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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 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dِl-m.Z. e.G ddۄ dۃZ/dS )z8Compatibility interface between dense and sparse polys.     )annotations)TYPE_CHECKING)Expr)Domain)MonomialOrderPolyElement)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U ded< ded< ded< ded< d	ed
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d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Z	dd Z
dd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG Z d_dHdIZ!dJdK Z"dLdM Z#dNdO Z$dPdQ Z%dRdS Z&dTdU Z'dVdW Z(dXdY Z)dfdZd[Z*d\d] Z+dS (g  IPolysztuple[PolyElement, ...]gensztuple[Expr, ...]symbolsintngensr   domainr   orderc                 C     d S N )selfgenr+  r+  [/home/air/sanwanet/backup_V2/venv/lib/python3.10/site-packages/sympy/polys/compatibility.pydrop      zIPolys.dropNc                 C  r)  r*  r+  )r,  r$  r'  r(  r+  r+  r.  clone   r0  zIPolys.clonec                 C  r)  r*  r+  r,  r+  r+  r.  	to_ground   r0  zIPolys.to_groundc                 C  r)  r*  r+  r,  elementr+  r+  r.  
ground_new  r0  zIPolys.ground_newc                 C  r)  r*  r+  r4  r+  r+  r.  
domain_new  r0  zIPolys.domain_newc                 C  r)  r*  r+  )r,  dr+  r+  r.  	from_dict  r0  zIPolys.from_dictc                 C  s6   ddl m} t||r|j| kr|S td| |S )Nr   r   zdomain conversions)sympy.polys.ringsr   
isinstanceringNotImplementedErrorr6  )r,  r5  r   r+  r+  r.  wrap  s   


zIPolys.wrapc                 C  s   |  | S r*  )r>  to_denser4  r+  r+  r.  r?       zIPolys.to_densec                 C  s   |  t|| jd | jS N   )r9  rR   r&  r'  r4  r+  r+  r.  
from_dense     zIPolys.from_densec                 C     |  t| |||| jS r*  )rC  r	   r?  r'  r,  fcir+  r+  r.  r	        zIPolys.dup_add_termc                 C  4   |  t| || |d || jd | jS Nr   rB  )rC  r
   r?  r>  r/  r&  r'  rF  r+  r+  r.  r
        4zIPolys.dmp_add_termc                 C  rE  r*  )rC  r   r?  r'  rF  r+  r+  r.  r     rJ  zIPolys.dup_sub_termc                 C  rK  rL  )rC  r   r?  r>  r/  r&  r'  rF  r+  r+  r.  r   !  rM  zIPolys.dmp_sub_termc                 C  rE  r*  )rC  r   r?  r'  rF  r+  r+  r.  r   #  rJ  zIPolys.dup_mul_termc                 C  rK  rL  )rC  r   r?  r>  r/  r&  r'  rF  r+  r+  r.  r   %  rM  zIPolys.dmp_mul_termc                 C     |  t| ||| jS r*  )rC  r   r?  r'  r,  rG  rH  r+  r+  r.  r   (  rD  zIPolys.dup_add_groundc                 C  "   |  t| ||| jd | jS rA  )rC  r   r?  r&  r'  rO  r+  r+  r.  r   *     "zIPolys.dmp_add_groundc                 C  rN  r*  )rC  r   r?  r'  rO  r+  r+  r.  r   ,  rD  zIPolys.dup_sub_groundc                 C  rP  rA  )rC  r   r?  r&  r'  rO  r+  r+  r.  r   .  rQ  zIPolys.dmp_sub_groundc                 C  rN  r*  )rC  r   r?  r'  rO  r+  r+  r.  r   0  rD  zIPolys.dup_mul_groundc                 C  rP  rA  )rC  r   r?  r&  r'  rO  r+  r+  r.  r   2  rQ  zIPolys.dmp_mul_groundc                 C  rN  r*  )rC  r   r?  r'  rO  r+  r+  r.  r   4  rD  zIPolys.dup_quo_groundc                 C  rP  rA  )rC  r   r?  r&  r'  rO  r+  r+  r.  r   6  rQ  zIPolys.dmp_quo_groundc                 C  rN  r*  )rC  r   r?  r'  rO  r+  r+  r.  r   8  rD  zIPolys.dup_exquo_groundc                 C  rP  rA  )rC  r   r?  r&  r'  rO  r+  r+  r.  r   :  rQ  zIPolys.dmp_exquo_groundc                 C  rN  r*  )rC  r   r?  r'  r,  rG  nr+  r+  r.  r   =  rD  zIPolys.dup_lshiftc                 C  rN  r*  )rC  r   r?  r'  rR  r+  r+  r.  r   ?  rD  zIPolys.dup_rshiftc                 C     |  t| || jS r*  )rC  r   r?  r'  r,  rG  r+  r+  r.  r   B     zIPolys.dup_absc                 C      |  t| || jd | jS rA  )rC  r   r?  r&  r'  rU  r+  r+  r.  r   D      zIPolys.dmp_absc                 C  rT  r*  )rC  r   r?  r'  rU  r+  r+  r.  r   G  rV  zIPolys.dup_negc                 C  rW  rA  )rC  r   r?  r&  r'  rU  r+  r+  r.  r   I  rX  zIPolys.dmp_negc                 C      |  t| || || jS r*  )rC  r   r?  r'  r,  rG  gr+  r+  r.  r   L  rX  zIPolys.dup_addc                 C  (   |  t| || || jd | jS rA  )rC  r    r?  r&  r'  rZ  r+  r+  r.  r    N     (zIPolys.dmp_addc                 C  rY  r*  )rC  r!   r?  r'  rZ  r+  r+  r.  r!   Q  rX  zIPolys.dup_subc                 C  r\  rA  )rC  r"   r?  r&  r'  rZ  r+  r+  r.  r"   S  r]  zIPolys.dmp_subc                 C  (   |  t| || || || jS r*  )rC  r#   r?  r'  r,  rG  r[  hr+  r+  r.  r#   V  r]  zIPolys.dup_add_mulc                 C  0   |  t| || || || jd | jS rA  )rC  r$   r?  r&  r'  r_  r+  r+  r.  r$   X     0zIPolys.dmp_add_mulc                 C  r^  r*  )rC  r%   r?  r'  r_  r+  r+  r.  r%   Z  r]  zIPolys.dup_sub_mulc                 C  ra  rA  )rC  r&   r?  r&  r'  r_  r+  r+  r.  r&   \  rb  zIPolys.dmp_sub_mulc                 C  rY  r*  )rC  r'   r?  r'  rZ  r+  r+  r.  r'   _  rX  zIPolys.dup_mulc                 C  r\  rA  )rC  r(   r?  r&  r'  rZ  r+  r+  r.  r(   a  r]  zIPolys.dmp_mulc                 C  rT  r*  )rC  r)   r?  r'  rU  r+  r+  r.  r)   d  rV  zIPolys.dup_sqrc                 C  rW  rA  )rC  r*   r?  r&  r'  rU  r+  r+  r.  r*   f  rX  zIPolys.dmp_sqrc                 C  rN  r*  )rC  r+   r?  r'  rR  r+  r+  r.  r+   h  rD  zIPolys.dup_powc                 C  rP  rA  )rC  r,   r?  r&  r'  rR  r+  r+  r.  r,   j  rQ  zIPolys.dmp_powc                 C  2   t | || || j\}}| || |fS r*  )r-   r?  r'  rC  r,  rG  r[  qrr+  r+  r.  r-   m     zIPolys.dup_pdivc                 C  rY  r*  )rC  r.   r?  r'  rZ  r+  r+  r.  r.   p  rX  zIPolys.dup_premc                 C  rY  r*  )rC  r/   r?  r'  rZ  r+  r+  r.  r/   r  rX  zIPolys.dup_pquoc                 C  rY  r*  )rC  r0   r?  r'  rZ  r+  r+  r.  r0   t  rX  zIPolys.dup_pexquoc                 C  :   t | || || jd | j\}}| || |fS rA  )r1   r?  r&  r'  rC  rd  r+  r+  r.  r1   w     &zIPolys.dmp_pdivc                 C  r\  rA  )rC  r2   r?  r&  r'  rZ  r+  r+  r.  r2   z  r]  zIPolys.dmp_premc                 C  r\  rA  )rC  r3   r?  r&  r'  rZ  r+  r+  r.  r3   |  r]  zIPolys.dmp_pquoc                 C  r\  rA  )rC  r4   r?  r&  r'  rZ  r+  r+  r.  r4   ~  r]  zIPolys.dmp_pexquoc                 C  rc  r*  )r5   r?  r'  rC  rd  r+  r+  r.  r5     rg  zIPolys.dup_rr_divc                 C  rh  rA  )r6   r?  r&  r'  rC  rd  r+  r+  r.  r6     ri  zIPolys.dmp_rr_divc                 C  rc  r*  )r7   r?  r'  rC  rd  r+  r+  r.  r7     rg  zIPolys.dup_ff_divc                 C  rh  rA  )r8   r?  r&  r'  rC  rd  r+  r+  r.  r8     ri  zIPolys.dmp_ff_divc                 C  rc  r*  )r9   r?  r'  rC  rd  r+  r+  r.  r9     rg  zIPolys.dup_divc                 C  rY  r*  )rC  r:   r?  r'  rZ  r+  r+  r.  r:     rX  zIPolys.dup_remc                 C  rY  r*  )rC  r;   r?  r'  rZ  r+  r+  r.  r;     rX  zIPolys.dup_quoc                 C  rY  r*  )rC  r<   r?  r'  rZ  r+  r+  r.  r<     rX  zIPolys.dup_exquoc                 C  rh  rA  )r=   r?  r&  r'  rC  rd  r+  r+  r.  r=     ri  zIPolys.dmp_divc                 C  r\  rA  )rC  r>   r?  r&  r'  rZ  r+  r+  r.  r>     r]  zIPolys.dmp_remc                 C  r\  rA  )rC  r?   r?  r&  r'  rZ  r+  r+  r.  r?     r]  zIPolys.dmp_quoc                 C  r\  rA  )rC  r@   r?  r&  r'  rZ  r+  r+  r.  r@     r]  zIPolys.dmp_exquoc                 C     t | || jS r*  )rA   r?  r'  rU  r+  r+  r.  rA        zIPolys.dup_max_normc                 C     t | || jd | jS rA  )rB   r?  r&  r'  rU  r+  r+  r.  rB     rD  zIPolys.dmp_max_normc                 C  rj  r*  )rC   r?  r'  rU  r+  r+  r.  rC     rk  zIPolys.dup_l1_normc                 C  rl  rA  )rD   r?  r&  r'  rU  r+  r+  r.  rD     rD  zIPolys.dmp_l1_normc                 C  rj  r*  )rE   r?  r'  rU  r+  r+  r.  rE     rk  zIPolys.dup_l2_norm_squaredc                 C  rl  rA  )rF   r?  r&  r'  rU  r+  r+  r.  rF     rD  zIPolys.dmp_l2_norm_squaredc                 C  s   |  ttt| j|| jS r*  )rC  rG   listmapr?  r'  r,  polysr+  r+  r.  rG        zIPolys.dup_expandc                 C  s&   |  ttt| j|| jd | jS rA  )rC  rH   rm  rn  r?  r&  r'  ro  r+  r+  r.  rH        &zIPolys.dmp_expandc                 C  rj  r*  )rI   r?  r'  rU  r+  r+  r.  rI     rk  zIPolys.dup_LCc                 C  2   t | || j}t|tr| dd  |S |S rA  )rJ   r?  r'  r;  rm  rC  )r,  rG  LCr+  r+  r.  rJ        
zIPolys.dmp_LCc                 C  rj  r*  )rK   r?  r'  rU  r+  r+  r.  rK     rk  zIPolys.dup_TCc                 C  rs  rA  )rL   r?  r'  r;  rm  rC  )r,  rG  TCr+  r+  r.  rL     ru  zIPolys.dmp_TCc                 C  rl  rA  )rM   r?  r&  r'  rU  r+  r+  r.  rM     rD  zIPolys.dmp_ground_LCc                 C  rl  rA  )rN   r?  r&  r'  rU  r+  r+  r.  rN     rD  zIPolys.dmp_ground_TCc                 C     t | |S r*  )rO   r?  rU  r+  r+  r.  rO     r@  zIPolys.dup_degreec                 C  s   t | || jd S rA  )rP   r?  r&  rU  r+  r+  r.  rP        zIPolys.dmp_degreec                 C  s   t | ||| jd S rA  )rQ   r?  r&  )r,  rG  jr+  r+  r.  rQ     rV  zIPolys.dmp_degree_inc                 C  rN  r*  )rC  rS   r?  r'  r,  rG  mr+  r+  r.  rS     rD  zIPolys.dup_integratec                 C  rP  rA  )rC  rT   r?  r&  r'  rz  r+  r+  r.  rT     rQ  zIPolys.dmp_integratec                 C  rN  r*  )rC  rV   r?  r'  rz  r+  r+  r.  rV     rD  zIPolys.dup_diffc                 C  rP  rA  )rC  rW   r?  r&  r'  rz  r+  r+  r.  rW     rQ  zIPolys.dmp_diffc                 C  $   |  t| |||| jd | jS rA  )rC  rX   r?  r&  r'  r,  rG  r{  ry  r+  r+  r.  rX        $zIPolys.dmp_diff_inc                 C  r|  rA  )rC  rU   r?  r&  r'  r}  r+  r+  r.  rU     r~  zIPolys.dmp_integrate_inc                 C  s   t | ||| jS r*  )rY   r?  r'  r,  rG  ar+  r+  r.  rY        zIPolys.dup_evalc                 C  s.   t | ||| jd | j}| dd  |S rA  )rZ   r?  r&  r'  rC  )r,  rG  r  resultr+  r+  r.  rZ     s   zIPolys.dmp_evalc                 C  s.   t | |||| jd | j}| ||S rA  )r[   r?  r&  r'  r/  rC  )r,  rG  r  ry  r  r+  r+  r.  r[     s   zIPolys.dmp_eval_inc                 C  s0   t | ||||| jd | j}| ||S rA  )r]   r?  r&  r'  r/  rC  )r,  rG  r{  r  ry  r  r+  r+  r.  r]     s    zIPolys.dmp_diff_eval_inc                 C  sB   t | ||| jd | j}t|tr| d t|  |S |S rA  )r\   r?  r&  r'  r;  rm  lenrC  )r,  rG  Ar  r+  r+  r.  r\     s   
zIPolys.dmp_eval_tailc                 C  rN  r*  )rC  r^   r?  r'  r,  rG  pr+  r+  r.  r^     rD  zIPolys.dup_truncc                 C  s0   |  t| || dd  || jd | jS rA  )rC  r_   r?  r&  r'  rZ  r+  r+  r.  r_     rb  zIPolys.dmp_truncc                 C  rP  rA  )rC  r`   r?  r&  r'  r  r+  r+  r.  r`     rQ  zIPolys.dmp_ground_truncc                 C  rT  r*  )rC  ra   r?  r'  rU  r+  r+  r.  ra     rV  zIPolys.dup_monicc                 C  rW  rA  )rC  rb   r?  r&  r'  rU  r+  r+  r.  rb     rX  zIPolys.dmp_ground_monicc                 C  s6   t | || || j\}}}|| || |fS r*  )rg   r?  r'  rC  r,  rG  r[  rH  FGr+  r+  r.  rg     s    zIPolys.dup_extractc                 C  s>   t | || || jd | j\}}}|| || |fS rA  )rh   r?  r&  r'  rC  r  r+  r+  r.  rh     s   (zIPolys.dmp_ground_extractc                 C  s4   t | |d | j\}}| || |fS rA  )ri   r>  r/  r?  r'  rC  r,  rG  r  re  r+  r+  r.  ri     s    zIPolys.dup_real_imagc                 C  rT  r*  )rC  rj   r?  r'  rU  r+  r+  r.  rj     rV  zIPolys.dup_mirrorc                 C  rN  r*  )rC  rk   r?  r'  r  r+  r+  r.  rk     rD  zIPolys.dup_scalec                 C  rN  r*  )rC  rl   r?  r'  r  r+  r+  r.  rl     rD  zIPolys.dup_shiftc                 C  rP  rA  )rC  rm   r?  r&  r'  r  r+  r+  r.  rm     rQ  zIPolys.dmp_shiftc                 C  r^  r*  )rC  rn   r?  r'  r  r+  r+  r.  rn     r]  zIPolys.dup_transformc                 C  rY  r*  )rC  ro   r?  r'  rZ  r+  r+  r.  ro     rX  zIPolys.dup_composec                 C  r\  rA  )rC  rp   r?  r&  r'  rZ  r+  r+  r.  rp     r]  zIPolys.dmp_composec                 C  "   t | || j}tt| j|S r*  )rq   r?  r'  rm  rn  rC  )r,  rG  
componentsr+  r+  r.  rq        zIPolys.dup_decomposec                 C  (   t | || jd | j}|  |S rA  )rr   r?  r&  r'  r3  rC  r,  rG  r  r+  r+  r.  rr         zIPolys.dmp_liftc                 C  rj  r*  )rs   r?  r'  rU  r+  r+  r.  rs   $  rk  zIPolys.dup_sign_variationsFc                 C  sD   t | || j|d\}}|r| j| j d}n| }|||fS )Nconvertr'  )rt   r?  r'  r1  get_ringrC  r,  rG  r  rH  r  r<  r+  r+  r.  rt   '  s
   zIPolys.dup_clear_denomsc                 C  sL   t | || jd | j|d\}}|r| j| j d}n| }|||fS )NrB  r  r  )ru   r?  r&  r'  r1  r  rC  r  r+  r+  r.  ru   .  s
   "zIPolys.dmp_clear_denomsc                 C  rN  r*  )rC  rv   r?  r'  rR  r+  r+  r.  rv   6  rD  zIPolys.dup_revertc                 C  rc  r*  )rw   r?  r'  rC  r,  rG  r[  sr`  r+  r+  r.  rw   9  rg  zIPolys.dup_half_gcdexc                 C  rh  rA  )rx   r?  r&  r'  rC  r  r+  r+  r.  rx   <  ri  zIPolys.dmp_half_gcdexc                 C  <   t | || || j\}}}| || || |fS r*  )ry   r?  r'  rC  r,  rG  r[  r  tr`  r+  r+  r.  ry   ?      zIPolys.dup_gcdexc                 C  D   t | || || jd | j\}}}| || || |fS rA  )rz   r?  r&  r'  rC  r  r+  r+  r.  rz   B     (zIPolys.dmp_gcdexc                 C  rY  r*  )rC  r{   r?  r'  rZ  r+  r+  r.  r{   F  rX  zIPolys.dup_invertc                 C  r\  rA  )rC  r|   r?  r&  r'  rZ  r+  r+  r.  r|   H  r]  zIPolys.dmp_invertc                 C  *   t | || || j}tt| j|S r*  )r}   r?  r'  rm  rn  rC  r,  rG  r[  prsr+  r+  r.  r}   K     zIPolys.dup_euclidean_prsc                 C  2   t | || || jd | j}tt| j|S rA  )r~   r?  r&  r'  rm  rn  rC  r  r+  r+  r.  r~   N     "zIPolys.dmp_euclidean_prsc                 C  r  r*  )r   r?  r'  rm  rn  rC  r  r+  r+  r.  r   Q  r  zIPolys.dup_primitive_prsc                 C  r  rA  )r   r?  r&  r'  rm  rn  rC  r  r+  r+  r.  r   T  r  zIPolys.dmp_primitive_prsc                 C  s2   t | || || j\}}tt| j||fS r*  )r   r?  r'  rm  rn  rC  r,  rG  r[  r  sresr+  r+  r.  r   X  rg  zIPolys.dup_inner_subresultantsc                 C  s:   t | || || jd | j\}}tt| j||fS rA  )r   r?  r&  r'  rm  rn  rC  r  r+  r+  r.  r   [  ri  zIPolys.dmp_inner_subresultantsc                 C  r  r*  )r   r?  r'  rm  rn  rC  r  r+  r+  r.  r   _  r  zIPolys.dup_subresultantsc                 C  r  rA  )r   r?  r&  r'  rm  rn  rC  r  r+  r+  r.  r   b  r  zIPolys.dmp_subresultantsc                 C  s2   t | || || j\}}|tt| j|fS r*  )r   r?  r'  rm  rn  rC  r,  rG  r[  resr  r+  r+  r.  r   f  rg  zIPolys.dup_prs_resultantc                 C  sH   t | || || jd | j\}}| dd  |tt| j|fS rA  )r   r?  r&  r'  rC  rm  rn  r  r+  r+  r.  r   i  s   &"zIPolys.dmp_prs_resultantc                 C  s<   t | || || || jd | j}| dd  |S rA  )r   r?  r7  r&  r'  rC  )r,  rG  r[  r  r  r+  r+  r.  r   m  s   *zIPolys.dmp_zz_modular_resultantc                 C  4   t | || || jd | j}| dd  |S rA  )r   r?  r&  r'  rC  r,  rG  r[  r  r+  r+  r.  r   p     "zIPolys.dmp_zz_collins_resultantc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r   s  r  zIPolys.dmp_qq_collins_resultantc                 C  s   t | || || jS r*  )r   r?  r'  rZ  r+  r+  r.  r   w  rD  zIPolys.dup_resultantc                 C  sB   t | || || jd | j}t|tr| dd  |S |S rA  )r   r?  r&  r'  r;  rm  rC  r  r+  r+  r.  r   y  s   "
zIPolys.dmp_resultantc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r     rk  zIPolys.dup_discriminantc                 C  :   t | || jd | j}t|tr| dd  |S |S rA  )r   r?  r&  r'  r;  rm  rC  )r,  rG  discr+  r+  r.  r        
zIPolys.dmp_discriminantc                 C  r  r*  )r   r?  r'  rC  r,  rG  r[  Hr  r  r+  r+  r.  r     r  zIPolys.dup_rr_prs_gcdc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_ff_prs_gcdc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_rr_prs_gcdc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_ff_prs_gcdc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_zz_heu_gcdc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_zz_heu_gcdc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_qq_heu_gcdc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_qq_heu_gcdc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_inner_gcdc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_inner_gcdc                 C  $   t | || || j}| |S r*  )r   r?  r'  rC  r,  rG  r[  r  r+  r+  r.  r        
zIPolys.dup_gcdc                 C  ,   t | || || jd | j}| |S rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r        "
zIPolys.dmp_gcdc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_rr_lcmc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_ff_lcmc                 C  r  r*  )r   r?  r'  rC  r  r+  r+  r.  r     r  zIPolys.dup_lcmc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_rr_lcmc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_ff_lcmc                 C  r  rA  )r   r?  r&  r'  rC  r  r+  r+  r.  r     r  zIPolys.dmp_lcmc                 C  s   t | || j}|S r*  )rc   r?  r'  r,  rG  contr+  r+  r.  rc     s   zIPolys.dup_contentc                 C  s$   t | || j\}}|| |fS r*  )re   r?  r'  rC  r,  rG  r  primr+  r+  r.  re     s   zIPolys.dup_primitivec                 C  r  rA  )r   r?  r&  r'  r;  rm  rC  r  r+  r+  r.  r     r  zIPolys.dmp_contentc                 C  sR   t | || jd | j\}}t|tr"| dd  || |fS || |fS rA  )r   r?  r&  r'  r;  rm  rC  r  r+  r+  r.  r     s   
zIPolys.dmp_primitivec                 C  s   t | || jd | j}|S rA  )rd   r?  r&  r'  r  r+  r+  r.  rd     s   zIPolys.dmp_ground_contentc                 C  s,   t | || jd | j\}}|| |fS rA  )rf   r?  r&  r'  rC  r  r+  r+  r.  rf     s   zIPolys.dmp_ground_primitiveTc           	      C  sb   t | || || j|d}|s#|\}}}}||| || |fS |\}}| || |fS )Ninclude)r   r?  r'  rC  	r,  rG  r[  r  r  cfcgr  r  r+  r+  r.  r     s   zIPolys.dup_cancelc           	      C  sj   t | || || jd | j|d}|s'|\}}}}||| || |fS |\}}| || |fS )NrB  r  )r   r?  r&  r'  rC  r  r+  r+  r.  r     s   &zIPolys.dmp_cancelc                   s2   t  |tt j| j} fdd|D S )Nc                      g | ]\}}  ||fqS r+  rC  .0r[  kr2  r+  r.  
<listcomp>      z-IPolys.dup_trial_division.<locals>.<listcomp>)r   r?  rm  rn  r'  r,  rG  factorsr+  r2  r.  r         zIPolys.dup_trial_divisionc                   s:   t  |tt j| jd  j} fdd|D S )NrB  c                   r  r+  r  r  r2  r+  r.  r    r  z-IPolys.dmp_trial_division.<locals>.<listcomp>)r   r?  rm  rn  r&  r'  r  r+  r2  r.  r     s   (zIPolys.dmp_trial_divisionc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r     rk  zIPolys.dup_zz_mignotte_boundc                 C  rl  rA  )r   r?  r&  r'  rU  r+  r+  r.  r     rD  zIPolys.dmp_zz_mignotte_boundc                 C  s\   | j }t|||||||||||| j\}}	}
}| || |	| |
| |fS r*  )r?  r   r'  rC  )r,  r{  rG  r[  r`  r  r  Dr  r  STr+  r+  r.  r     s   2$zIPolys.dup_zz_hensel_stepc                 C  s6   | j }t|||tt|||| j}tt| j|S r*  )r?  r   rm  rn  r'  rC  )r,  r  rG  f_listlr  rp  r+  r+  r.  r     s    zIPolys.dup_zz_hensel_liftc                   $   t  | j} fdd|D S )Nc                   r  r+  r  r  r2  r+  r.  r    r  z,IPolys.dup_zz_zassenhaus.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r        zIPolys.dup_zz_zassenhausc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r     rk  zIPolys.dup_zz_irreducible_pc                 C  s   t | || j|dS )N)irreducible)r   r?  r'  )r,  rG  r  r+  r+  r.  r     rx  zIPolys.dup_cyclotomic_pc                 C  s   t || j}| |S r*  )r   r'  rC  )r,  rS  r  r+  r+  r.  r   	  s   
zIPolys.dup_zz_cyclotomic_polyc                 C  s.   t | || j}|d u r|S tt| j|S r*  )r   r?  r'  rm  rn  rC  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 )NrB  c                   r  r+  )r?  )r  r  r  mvr+  r.  r    r  z2IPolys.dmp_zz_wang_lead_coeffs.<locals>.<listcomp>)rm  rn  r?  r   r&  r'  rC  )
r,  rG  r  r  r  r  r  uv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   rm  rn  r?  r'  rC  )r,  r  r{  r  r  r+  r+  r.  r   %  s   zIPolys.dup_zz_diophantinec                 C  s>   t tt| j|| ||||| jd | j}tt| j|S rA  )r   rm  rn  r?  r&  r'  rC  )r,  r  rH  r  r8  r  r  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 rA  )rm  rn  r?  r   r&  r'  rC  )	r,  rG  r  rt  r  r  r  r  r  r+  r+  r.  r   /  s   "z!IPolys.dmp_zz_wang_hensel_liftingc                   s2   t  | jd  j||d} fdd|D S )NrB  )modseedc                      g | ]}  |qS r+  r  r  r[  r2  r+  r.  r  9      z&IPolys.dmp_zz_wang.<locals>.<listcomp>)r   r?  r&  r'  )r,  rG  r  r  r  r+  r2  r.  r   7  r  zIPolys.dmp_zz_wangc                   ,   t  | j\}}| fdd|D fS )Nc                   r  r+  r  r  r2  r+  r.  r  =  r  z,IPolys.dup_zz_factor_sqf.<locals>.<listcomp>)r   r?  r'  r,  rG  coeffr  r+  r2  r.  r   ;     zIPolys.dup_zz_factor_sqfc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  A  r  z(IPolys.dup_zz_factor.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   ?  r  zIPolys.dup_zz_factorc                   4   t  | jd  j\}}| fdd|D fS )NrB  c                   r  r+  r  r  r2  r+  r.  r  D  r  z(IPolys.dmp_zz_factor.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   B     zIPolys.dmp_zz_factorc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  H  r  z*IPolys.dup_qq_i_factor.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   F  r  zIPolys.dup_qq_i_factorc                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r  K  r  z*IPolys.dmp_qq_i_factor.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   I  r  zIPolys.dmp_qq_i_factorc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  O  r  z*IPolys.dup_zz_i_factor.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   M  r  zIPolys.dup_zz_i_factorc                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r  R  r  z*IPolys.dmp_zz_i_factor.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   P  r  zIPolys.dmp_zz_i_factorc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  V  r  z)IPolys.dup_ext_factor.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   T  r  zIPolys.dup_ext_factorc                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r  Y  r  z)IPolys.dmp_ext_factor.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   W  r  zIPolys.dmp_ext_factorc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  ]  r  z(IPolys.dup_gf_factor.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   [  r  zIPolys.dup_gf_factorc                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r  `  r  z(IPolys.dmp_gf_factor.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   ^  r  zIPolys.dmp_gf_factorc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  d  r  z*IPolys.dup_factor_list.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   b  r  zIPolys.dup_factor_listc                   r  )Nc                   r  r+  r  r  r2  r+  r.  r  g  r  z2IPolys.dup_factor_list_include.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r   e  r  zIPolys.dup_factor_list_includec                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r  k  r  z*IPolys.dmp_factor_list.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   i  r  zIPolys.dmp_factor_listc                   ,   t  | jd  j} fdd|D S )NrB  c                   r  r+  r  r  r2  r+  r.  r  n  r  z2IPolys.dmp_factor_list_include.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r   l     zIPolys.dmp_factor_list_includec                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r   p  rk  zIPolys.dup_irreducible_pc                 C  rl  rA  )r   r?  r&  r'  rU  r+  r+  r.  r   r  rD  zIPolys.dmp_irreducible_pc                 C  r  r*  )r   r?  r'  rm  rn  rC  )r,  rG  seqr+  r+  r.  r   u  r  zIPolys.dup_sturmc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r   y  rk  zIPolys.dup_sqf_pc                 C  rl  rA  )r   r?  r&  r'  rU  r+  r+  r.  r   {  rD  zIPolys.dmp_sqf_pc                 C  r  rA  )r   r?  r&  r'  r3  rC  rR  r+  r+  r.  r   ~  r  zIPolys.dmp_normc                 C  s2   t | || j\}}}|| ||  |fS r*  )r   r?  r'  rC  r3  r,  rG  r  r  Rr+  r+  r.  r     s   zIPolys.dup_sqf_normc                 C  s:   t | || jd | j\}}}|| ||  |fS rA  )r   r?  r&  r'  rC  r3  r  r+  r+  r.  r     s    zIPolys.dmp_sqf_normc                 C  rT  r*  )rC  r   r?  r'  rU  r+  r+  r.  r     rV  zIPolys.dup_gf_sqf_partc                 C  rT  r*  )rC  r   r?  r'  rU  r+  r+  r.  r     rV  zIPolys.dmp_gf_sqf_partc                 C  rT  r*  )rC  r   r?  r'  rU  r+  r+  r.  r     rV  zIPolys.dup_sqf_partc                 C  rW  rA  )rC  r   r?  r&  r'  rU  r+  r+  r.  r     rX  zIPolys.dmp_sqf_partc                   0   t  | j|d\}}| fdd|D fS )Nallc                   r  r+  r  r  r2  r+  r.  r    r  z*IPolys.dup_gf_sqf_list.<locals>.<listcomp>)r   r?  r'  r,  rG  r  r  r  r+  r2  r.  r        zIPolys.dup_gf_sqf_listc                   8   t  | jd  j|d\}}| fdd|D fS )NrB  r  c                   r  r+  r  r  r2  r+  r.  r    r  z*IPolys.dmp_gf_sqf_list.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r        "zIPolys.dmp_gf_sqf_listc                   r  )Nr  c                   r  r+  r  r  r2  r+  r.  r    r  z'IPolys.dup_sqf_list.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r     r  zIPolys.dup_sqf_listc                   s(   t  | j|d} fdd|D S )Nr  c                   r  r+  r  r  r2  r+  r.  r    r  z/IPolys.dup_sqf_list_include.<locals>.<listcomp>)r   r?  r'  r,  rG  r  r  r+  r2  r.  r     s   zIPolys.dup_sqf_list_includec                   r  )NrB  r  c                   r  r+  r  r  r2  r+  r.  r    r  z'IPolys.dmp_sqf_list.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r     r  zIPolys.dmp_sqf_listc                   s0   t  | jd  j|d} fdd|D S )NrB  r  c                   r  r+  r  r  r2  r+  r.  r    r  z/IPolys.dmp_sqf_list_include.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r     s   zIPolys.dmp_sqf_list_includec                   r  )Nc                   r  r+  r  r  r2  r+  r.  r    r  z'IPolys.dup_gff_list.<locals>.<listcomp>)r   r?  r'  r  r+  r2  r.  r     r  zIPolys.dup_gff_listc                   r  )NrB  c                   r  r+  r  r  r2  r+  r.  r    r  z'IPolys.dmp_gff_list.<locals>.<listcomp>)r   r?  r&  r'  r  r+  r2  r.  r     r  zIPolys.dmp_gff_listc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r     rk  zIPolys.dup_root_upper_boundc                 C  rj  r*  )r   r?  r'  rU  r+  r+  r.  r     rk  zIPolys.dup_root_lower_boundc                 C  s   t | ||| j|dS )N)fast)r   r?  r'  )r,  rG  Mr  r+  r+  r.  r     rV  z IPolys.dup_step_refine_real_rootc              
   C  s    t | ||| j|||||dS )N)epsstepsdisjointr  mobius)r   r?  r'  )r,  rG  r  r  r  r  r  r  r+  r+  r.  r     rX  z!IPolys.dup_inner_refine_real_rootc              
   C      t | |||| j||||dS N)r  r  r  r  )r   r?  r'  r,  rG  r  r  r  r  r  r  r+  r+  r.  r     rX  z!IPolys.dup_outer_refine_real_rootc              
   C  r  r  )r   r?  r'  r  r+  r+  r.  r     rX  zIPolys.dup_refine_real_rootc                 C     t | || j||dS )N)r  r  )r   r?  r'  )r,  rG  r  r  r+  r+  r.  r     rV  z#IPolys.dup_inner_isolate_real_rootsc              	   C     t | || j|||||dS )N)r  infsupr  r  )r   r?  r'  )r,  rG  r  r  r  r  r  r+  r+  r.  r     rq  z'IPolys.dup_inner_isolate_positive_rootsc              	   C  r  )N)r  r  r  r  r  )r   r?  r'  )r,  rG  r  r  r  r  r  r+  r+  r.  r     rq  z'IPolys.dup_inner_isolate_negative_rootsc              	   C  r  N)r  r  r  r  blackbox)r   r?  r'  r,  rG  r  r  r  r  r  r+  r+  r.  r     rq  z!IPolys.dup_isolate_real_roots_sqfc              	   C  r  )N)r  r  r  basisr  )r   r?  r'  )r,  rG  r  r  r  r   r  r+  r+  r.  r     rq  zIPolys.dup_isolate_real_rootsc              
   C  s&   t tt| j|| j||||||dS )N)r  r  r  strictr   r  )r   rm  rn  r?  r'  )r,  rp  r  r  r  r  r   r  r+  r+  r.  r     rr  z"IPolys.dup_isolate_real_roots_listc                 C  r  )N)r  r  )r   r?  r'  )r,  rG  r  r  r+  r+  r.  r     rV  zIPolys.dup_count_real_rootsc                 C  s   t | || j|||dS )N)r  r  exclude)r   r?  r'  )r,  rG  r  r  r  r+  r+  r.  r     rD  zIPolys.dup_count_complex_rootsc                 C     t | || j||||dS )N)r  r  r  r  )r   r?  r'  )r,  rG  r  r  r  r  r+  r+  r.  r     rJ  z$IPolys.dup_isolate_complex_roots_sqfc              	   C  r  r  )r   r?  r'  r  r+  r+  r.  r     rq  z IPolys.dup_isolate_all_roots_sqfc                 C  r  )N)r  r  r  r  )r   r?  r'  )r,  rG  r  r  r  r  r+  r+  r.  r     rJ  zIPolys.dup_isolate_all_rootsc                 C  *   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_1rB  )sympy.polys.specialpolysr  tuplern  rC  r&  r'  )r,  r  r+  r+  r.  fateman_poly_F_1     zIPolys.fateman_poly_F_1c                 C  r  )Nr   )dmp_fateman_poly_F_2rB  )r  r
  r  rn  rC  r&  r'  )r,  r
  r+  r+  r.  fateman_poly_F_2  r	  zIPolys.fateman_poly_F_2c                 C  r  )Nr   )dmp_fateman_poly_F_3rB  )r  r  r  rn  rC  r&  r'  )r,  r  r+  r+  r.  fateman_poly_F_3  r	  zIPolys.fateman_poly_F_3c                   s    t  fdd | D S )Nc                   s   g | ]} j j| j qS r+  )r'  domr  )r  rH  r2  r+  r.  r    r  z&IPolys.to_gf_dense.<locals>.<listcomp>)r   r>  r?  r4  r+  r2  r.  to_gf_dense  rX  zIPolys.to_gf_densec                 C  s   |  t|| jd | jjS rA  )r9  rR   r&  r'  r  r4  r+  r+  r.  from_gf_dense  rJ  zIPolys.from_gf_densec                 C  rw  r*  )r   r  rU  r+  r+  r.  r     r@  zIPolys.gf_degreec                 C     t | || jjS r*  )r   r  r'  r  rU  r+  r+  r.  r     r  zIPolys.gf_LCc                 C  r  r*  )r   r  r'  r  rU  r+  r+  r.  r     r  zIPolys.gf_TCc                 C  s   |  t| |S r*  )r  r   r  rU  r+  r+  r.  r     r  zIPolys.gf_stripc                 C  s   |  t| || jjS r*  )r  r   r  r'  r  rU  r+  r+  r.  gf_trunc  rD  zIPolys.gf_truncc                 C      |  t| || jj| jjS r*  )r  r   r  r'  r  r  rU  r+  r+  r.  	gf_normal  rX  zIPolys.gf_normalc                 C     |  t|| jj| jjS r*  )r  r   r'  r  r  rU  r+  r+  r.  r     rD  zIPolys.gf_from_dictc                 C     t | || jj|dS N)	symmetric)r   r  r'  r  r,  rG  r  r+  r+  r.  r     rV  zIPolys.gf_to_dictc                 C  s   |  t|| jjS r*  )r  r   r'  r  rU  r+  r+  r.  r     r  zIPolys.gf_from_int_polyc                 C  r  r  )r   r  r'  r  r  r+  r+  r.  r     rV  zIPolys.gf_to_int_polyc                 C  r  r*  )r  r   r  r'  r  r  rU  r+  r+  r.  r     rX  zIPolys.gf_negc                 C  "   |  t| ||| jj| jjS r*  )r  r   r  r'  r  r  r  r+  r+  r.  r     rQ  zIPolys.gf_add_groundc                 C  r  r*  )r  r   r  r'  r  r  r  r+  r+  r.  r     rQ  zIPolys.gf_sub_groundc                 C  r  r*  )r  r   r  r'  r  r  r  r+  r+  r.  r     rQ  zIPolys.gf_mul_groundc                 C  r  r*  )r  r   r  r'  r  r  r  r+  r+  r.  r     rQ  zIPolys.gf_quo_groundc                 C  (   |  t| || || jj| jjS r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r     r]  zIPolys.gf_addc                 C  r  r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r     r]  zIPolys.gf_subc                 C  r  r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r   
  r]  zIPolys.gf_mulc                 C  r  r*  )r  r   r  r'  r  r  rU  r+  r+  r.  r     rX  zIPolys.gf_sqrc                 C  0   |  t| || || || jj| jjS r*  )r  r   r  r'  r  r  r_  r+  r+  r.  r     rb  zIPolys.gf_add_mulc                 C  r  r*  )r  r   r  r'  r  r  r_  r+  r+  r.  r     rb  zIPolys.gf_sub_mulc                 C  s&   |  ttt| j|| jj| jjS r*  )r  r   rm  rn  r  r'  r  r  )r,  r  r+  r+  r.  r     rr  zIPolys.gf_expandc                 C  s:   t | || || jj| jj\}}| || |fS r*  )r   r  r'  r  r  r  rd  r+  r+  r.  r     ri  zIPolys.gf_divc                 C  r  r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r     r]  zIPolys.gf_remc                 C  r  r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r     r]  zIPolys.gf_quoc                 C  r  r*  )r  r   r  r'  r  r  rZ  r+  r+  r.  r     r]  zIPolys.gf_exquoc                 C     |  t| ||| jjS r*  )r  r  r  r'  r  rR  r+  r+  r.  r  !  rJ  zIPolys.gf_lshiftc                 C  r  r*  )r  r  r  r'  r  rR  r+  r+  r.  r  #  rJ  zIPolys.gf_rshiftc                 C  r  r*  )r  r  r  r'  r  r  rR  r+  r+  r.  r  &  rQ  zIPolys.gf_powc                 C  s*   |  t| ||| || jj| jjS r*  )r  r  r  r'  r  r  )r,  rG  rS  r[  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,  rG  r[  r`  cffcfgr+  r+  r.  r  +  r  zIPolys.gf_cofactorsc                 C  r  r*  )r  r  r  r'  r  r  rZ  r+  r+  r.  r  .  r]  zIPolys.gf_gcdc                 C  r  r*  )r  r  r  r'  r  r  rZ  r+  r+  r.  r  0  r]  zIPolys.gf_lcmc                 C  r  r*  )r  r  r  r'  r  r  rZ  r+  r+  r.  r  2  r]  zIPolys.gf_gcdexc                 C  r  r*  )r  r	  r  r'  r  r  rU  r+  r+  r.  r	  5  rX  zIPolys.gf_monicc                 C  r  r*  )r  r
  r  r'  r  r  rU  r+  r+  r.  r
  7  rX  zIPolys.gf_diffc                 C     t | ||| jj| jjS r*  )r  r  r'  r  r  r  r+  r+  r.  r  :  rJ  zIPolys.gf_evalc                 C  r   r*  )r  r  r'  r  r  )r,  rG  r  r+  r+  r.  r  <  rJ  zIPolys.gf_multi_evalc                 C  r  r*  )r  r  r  r'  r  r  rZ  r+  r+  r.  r  ?  r]  zIPolys.gf_composec                 C  r  r*  )r  r  r  r'  r  r  )r,  r[  r`  rG  r+  r+  r.  r  A  rb  zIPolys.gf_compose_modc                 C  s\   |  |}|  |}|  |}|  |}t|||||| jj| jj\}}| || |fS r*  )r  r  r'  r  r  r  )r,  r  brH  rS  rG  UVr+  r+  r.  r  D  s   



 zIPolys.gf_trace_mapc                 C  r  r*  )r  r  r'  r  r  r,  rS  r+  r+  r.  r  L  rD  zIPolys.gf_randomc                 C  r  r*  )r  r  r'  r  r  r$  r+  r+  r.  r  N  rD  zIPolys.gf_irreduciblec                 C     t | || jj| jjS r*  )r  r  r'  r  r  rU  r+  r+  r.  r  Q  rD  zIPolys.gf_irred_p_ben_orc                 C  r%  r*  )r  r  r'  r  r  rU  r+  r+  r.  r  S  rD  zIPolys.gf_irred_p_rabinc                 C  r%  r*  )r  r  r'  r  r  rU  r+  r+  r.  r  U  rD  zIPolys.gf_irreducible_pc                 C  r%  r*  )r  r  r'  r  r  rU  r+  r+  r.  r  W  rD  zIPolys.gf_sqf_pc                 C  r  r*  )r  r  r  r'  r  r  rU  r+  r+  r.  r  Z  rX  zIPolys.gf_sqf_partc                   s4   t  | jj jj\}}| fdd|D fS )Nc                   r  r+  r  r  r2  r+  r.  r  ^  r  z&IPolys.gf_sqf_list.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  gf_sqf_list\  r  zIPolys.gf_sqf_listc                 C  r%  r*  )r  r  r'  r  r  rU  r+  r+  r.  r  `  rD  zIPolys.gf_Qmatrixc                   ,   t  | jj jj} fdd|D S )Nc                   r  r+  r&  r  r2  r+  r.  r  d  r  z'IPolys.gf_berlekamp.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  r  b  r  zIPolys.gf_berlekampc                   r(  )Nc                   r  r+  r&  r  r2  r+  r.  r  h  r  z,IPolys.gf_ddf_zassenhaus.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  r  f  r  zIPolys.gf_ddf_zassenhausc                   ,   t  | jj jj} fdd|D S )Nc                   r  r+  r&  r  r2  r+  r.  r  k  r  z,IPolys.gf_edf_zassenhaus.<locals>.<listcomp>)r  r  r'  r  r  r,  rG  rS  r  r+  r2  r.  r  i  r  zIPolys.gf_edf_zassenhausc                   r(  )Nc                   r  r+  r&  r  r2  r+  r.  r  o  r  z'IPolys.gf_ddf_shoup.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  r  m  r  zIPolys.gf_ddf_shoupc                   r)  )Nc                   r  r+  r&  r  r2  r+  r.  r  r  r  z'IPolys.gf_edf_shoup.<locals>.<listcomp>)r  r  r'  r  r  r*  r+  r2  r.  r  p  r  zIPolys.gf_edf_shoupc                   r(  )Nc                   r  r+  r&  r  r2  r+  r.  r  v  r  z(IPolys.gf_zassenhaus.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  r  t  r  zIPolys.gf_zassenhausc                   r(  )Nc                   r  r+  r&  r  r2  r+  r.  r  y  r  z#IPolys.gf_shoup.<locals>.<listcomp>)r  r  r'  r  r  r  r+  r2  r.  r  w  r  zIPolys.gf_shoupc                   s8   t  | jj jj|d\}}| fdd|D fS )N)methodc                   r  r+  r&  r  r2  r+  r.  r  }  r  z(IPolys.gf_factor_sqf.<locals>.<listcomp>)r  r  r'  r  r  )r,  rG  r+  r  r  r+  r2  r.  r  {  r  zIPolys.gf_factor_sqfc                   s4   t  | jj jj\}}| fdd|D fS )Nc                   r  r+  r&  r  r2  r+  r.  r    r  z$IPolys.gf_factor.<locals>.<listcomp>)r   r  r'  r  r  r  r+  r2  r.  r   ~  r  zIPolys.gf_factor)NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr*  (,  __name__
__module____qualname____annotations__r/  r1  r3  r6  r7  r9  r>  r?  rC  r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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   rK   rL   rM   rN   rO   rP   rQ   rS   rT   rV   rW   rX   rU   rY   rZ   r[   r]   r\   r^   r_   r`   ra   rb   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   rc   re   r   r   rd   rf   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"     s\  
 

		r"  N(0  __doc__
__future__r   typingr   sympy.core.exprr   sympy.polys.domains.domainr   sympy.polys.orderingsr   r:  r   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/   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   sympy.polys.densebasicrI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   sympy.polys.densetoolsrS   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   rp   rq   rr   rs   rt   ru   rv   sympy.polys.euclidtoolsrw   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   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   sympy.polys.rootisolationr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   sympy.polys.sqfreetoolsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   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   sympy.utilitiesr!  r"  r+  r+  r+  r.  <module>   s   L 