r6  r#  rA  r  r  r   r8     s    zIPolys.dmp_quoc                 C   s(   |  t| || || jd | jS r4  )r7  r9   r3  r6  r#  rA  r  r  r   r9     s    zIPolys.dmp_exquoc                 C   s   t | || jS r  )r:   r3  r#  r@  r  r  r   r:     s    zIPolys.dup_max_normc                 C   s   t | || jd | jS r4  )r;   r3  r6  r#  r@  r  r  r   r;     s    zIPolys.dmp_max_normc                 C   s   t | || jS r  )r<   r3  r#  r@  r  r  r   r<     s    zIPolys.dup_l1_normc                 C   s   t | || jd | jS r4  )r=   r3  r6  r#  r@  r  r  r   r=     s    zIPolys.dmp_l1_normc                 C   s   t | || jS r  )r>   r3  r#  r@  r  r  r   r>     s    zIPolys.dup_l2_norm_squaredc                 C   s   t | || jd | jS r4  )r?   r3  r6  r#  r@  r  r  r   r?     s    zIPolys.dmp_l2_norm_squaredc                 C   s   |  ttt| j|| jS r  )r7  r@   listmapr3  r#  r  polysr  r  r   r@     s    zIPolys.dup_expandc                 C   s&   |  ttt| j|| jd | jS r4  )r7  rA   rH  rI  r3  r6  r#  rJ  r  r  r   rA     s    zIPolys.dmp_expandc                 C   s   t | || jS r  )rB   r3  r#  r@  r  r  r   rB     s    zIPolys.dup_LCc                 C   s6   t | || j}t|tr.| dd  |S |S d S r4  )rC   r3  r#  r/  rH  r7  )r  r9  LCr  r  r   rC     s    
zIPolys.dmp_LCc                 C   s   t | || jS r  )rD   r3  r#  r@  r  r  r   rD     s    zIPolys.dup_TCc                 C   s6   t | || j}t|tr.| dd  |S |S d S r4  )rE   r3  r#  r/  rH  r7  )r  r9  ZTCr  r  r   rE     s    
zIPolys.dmp_TCc                 C   s   t | || jd | jS r4  )rF   r3  r6  r#  r@  r  r  r   rF     s    zIPolys.dmp_ground_LCc                 C   s   t | || jd | jS r4  )rG   r3  r6  r#  r@  r  r  r   rG     s    zIPolys.dmp_ground_TCc                 C   s   t | |S r  )rH   r3  r@  r  r  r   rH     s    zIPolys.dup_degreec                 C   s   t | || jd S r4  )rI   r3  r6  r@  r  r  r   rI     s    zIPolys.dmp_degreec                 C   s   t | ||| jd S r4  )rJ   r3  r6  )r  r9  jr  r  r   rJ     s    zIPolys.dmp_degree_inc                 C   s   |  t| ||| jS r  )r7  rL   r3  r#  r  r9  mr  r  r   rL     s    zIPolys.dup_integratec                 C   s"   |  t| ||| jd | jS r4  )r7  rM   r3  r6  r#  rN  r  r  r   rM     s    zIPolys.dmp_integratec                 C   s   |  t| ||| jS r  )r7  rO   r3  r#  rN  r  r  r   rO     s    zIPolys.dup_diffc                 C   s"   |  t| ||| jd | jS r4  )r7  rP   r3  r6  r#  rN  r  r  r   rP     s    zIPolys.dmp_diffc                 C   s$   |  t| |||| jd | jS r4  )r7  rQ   r3  r6  r#  r  r9  rO  rM  r  r  r   rQ     s    zIPolys.dmp_diff_inc                 C   s$   |  t| |||| jd | jS r4  )r7  rN   r3  r6  r#  rP  r  r  r   rN     s    zIPolys.dmp_integrate_inc                 C   s   t | ||| jS r  )rR   r3  r#  r  r9  ar  r  r   rR     s    zIPolys.dup_evalc                 C   s.   t | ||| jd | j}| dd  |S r4  )rS   r3  r6  r#  r7  )r  r9  rR  resultr  r  r   rS     s    zIPolys.dmp_evalc                 C   s.   t | |||| jd | j}| ||S r4  )rT   r3  r6  r#  r!  r7  )r  r9  rR  rM  rS  r  r  r   rT     s    zIPolys.dmp_eval_inc                 C   s0   t | ||||| jd | j}| ||S r4  )rV   r3  r6  r#  r!  r7  )r  r9  rO  rR  rM  rS  r  r  r   rV     s     zIPolys.dmp_diff_eval_inc                 C   sF   t | ||| jd | j}t|tr>| d t|  |S |S d S r4  )rU   r3  r6  r#  r/  rH  lenr7  )r  r9  ArS  r  r  r   rU     s    
zIPolys.dmp_eval_tailc                 C   s   |  t| ||| jS r  )r7  rW   r3  r#  r  r9  pr  r  r   rW     s    zIPolys.dup_truncc                 C   s0   |  t| || dd  || jd | jS r4  )r7  rX   r3  r6  r#  rA  r  r  r   rX     s    zIPolys.dmp_truncc                 C   s"   |  t| ||| jd | jS r4  )r7  rY   r3  r6  r#  rV  r  r  r   rY     s    zIPolys.dmp_ground_truncc                 C   s   |  t| || jS r  )r7  rZ   r3  r#  r@  r  r  r   rZ     s    zIPolys.dup_monicc                 C   s    |  t| || jd | jS r4  )r7  r[   r3  r6  r#  r@  r  r  r   r[     s    zIPolys.dmp_ground_monicc                 C   s6   t | || || j\}}}|| || |fS r  )r`   r3  r#  r7  r  r9  rB  r:  FGr  r  r   r`     s     zIPolys.dup_extractc                 C   s>   t | || || jd | j\}}}|| || |fS r4  )ra   r3  r6  r#  r7  rX  r  r  r   ra     s    (zIPolys.dmp_ground_extractc                 C   s4   t | |d | j\}}| || |fS r4  )rb   r2  r!  r3  r#  r7  r  r9  rW  rF  r  r  r   rb     s     zIPolys.dup_real_imagc                 C   s   |  t| || jS r  )r7  rc   r3  r#  r@  r  r  r   rc     s    zIPolys.dup_mirrorc                 C   s   |  t| ||| jS r  )r7  rd   r3  r#  rQ  r  r  r   rd     s    zIPolys.dup_scalec                 C   s   |  t| ||| jS r  )r7  re   r3  r#  rQ  r  r  r   re     s    zIPolys.dup_shiftc                 C   s"   |  t| ||| jd | jS r4  )r7  rf   r3  r6  r#  rQ  r  r  r   rf     s    zIPolys.dmp_shiftc                 C   s(   |  t| || || || jS r  )r7  rg   r3  r#  r[  r  r  r   rg   
  s    zIPolys.dup_transformc                 C   s    |  t| || || jS r  )r7  rh   r3  r#  rA  r  r  r   rh     s    zIPolys.dup_composec                 C   s(   |  t| || || jd | jS r4  )r7  ri   r3  r6  r#  rA  r  r  r   ri     s    zIPolys.dmp_composec                 C   s"   t | || j}tt| j|S r  )rj   r3  r#  rH  rI  r7  )r  r9  
componentsr  r  r   rj     s    zIPolys.dup_decomposec                 C   s(   t | || jd | j}|  |S r4  )rk   r3  r6  r#  r'  r7  r  r9  rS  r  r  r   rk     s    zIPolys.dmp_liftc                 C   s   t | || jS r  )rl   r3  r#  r@  r  r  r   rl     s    zIPolys.dup_sign_variationsFc                 C   sD   t | || j|d\}}|r2| j| j d}n| }|||fS )Nconvertr#  )rm   r3  r#  r%  get_ringr7  r  r9  r_  r:  rY  r0  r  r  r   rm     s
    zIPolys.dup_clear_denomsc                 C   sL   t | || jd | j|d\}}|r:| j| j d}n| }|||fS )Nr5  r^  r`  )rn   r3  r6  r#  r%  ra  r7  rb  r  r  r   rn   $  s
    "zIPolys.dmp_clear_denomsc                 C   s   |  t| ||| jS r  )r7  ro   r3  r#  r>  r  r  r   ro   ,  s    zIPolys.dup_revertc                 C   s2   t | || || j\}}| || |fS r  )rp   r3  r#  r7  r  r9  rB  srD  r  r  r   rp   /  s    zIPolys.dup_half_gcdexc                 C   s:   t | || || jd | j\}}| || |fS r4  )rq   r3  r6  r#  r7  rc  r  r  r   rq   2  s    &zIPolys.dmp_half_gcdexc                 C   s<   t | || || j\}}}| || || |fS r  )rr   r3  r#  r7  r  r9  rB  rd  trD  r  r  r   rr   5  s     zIPolys.dup_gcdexc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )rs   r3  r6  r#  r7  re  r  r  r   rs   8  s    (zIPolys.dmp_gcdexc                 C   s    |  t| || || jS r  )r7  rt   r3  r#  rA  r  r  r   rt   <  s    zIPolys.dup_invertc                 C   s(   |  t| || || jd | jS r4  )r7  ru   r3  r6  r#  rA  r  r  r   ru   >  s    zIPolys.dmp_invertc                 C   s*   t | || || j}tt| j|S r  )rv   r3  r#  rH  rI  r7  r  r9  rB  prsr  r  r   rv   A  s    zIPolys.dup_euclidean_prsc                 C   s2   t | || || jd | j}tt| j|S r4  )rw   r3  r6  r#  rH  rI  r7  rg  r  r  r   rw   D  s    "zIPolys.dmp_euclidean_prsc                 C   s*   t | || || j}tt| j|S r  )rx   r3  r#  rH  rI  r7  rg  r  r  r   rx   G  s    zIPolys.dup_primitive_prsc                 C   s2   t | || || jd | j}tt| j|S r4  )ry   r3  r6  r#  rH  rI  r7  rg  r  r  r   ry   J  s    "zIPolys.dmp_primitive_prsc                 C   s2   t | || || j\}}tt| j||fS r  )rz   r3  r#  rH  rI  r7  r  r9  rB  rh  sresr  r  r   rz   N  s    zIPolys.dup_inner_subresultantsc                 C   s:   t | || || jd | j\}}tt| j||fS r4  )r~   r3  r6  r#  rH  rI  r7  ri  r  r  r   r~   Q  s    &zIPolys.dmp_inner_subresultantsc                 C   s*   t | || || j}tt| j|S r  )r{   r3  r#  rH  rI  r7  rg  r  r  r   r{   U  s    zIPolys.dup_subresultantsc                 C   s2   t | || || jd | j}tt| j|S r4  )r   r3  r6  r#  rH  rI  r7  rg  r  r  r   r   X  s    "zIPolys.dmp_subresultantsc                 C   s2   t | || || j\}}|tt| j|fS r  )r|   r3  r#  rH  rI  r7  r  r9  rB  resrh  r  r  r   r|   \  s    zIPolys.dup_prs_resultantc                 C   sH   t | || || jd | j\}}| dd  |tt| j|fS r4  )r   r3  r6  r#  r7  rH  rI  rk  r  r  r   r   _  s    &zIPolys.dmp_prs_resultantc                 C   s<   t | || || || jd | j}| dd  |S r4  )r   r3  r+  r6  r#  r7  )r  r9  rB  rW  rl  r  r  r   r   c  s    *zIPolys.dmp_zz_modular_resultantc                 C   s4   t | || || jd | j}| dd  |S r4  )r   r3  r6  r#  r7  r  r9  rB  rl  r  r  r   r   f  s    "zIPolys.dmp_zz_collins_resultantc                 C   s4   t | || || jd | j}| dd  |S r4  )r   r3  r6  r#  r7  rm  r  r  r   r   i  s    "zIPolys.dmp_qq_collins_resultantc                 C   s   t | || || jS r  )r}   r3  r#  rA  r  r  r   r}   m  s    zIPolys.dup_resultantc                 C   sF   t | || || jd | j}t|tr>| dd  |S |S d S r4  )r   r3  r6  r#  r/  rH  r7  rm  r  r  r   r   o  s    "
zIPolys.dmp_resultantc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r   v  s    zIPolys.dup_discriminantc                 C   s>   t | || jd | j}t|tr6| dd  |S |S d S r4  )r   r3  r6  r#  r/  rH  r7  )r  r9  Zdiscr  r  r   r   x  s    
zIPolys.dmp_discriminantc                 C   s<   t | || || j\}}}| || || |fS r  )r   r3  r#  r7  r  r9  rB  HrY  rZ  r  r  r   r     s     zIPolys.dup_rr_prs_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r3  r#  r7  rn  r  r  r   r     s     zIPolys.dup_ff_prs_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )r   r3  r6  r#  r7  rn  r  r  r   r     s    (zIPolys.dmp_rr_prs_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )r   r3  r6  r#  r7  rn  r  r  r   r     s    (zIPolys.dmp_ff_prs_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r3  r#  r7  rn  r  r  r   r     s     zIPolys.dup_zz_heu_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )r   r3  r6  r#  r7  rn  r  r  r   r     s    (zIPolys.dmp_zz_heu_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r3  r#  r7  rn  r  r  r   r     s     zIPolys.dup_qq_heu_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )r   r3  r6  r#  r7  rn  r  r  r   r     s    (zIPolys.dmp_qq_heu_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r3  r#  r7  rn  r  r  r   r     s     zIPolys.dup_inner_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r4  )r   r3  r6  r#  r7  rn  r  r  r   r     s    (zIPolys.dmp_inner_gcdc                 C   s$   t | || || j}| |S r  )r   r3  r#  r7  r  r9  rB  ro  r  r  r   r     s    zIPolys.dup_gcdc                 C   s,   t | || || jd | j}| |S r4  )r   r3  r6  r#  r7  rp  r  r  r   r     s    "zIPolys.dmp_gcdc                 C   s$   t | || || j}| |S r  )r   r3  r#  r7  rp  r  r  r   r     s    zIPolys.dup_rr_lcmc                 C   s$   t | || || j}| |S r  )r   r3  r#  r7  rp  r  r  r   r     s    zIPolys.dup_ff_lcmc                 C   s$   t | || || j}| |S r  )r   r3  r#  r7  rp  r  r  r   r     s    zIPolys.dup_lcmc                 C   s,   t | || || jd | j}| |S r4  )r   r3  r6  r#  r7  rp  r  r  r   r     s    "zIPolys.dmp_rr_lcmc                 C   s,   t | || || jd | j}| |S r4  )r   r3  r6  r#  r7  rp  r  r  r   r     s    "zIPolys.dmp_ff_lcmc                 C   s,   t | || || jd | j}| |S r4  )r   r3  r6  r#  r7  rp  r  r  r   r     s    "zIPolys.dmp_lcmc                 C   s   t | || j}|S r  )r\   r3  r#  r  r9  contr  r  r   r\     s    zIPolys.dup_contentc                 C   s$   t | || j\}}|| |fS r  )r^   r3  r#  r7  r  r9  rr  Zprimr  r  r   r^     s    zIPolys.dup_primitivec                 C   s>   t | || jd | j}t|tr6| dd  |S |S d S r4  )r   r3  r6  r#  r/  rH  r7  rq  r  r  r   r     s    
zIPolys.dmp_contentc                 C   sV   t | || jd | j\}}t|trD| dd  || |fS || |fS d S r4  )r   r3  r6  r#  r/  rH  r7  rs  r  r  r   r     s    
zIPolys.dmp_primitivec                 C   s   t | || jd | j}|S r4  )r]   r3  r6  r#  rq  r  r  r   r]     s    zIPolys.dmp_ground_contentc                 C   s,   t | || jd | j\}}|| |fS r4  )r_   r3  r6  r#  r7  rs  r  r  r   r_     s    zIPolys.dmp_ground_primitiveTc           	      C   sf   t | || || j|d}|sF|\}}}}||| || |fS |\}}| || |fS d S )Ninclude)r   r3  r#  r7  	r  r9  rB  ru  rS  cfZcgrY  rZ  r  r  r   r     s    zIPolys.dup_cancelc           	      C   sn   t | || || jd | j|d}|sN|\}}}}||| || |fS |\}}| || |fS d S )Nr5  rt  )r   r3  r6  r#  r7  rv  r  r  r   r     s    &zIPolys.dmp_cancelc                    s2   t  |tt j| j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r7  .0rB  kr&  r  r   
<listcomp>  s     z-IPolys.dup_trial_division.<locals>.<listcomp>)r   r3  rH  rI  r#  r  r9  factorsr  r&  r   r     s     zIPolys.dup_trial_divisionc                    s:   t  |tt j| jd  j} fdd|D S )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z-IPolys.dmp_trial_division.<locals>.<listcomp>)r   r3  rH  rI  r6  r#  r}  r  r&  r   r     s    (zIPolys.dmp_trial_divisionc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_zz_mignotte_boundc                 C   s   t | || jd | jS r4  )r   r3  r6  r#  r@  r  r  r   r     s    zIPolys.dmp_zz_mignotte_boundc                 C   s\   | j }t|||||||||||| j\}}	}
}| || |	| |
| |fS r  )r3  r   r#  r7  )r  rO  r9  rB  rD  rd  rf  DrZ  ro  STr  r  r   r     s    2zIPolys.dup_zz_hensel_stepc                 C   s6   | j }t|||tt|||| j}tt| j|S r  )r3  r   rH  rI  r#  r7  )r  rW  r9  Zf_listlr  rK  r  r  r   r     s     zIPolys.dup_zz_hensel_liftc                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z,IPolys.dup_zz_zassenhaus.<locals>.<listcomp>)r   r3  r#  r}  r  r&  r   r     s    zIPolys.dup_zz_zassenhausc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_zz_irreducible_pc                 C   s   t | || j|dS )N)irreducible)r   r3  r#  )r  r9  r  r  r  r   r     s    zIPolys.dup_cyclotomic_pc                 C   s   t || j}| |S r  )r   r#  r7  )r  r?  rY  r  r  r   r     s    zIPolys.dup_zz_cyclotomic_polyc                 C   s2   t | || j}|d kr|S tt| j|S d S r  )r   r3  r#  rH  rI  r7  r]  r  r  r   r     s    zIPolys.dup_zz_cyclotomic_factorc                 C   s   t |||| jS r  )r   r#  )r  Ecsctr  r  r   r   
  s    zIPolys.dmp_zz_wang_non_divisorsc           
   	      s   | dd    fdd|D }| d d }t t|j|}t| ||||||| jd | j\}}}	| |t t|j|t t j|	fS )Nr5  c                    s   g | ]\}}  ||fqS r  )r3  )rz  rf  r{  mvr  r   r|    s     z2IPolys.dmp_zz_wang_lead_coeffs.<locals>.<listcomp>)rH  rI  r3  r   r6  r#  r7  )
r  r9  r  r  r  ro  rU  uvZHHCCr  r  r   r     s    *zIPolys.dmp_zz_wang_lead_coeffsc                 C   s,   t tt| j|||| j}tt| j|S r  )r   rH  rI  r3  r#  r7  )r  rY  rO  rW  rS  r  r  r   r     s    zIPolys.dup_zz_diophantinec                 C   s>   t tt| j|| ||||| jd | j}tt| j|S r4  )r   rH  rI  r3  r6  r#  r7  )r  rY  r:  rU  r,  rW  rS  r  r  r   r      s    .zIPolys.dmp_zz_diophantinec           	      C   sj   | d d }| dd  }t t|j|}t t|j|}t| |||||| jd | j}t t| j|S r4  )rH  rI  r3  r   r6  r#  r7  )	r  r9  ro  rL  rU  rW  r  r  rS  r  r  r   r   %  s    "z!IPolys.dmp_zz_wang_hensel_liftingc                    s2   t  | jd  j||d} fdd|D S )Nr5  )modseedc                    s   g | ]}  |qS r  rx  rz  rB  r&  r  r   r|  /  s     z&IPolys.dmp_zz_wang.<locals>.<listcomp>)r   r3  r6  r#  )r  r9  r  r  r~  r  r&  r   r   -  s     zIPolys.dmp_zz_wangc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]}  |qS r  rx  r  r&  r  r   r|  3  s     z,IPolys.dup_zz_factor_sqf.<locals>.<listcomp>)r   r3  r#  r  r9  coeffr~  r  r&  r   r   1  s    zIPolys.dup_zz_factor_sqfc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  7  s     z(IPolys.dup_zz_factor.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   5  s    zIPolys.dup_zz_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  :  s     z(IPolys.dmp_zz_factor.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   8  s    zIPolys.dmp_zz_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  >  s     z*IPolys.dup_qq_i_factor.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   <  s    zIPolys.dup_qq_i_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  A  s     z*IPolys.dmp_qq_i_factor.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   ?  s    zIPolys.dmp_qq_i_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  E  s     z*IPolys.dup_zz_i_factor.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   C  s    zIPolys.dup_zz_i_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  H  s     z*IPolys.dmp_zz_i_factor.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   F  s    zIPolys.dmp_zz_i_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  L  s     z)IPolys.dup_ext_factor.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   J  s    zIPolys.dup_ext_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  O  s     z)IPolys.dmp_ext_factor.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   M  s    zIPolys.dmp_ext_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  S  s     z(IPolys.dup_gf_factor.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   Q  s    zIPolys.dup_gf_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  V  s     z(IPolys.dmp_gf_factor.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   T  s    zIPolys.dmp_gf_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  Z  s     z*IPolys.dup_factor_list.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r   X  s    zIPolys.dup_factor_listc                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  ]  s     z2IPolys.dup_factor_list_include.<locals>.<listcomp>)r   r3  r#  r}  r  r&  r   r   [  s    zIPolys.dup_factor_list_includec                    s4   t  | jd  j\}}| fdd|D fS )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  a  s     z*IPolys.dmp_factor_list.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r   _  s    zIPolys.dmp_factor_listc                    s,   t  | jd  j} fdd|D S )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|  d  s     z2IPolys.dmp_factor_list_include.<locals>.<listcomp>)r   r3  r6  r#  r}  r  r&  r   r   b  s    zIPolys.dmp_factor_list_includec                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r   f  s    zIPolys.dup_irreducible_pc                 C   s   t | || jd | jS r4  )r   r3  r6  r#  r@  r  r  r   r   h  s    zIPolys.dmp_irreducible_pc                 C   s"   t | || j}tt| j|S r  )r   r3  r#  rH  rI  r7  )r  r9  seqr  r  r   r   k  s    zIPolys.dup_sturmc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r   o  s    zIPolys.dup_sqf_pc                 C   s   t | || jd | jS r4  )r   r3  r6  r#  r@  r  r  r   r   q  s    zIPolys.dmp_sqf_pc                 C   s(   t | || jd | j}|  |S r4  )r   r3  r6  r#  r'  r7  r>  r  r  r   r   t  s    zIPolys.dmp_normc                 C   s2   t | || j\}}}|| ||  |fS r  )r   r3  r#  r7  r'  r  r9  rd  rY  Rr  r  r   r   x  s    zIPolys.dup_sqf_normc                 C   s:   t | || jd | j\}}}|| ||  |fS r4  )r   r3  r6  r#  r7  r'  r  r  r  r   r   {  s     zIPolys.dmp_sqf_normc                 C   s   |  t| || jS r  )r7  r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_gf_sqf_partc                 C   s   |  t| || jS r  )r7  r   r3  r#  r@  r  r  r   r     s    zIPolys.dmp_gf_sqf_partc                 C   s   |  t| || jS r  )r7  r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_sqf_partc                 C   s    |  t| || jd | jS r4  )r7  r   r3  r6  r#  r@  r  r  r   r     s    zIPolys.dmp_sqf_partc                    s0   t  | j|d\}}| fdd|D fS )Nallc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z*IPolys.dup_gf_sqf_list.<locals>.<listcomp>)r   r3  r#  r  r9  r  r  r~  r  r&  r   r     s    zIPolys.dup_gf_sqf_listc                    s8   t  | jd  j|d\}}| fdd|D fS )Nr5  r  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z*IPolys.dmp_gf_sqf_list.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r     s    "zIPolys.dmp_gf_sqf_listc                    s0   t  | j|d\}}| fdd|D fS )Nr  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z'IPolys.dup_sqf_list.<locals>.<listcomp>)r   r3  r#  r  r  r&  r   r     s    zIPolys.dup_sqf_listc                    s(   t  | j|d} fdd|D S )Nr  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z/IPolys.dup_sqf_list_include.<locals>.<listcomp>)r   r3  r#  r  r9  r  r~  r  r&  r   r     s    zIPolys.dup_sqf_list_includec                    s8   t  | jd  j|d\}}| fdd|D fS )Nr5  r  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z'IPolys.dmp_sqf_list.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r     s    "zIPolys.dmp_sqf_listc                    s0   t  | jd  j|d} fdd|D S )Nr5  r  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z/IPolys.dmp_sqf_list_include.<locals>.<listcomp>)r   r3  r6  r#  r  r  r&  r   r     s    zIPolys.dmp_sqf_list_includec                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z'IPolys.dup_gff_list.<locals>.<listcomp>)r   r3  r#  r}  r  r&  r   r     s    zIPolys.dup_gff_listc                    s,   t  | jd  j} fdd|D S )Nr5  c                    s   g | ]\}}  ||fqS r  rx  ry  r&  r  r   r|    s     z'IPolys.dmp_gff_list.<locals>.<listcomp>)r   r3  r6  r#  r}  r  r&  r   r     s    zIPolys.dmp_gff_listc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_root_upper_boundc                 C   s   t | || jS r  )r   r3  r#  r@  r  r  r   r     s    zIPolys.dup_root_lower_boundc                 C   s   t | ||| j|dS )N)fast)r   r3  r#  )r  r9  Mr  r  r  r   r     s    z IPolys.dup_step_refine_real_rootc              
   C   s    t | ||| j|||||dS )N)epsstepsdisjointr  mobius)r   r3  r#  )r  r9  r  r  r  r  r  r  r  r  r   r     s    z!IPolys.dup_inner_refine_real_rootc              
   C   s    t | |||| j||||dS N)r  r  r  r  )r   r3  r#  r  r9  rd  rf  r  r  r  r  r  r  r   r     s    z!IPolys.dup_outer_refine_real_rootc              
   C   s    t | |||| j||||dS r  )r   r3  r#  r  r  r  r   r     s    zIPolys.dup_refine_real_rootc                 C   s   t | || j||dS )N)r  r  )r   r3  r#  )r  r9  r  r  r  r  r   r     s    z#IPolys.dup_inner_isolate_real_rootsc              	   C   s   t | || j|||||dS )N)r  infsupr  r  )r   r3  r#  )r  r9  r  r  r  r  r  r  r  r   r     s    z'IPolys.dup_inner_isolate_positive_rootsc              	   C   s   t | || j|||||dS )N)r  r  r  r  r  )r   r3  r#  )r  r9  r  r  r  r  r  r  r  r   r     s    z'IPolys.dup_inner_isolate_negative_rootsc              	   C   s   t | || j|||||dS N)r  r  r  r  blackbox)r   r3  r#  r  r9  r  r  r  r  r  r  r  r   r     s    z!IPolys.dup_isolate_real_roots_sqfc              	   C   s   t | || j|||||dS )N)r  r  r  basisr  )r   r3  r#  )r  r9  r  r  r  r  r  r  r  r   r     s    zIPolys.dup_isolate_real_rootsc              
   C   s&   t tt| j|| j||||||dS )N)r  r  r  strictr  r  )r   rH  rI  r3  r#  )r  rK  r  r  r  r  r  r  r  r  r   r     s    z"IPolys.dup_isolate_real_roots_listc                 C   s   t | || j||dS )N)r  r  )r   r3  r#  )r  r9  r  r  r  r  r   r     s    zIPolys.dup_count_real_rootsc                 C   s   t | || j|||dS )N)r  r  exclude)r   r3  r#  )r  r9  r  r  r  r  r  r   r     s    zIPolys.dup_count_complex_rootsc                 C   s   t | || j||||dS )N)r  r  r  r  )r   r3  r#  )r  r9  r  r  r  r  r  r  r   r     s    z$IPolys.dup_isolate_complex_roots_sqfc              	   C   s   t | || j|||||dS r  )r   r3  r#  r  r  r  r   r     s    z IPolys.dup_isolate_all_roots_sqfc                 C   s   t | || j||||dS )N)r  r  r  r  )r   r3  r#  )r  r9  r  r  r  r  r  r  r   r     s    zIPolys.dup_isolate_all_rootsc                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_1r5  )sympy.polys.specialpolysr  tuplerI  r7  r6  r#  )r  r  r  r  r   fateman_poly_F_1  s    zIPolys.fateman_poly_F_1c                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_2r5  )r  r  r  rI  r7  r6  r#  )r  r  r  r  r   fateman_poly_F_2  s    zIPolys.fateman_poly_F_2c                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_3r5  )r  r  r  rI  r7  r6  r#  )r  r  r  r  r   fateman_poly_F_3  s    zIPolys.fateman_poly_F_3c                    s    t  fdd | D S )Nc                    s   g | ]} j j| j qS r  )r#  domr_  )rz  r:  r&  r  r   r|    s     z&IPolys.to_gf_dense.<locals>.<listcomp>)r   r2  r3  r(  r  r&  r   to_gf_dense  s    zIPolys.to_gf_densec                 C   s   |  t|| jd | jjS r4  )r-  rK   r6  r#  r  r(  r  r  r   from_gf_dense  s    zIPolys.from_gf_densec                 C   s   t | |S r  )r   r  r@  r  r  r   r     s    zIPolys.gf_degreec                 C   s   t | || jjS r  )r   r  r#  r  r@  r  r  r   r     s    zIPolys.gf_LCc                 C   s   t | || jjS r  )r   r  r#  r  r@  r  r  r   r     s    zIPolys.gf_TCc                 C   s   |  t| |S r  )r  r   r  r@  r  r  r   r     s    zIPolys.gf_stripc                 C   s   |  t| || jjS r  )r  r   r  r#  r  r@  r  r  r   gf_trunc  s    zIPolys.gf_truncc                 C   s    |  t| || jj| jjS r  )r  r   r  r#  r  r  r@  r  r  r   	gf_normal  s    zIPolys.gf_normalc                 C   s   |  t|| jj| jjS r  )r  r   r#  r  r  r@  r  r  r   r     s    zIPolys.gf_from_dictc                 C   s   t | || jj|dS N)	symmetric)r   r  r#  r  r  r9  r  r  r  r   r     s    zIPolys.gf_to_dictc                 C   s   |  t|| jjS r  )r  r   r#  r  r@  r  r  r   r     s    zIPolys.gf_from_int_polyc                 C   s   t | || jj|dS r  )r   r  r#  r  r  r  r  r   r     s    zIPolys.gf_to_int_polyc                 C   s    |  t| || jj| jjS r  )r  r   r  r#  r  r  r@  r  r  r   r     s    zIPolys.gf_negc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r#  r  r  rQ  r  r  r   r     s    zIPolys.gf_add_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r#  r  r  rQ  r  r  r   r     s    zIPolys.gf_sub_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r#  r  r  rQ  r  r  r   r     s    zIPolys.gf_mul_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r#  r  r  rQ  r  r  r   r     s    zIPolys.gf_quo_groundc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r     s    zIPolys.gf_addc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r     s    zIPolys.gf_subc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r      s    zIPolys.gf_mulc                 C   s    |  t| || jj| jjS r  )r  r   r  r#  r  r  r@  r  r  r   r     s    zIPolys.gf_sqrc                 C   s0   |  t| || || || jj| jjS r  )r  r   r  r#  r  r  rC  r  r  r   r     s    zIPolys.gf_add_mulc                 C   s0   |  t| || || || jj| jjS r  )r  r   r  r#  r  r  rC  r  r  r   r     s    zIPolys.gf_sub_mulc                 C   s&   |  ttt| j|| jj| jjS r  )r  r   rH  rI  r  r#  r  r  )r  rY  r  r  r   r   
  s    zIPolys.gf_expandc                 C   s:   t | || || jj| jj\}}| || |fS r  )r   r  r#  r  r  r  rE  r  r  r   r     s    &zIPolys.gf_divc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r     s    zIPolys.gf_remc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r     s    zIPolys.gf_quoc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r     s    zIPolys.gf_exquoc                 C   s   |  t| ||| jjS r  )r  r   r  r#  r  r>  r  r  r   r     s    zIPolys.gf_lshiftc                 C   s   |  t| ||| jjS r  )r  r   r  r#  r  r>  r  r  r   r     s    zIPolys.gf_rshiftc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r#  r  r  r>  r  r  r   r     s    zIPolys.gf_powc                 C   s*   |  t| ||| || jj| jjS r  )r  r   r  r#  r  r  )r  r9  r?  rB  r  r  r   r     s    zIPolys.gf_pow_modc                 C   sD   t | || || jj| jj\}}}| || || |fS r  )r   r  r#  r  r  r  )r  r9  rB  rD  Zcffcfgr  r  r   r   !  s    (zIPolys.gf_cofactorsc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r   $  s    zIPolys.gf_gcdc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r#  r  r  rA  r  r  r   r   &  s    zIPolys.gf_lcmc                 C   s(   |  t| || || jj| jjS r  )r  r  r  r#  r  r  rA  r  r  r   r  (  s    zIPolys.gf_gcdexc                 C   s    |  t| || jj| jjS r  )r  r  r  r#  r  r  r@  r  r  r   r  +  s    zIPolys.gf_monicc                 C   s    |  t| || jj| jjS r  )r  r  r  r#  r  r  r@  r  r  r   r  -  s    zIPolys.gf_diffc                 C   s   t | ||| jj| jjS r  )r  r  r#  r  r  rQ  r  r  r   r  0  s    zIPolys.gf_evalc                 C   s   t | ||| jj| jjS r  )r  r  r#  r  r  )r  r9  rU  r  r  r   r  2  s    zIPolys.gf_multi_evalc                 C   s(   |  t| || || jj| jjS r  )r  r  r  r#  r  r  rA  r  r  r   r  5  s    zIPolys.gf_composec                 C   s0   |  t| || || || jj| jjS r  )r  r  r  r#  r  r  )r  rB  rD  r9  r  r  r   r  7  s    zIPolys.gf_compose_modc                 C   s\   |  |}|  |}|  |}|  |}t|||||| jj| jj\}}| || |fS r  )r  r  r#  r  r  r  )r  rR  br:  r?  r9  UVr  r  r   r  :  s    



 zIPolys.gf_trace_mapc                 C   s   |  t|| jj| jjS r  )r  r	  r#  r  r  r  r?  r  r  r   r	  B  s    zIPolys.gf_randomc                 C   s   |  t|| jj| jjS r  )r  r
  r#  r  r  r  r  r  r   r
  D  s    zIPolys.gf_irreduciblec                 C   s   t | || jj| jjS r  )r  r  r#  r  r  r@  r  r  r   r  G  s    zIPolys.gf_irred_p_ben_orc                 C   s   t | || jj| jjS r  )r  r  r#  r  r  r@  r  r  r   r  I  s    zIPolys.gf_irred_p_rabinc                 C   s   t | || jj| jjS r  )r  r  r#  r  r  r@  r  r  r   r  K  s    zIPolys.gf_irreducible_pc                 C   s   t | || jj| jjS r  )r  r  r#  r  r  r@  r  r  r   r  M  s    zIPolys.gf_sqf_pc                 C   s    |  t| || jj| jjS r  )r  r  r  r#  r  r  r@  r  r  r   r  P  s    zIPolys.gf_sqf_partc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  r  ry  r&  r  r   r|  T  s     z&IPolys.gf_sqf_list.<locals>.<listcomp>)r  r  r#  r  r  r  r  r&  r   gf_sqf_listR  s    zIPolys.gf_sqf_listc                 C   s   t | || jj| jjS r  )r  r  r#  r  r  r@  r  r  r   r  V  s    zIPolys.gf_Qmatrixc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  Z  s     z'IPolys.gf_berlekamp.<locals>.<listcomp>)r  r  r#  r  r  r}  r  r&  r   r  X  s    zIPolys.gf_berlekampc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r  ry  r&  r  r   r|  ^  s     z,IPolys.gf_ddf_zassenhaus.<locals>.<listcomp>)r  r  r#  r  r  r}  r  r&  r   r  \  s    zIPolys.gf_ddf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  a  s     z,IPolys.gf_edf_zassenhaus.<locals>.<listcomp>)r  r  r#  r  r  r  r9  r?  r~  r  r&  r   r  _  s    zIPolys.gf_edf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r  ry  r&  r  r   r|  e  s     z'IPolys.gf_ddf_shoup.<locals>.<listcomp>)r  r  r#  r  r  r}  r  r&  r   r  c  s    zIPolys.gf_ddf_shoupc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  h  s     z'IPolys.gf_edf_shoup.<locals>.<listcomp>)r  r  r#  r  r  r  r  r&  r   r  f  s    zIPolys.gf_edf_shoupc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  l  s     z(IPolys.gf_zassenhaus.<locals>.<listcomp>)r  r  r#  r  r  r}  r  r&  r   r  j  s    zIPolys.gf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  o  s     z#IPolys.gf_shoup.<locals>.<listcomp>)r  r  r#  r  r  r}  r  r&  r   r  m  s    zIPolys.gf_shoupc                    s8   t  | jj jj|d\}}| fdd|D fS )N)methodc                    s   g | ]}  |qS r  r  r  r&  r  r   r|  s  s     z(IPolys.gf_factor_sqf.<locals>.<listcomp>)r  r  r#  r  r  )r  r9  r  r  r~  r  r&  r   r  q  s    "zIPolys.gf_factor_sqfc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  r  ry  r&  r  r   r|  v  s     z$IPolys.gf_factor.<locals>.<listcomp>)r  r  r#  r  r  r  r  r&  r   r  t  s    zIPolys.gf_factor)NNN)F)F)T)T)F)NN)F)F)F)F)F)F)F)NNNFF)NNNF)NNNF)NF)NNNFF)NNNFF)NNNFF)NNNFF)NNNFFF)NN)NNN)NNNF)NNNFF)NNNF)T)T)F)N(0  __name__
__module____qualname__r"  r6  r#  r$  Zgensr!  r%  r'  r*  r+  r-  r2  r3  r7  r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rL   rM   rO   rP   rQ   rN   rR   rS   rT   rV   rU   rW   rX   rY   rZ   r[   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r~   r{   r   r|   r   r   r   r   r}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r\   r^   r   r   r]   r_   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r   r   r   r   r  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r     sZ  

		r  N($  __doc__Zsympy.polys.densearithr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   Zsympy.polys.densebasicrB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   Zsympy.polys.densetoolsrL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   Zsympy.polys.euclidtoolsrp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.polys.factortoolsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.polys.rootisolationr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.polys.sqfreetoolsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   Zsympy.polys.galoistoolsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.utilitiesr  r  r  r  r  r   <module>   s  L m