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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, ...]Zgensztuple[Expr, ...]symbolsintngensr   domainr   orderc                 C     d S N )selfgenr*  r*  H/var/www/auris/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   r/  zIPolys.clonec                 C  r(  r)  r*  r+  r*  r*  r-  	to_ground   r/  zIPolys.to_groundc                 C  r(  r)  r*  r+  elementr*  r*  r-  
ground_new  r/  zIPolys.ground_newc                 C  r(  r)  r*  r3  r*  r*  r-  
domain_new  r/  zIPolys.domain_newc                 C  r(  r)  r*  )r+  dr*  r*  r-  	from_dict  r/  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NotImplementedErrorr5  )r+  r4  r   r*  r*  r-  wrap  s   


zIPolys.wrapc                 C  s   |  | S r)  )r=  to_denser3  r*  r*  r-  r>       zIPolys.to_densec                 C  s   |  t|| jd | jS N   )r8  rR   r%  r&  r3  r*  r*  r-  
from_dense     zIPolys.from_densec                 C     |  t| |||| jS r)  )rB  r	   r>  r&  r+  fcir*  r*  r-  r	        zIPolys.dup_add_termc                 C  4   |  t| || |d || jd | jS Nr   rA  )rB  r
   r>  r=  r.  r%  r&  rE  r*  r*  r-  r
        4zIPolys.dmp_add_termc                 C  rD  r)  )rB  r   r>  r&  rE  r*  r*  r-  r     rI  zIPolys.dup_sub_termc                 C  rJ  rK  )rB  r   r>  r=  r.  r%  r&  rE  r*  r*  r-  r   !  rL  zIPolys.dmp_sub_termc                 C  rD  r)  )rB  r   r>  r&  rE  r*  r*  r-  r   #  rI  zIPolys.dup_mul_termc                 C  rJ  rK  )rB  r   r>  r=  r.  r%  r&  rE  r*  r*  r-  r   %  rL  zIPolys.dmp_mul_termc                 C     |  t| ||| jS r)  )rB  r   r>  r&  r+  rF  rG  r*  r*  r-  r   (  rC  zIPolys.dup_add_groundc                 C  "   |  t| ||| jd | jS r@  )rB  r   r>  r%  r&  rN  r*  r*  r-  r   *     "zIPolys.dmp_add_groundc                 C  rM  r)  )rB  r   r>  r&  rN  r*  r*  r-  r   ,  rC  zIPolys.dup_sub_groundc                 C  rO  r@  )rB  r   r>  r%  r&  rN  r*  r*  r-  r   .  rP  zIPolys.dmp_sub_groundc                 C  rM  r)  )rB  r   r>  r&  rN  r*  r*  r-  r   0  rC  zIPolys.dup_mul_groundc                 C  rO  r@  )rB  r   r>  r%  r&  rN  r*  r*  r-  r   2  rP  zIPolys.dmp_mul_groundc                 C  rM  r)  )rB  r   r>  r&  rN  r*  r*  r-  r   4  rC  zIPolys.dup_quo_groundc                 C  rO  r@  )rB  r   r>  r%  r&  rN  r*  r*  r-  r   6  rP  zIPolys.dmp_quo_groundc                 C  rM  r)  )rB  r   r>  r&  rN  r*  r*  r-  r   8  rC  zIPolys.dup_exquo_groundc                 C  rO  r@  )rB  r   r>  r%  r&  rN  r*  r*  r-  r   :  rP  zIPolys.dmp_exquo_groundc                 C  rM  r)  )rB  r   r>  r&  r+  rF  nr*  r*  r-  r   =  rC  zIPolys.dup_lshiftc                 C  rM  r)  )rB  r   r>  r&  rQ  r*  r*  r-  r   ?  rC  zIPolys.dup_rshiftc                 C     |  t| || jS r)  )rB  r   r>  r&  r+  rF  r*  r*  r-  r   B     zIPolys.dup_absc                 C      |  t| || jd | jS r@  )rB  r   r>  r%  r&  rT  r*  r*  r-  r   D      zIPolys.dmp_absc                 C  rS  r)  )rB  r   r>  r&  rT  r*  r*  r-  r   G  rU  zIPolys.dup_negc                 C  rV  r@  )rB  r   r>  r%  r&  rT  r*  r*  r-  r   I  rW  zIPolys.dmp_negc                 C      |  t| || || jS r)  )rB  r   r>  r&  r+  rF  gr*  r*  r-  r   L  rW  zIPolys.dup_addc                 C  (   |  t| || || jd | jS r@  )rB  r    r>  r%  r&  rY  r*  r*  r-  r    N     (zIPolys.dmp_addc                 C  rX  r)  )rB  r!   r>  r&  rY  r*  r*  r-  r!   Q  rW  zIPolys.dup_subc                 C  r[  r@  )rB  r"   r>  r%  r&  rY  r*  r*  r-  r"   S  r\  zIPolys.dmp_subc                 C  (   |  t| || || || jS r)  )rB  r#   r>  r&  r+  rF  rZ  hr*  r*  r-  r#   V  r\  zIPolys.dup_add_mulc                 C  0   |  t| || || || jd | jS r@  )rB  r$   r>  r%  r&  r^  r*  r*  r-  r$   X     0zIPolys.dmp_add_mulc                 C  r]  r)  )rB  r%   r>  r&  r^  r*  r*  r-  r%   Z  r\  zIPolys.dup_sub_mulc                 C  r`  r@  )rB  r&   r>  r%  r&  r^  r*  r*  r-  r&   \  ra  zIPolys.dmp_sub_mulc                 C  rX  r)  )rB  r'   r>  r&  rY  r*  r*  r-  r'   _  rW  zIPolys.dup_mulc                 C  r[  r@  )rB  r(   r>  r%  r&  rY  r*  r*  r-  r(   a  r\  zIPolys.dmp_mulc                 C  rS  r)  )rB  r)   r>  r&  rT  r*  r*  r-  r)   d  rU  zIPolys.dup_sqrc                 C  rV  r@  )rB  r*   r>  r%  r&  rT  r*  r*  r-  r*   f  rW  zIPolys.dmp_sqrc                 C  rM  r)  )rB  r+   r>  r&  rQ  r*  r*  r-  r+   h  rC  zIPolys.dup_powc                 C  rO  r@  )rB  r,   r>  r%  r&  rQ  r*  r*  r-  r,   j  rP  zIPolys.dmp_powc                 C  2   t | || || j\}}| || |fS r)  )r-   r>  r&  rB  r+  rF  rZ  qrr*  r*  r-  r-   m     zIPolys.dup_pdivc                 C  rX  r)  )rB  r.   r>  r&  rY  r*  r*  r-  r.   p  rW  zIPolys.dup_premc                 C  rX  r)  )rB  r/   r>  r&  rY  r*  r*  r-  r/   r  rW  zIPolys.dup_pquoc                 C  rX  r)  )rB  r0   r>  r&  rY  r*  r*  r-  r0   t  rW  zIPolys.dup_pexquoc                 C  :   t | || || jd | j\}}| || |fS r@  )r1   r>  r%  r&  rB  rc  r*  r*  r-  r1   w     &zIPolys.dmp_pdivc                 C  r[  r@  )rB  r2   r>  r%  r&  rY  r*  r*  r-  r2   z  r\  zIPolys.dmp_premc                 C  r[  r@  )rB  r3   r>  r%  r&  rY  r*  r*  r-  r3   |  r\  zIPolys.dmp_pquoc                 C  r[  r@  )rB  r4   r>  r%  r&  rY  r*  r*  r-  r4   ~  r\  zIPolys.dmp_pexquoc                 C  rb  r)  )r5   r>  r&  rB  rc  r*  r*  r-  r5     rf  zIPolys.dup_rr_divc                 C  rg  r@  )r6   r>  r%  r&  rB  rc  r*  r*  r-  r6     rh  zIPolys.dmp_rr_divc                 C  rb  r)  )r7   r>  r&  rB  rc  r*  r*  r-  r7     rf  zIPolys.dup_ff_divc                 C  rg  r@  )r8   r>  r%  r&  rB  rc  r*  r*  r-  r8     rh  zIPolys.dmp_ff_divc                 C  rb  r)  )r9   r>  r&  rB  rc  r*  r*  r-  r9     rf  zIPolys.dup_divc                 C  rX  r)  )rB  r:   r>  r&  rY  r*  r*  r-  r:     rW  zIPolys.dup_remc                 C  rX  r)  )rB  r;   r>  r&  rY  r*  r*  r-  r;     rW  zIPolys.dup_quoc                 C  rX  r)  )rB  r<   r>  r&  rY  r*  r*  r-  r<     rW  zIPolys.dup_exquoc                 C  rg  r@  )r=   r>  r%  r&  rB  rc  r*  r*  r-  r=     rh  zIPolys.dmp_divc                 C  r[  r@  )rB  r>   r>  r%  r&  rY  r*  r*  r-  r>     r\  zIPolys.dmp_remc                 C  r[  r@  )rB  r?   r>  r%  r&  rY  r*  r*  r-  r?     r\  zIPolys.dmp_quoc                 C  r[  r@  )rB  r@   r>  r%  r&  rY  r*  r*  r-  r@     r\  zIPolys.dmp_exquoc                 C     t | || jS r)  )rA   r>  r&  rT  r*  r*  r-  rA        zIPolys.dup_max_normc                 C     t | || jd | jS r@  )rB   r>  r%  r&  rT  r*  r*  r-  rB     rC  zIPolys.dmp_max_normc                 C  ri  r)  )rC   r>  r&  rT  r*  r*  r-  rC     rj  zIPolys.dup_l1_normc                 C  rk  r@  )rD   r>  r%  r&  rT  r*  r*  r-  rD     rC  zIPolys.dmp_l1_normc                 C  ri  r)  )rE   r>  r&  rT  r*  r*  r-  rE     rj  zIPolys.dup_l2_norm_squaredc                 C  rk  r@  )rF   r>  r%  r&  rT  r*  r*  r-  rF     rC  zIPolys.dmp_l2_norm_squaredc                 C  s   |  ttt| j|| jS r)  )rB  rG   listmapr>  r&  r+  polysr*  r*  r-  rG        zIPolys.dup_expandc                 C  s&   |  ttt| j|| jd | jS r@  )rB  rH   rl  rm  r>  r%  r&  rn  r*  r*  r-  rH        &zIPolys.dmp_expandc                 C  ri  r)  )rI   r>  r&  rT  r*  r*  r-  rI     rj  zIPolys.dup_LCc                 C  2   t | || j}t|tr| dd  |S |S r@  )rJ   r>  r&  r:  rl  rB  )r+  rF  LCr*  r*  r-  rJ        
zIPolys.dmp_LCc                 C  ri  r)  )rK   r>  r&  rT  r*  r*  r-  rK     rj  zIPolys.dup_TCc                 C  rr  r@  )rL   r>  r&  r:  rl  rB  )r+  rF  ZTCr*  r*  r-  rL     rt  zIPolys.dmp_TCc                 C  rk  r@  )rM   r>  r%  r&  rT  r*  r*  r-  rM     rC  zIPolys.dmp_ground_LCc                 C  rk  r@  )rN   r>  r%  r&  rT  r*  r*  r-  rN     rC  zIPolys.dmp_ground_TCc                 C     t | |S r)  )rO   r>  rT  r*  r*  r-  rO     r?  zIPolys.dup_degreec                 C  s   t | || jd S r@  )rP   r>  r%  rT  r*  r*  r-  rP        zIPolys.dmp_degreec                 C  s   t | ||| jd S r@  )rQ   r>  r%  )r+  rF  jr*  r*  r-  rQ     rU  zIPolys.dmp_degree_inc                 C  rM  r)  )rB  rS   r>  r&  r+  rF  mr*  r*  r-  rS     rC  zIPolys.dup_integratec                 C  rO  r@  )rB  rT   r>  r%  r&  rx  r*  r*  r-  rT     rP  zIPolys.dmp_integratec                 C  rM  r)  )rB  rV   r>  r&  rx  r*  r*  r-  rV     rC  zIPolys.dup_diffc                 C  rO  r@  )rB  rW   r>  r%  r&  rx  r*  r*  r-  rW     rP  zIPolys.dmp_diffc                 C  $   |  t| |||| jd | jS r@  )rB  rX   r>  r%  r&  r+  rF  ry  rw  r*  r*  r-  rX        $zIPolys.dmp_diff_inc                 C  rz  r@  )rB  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+  rF  ar*  r*  r-  rY        zIPolys.dup_evalc                 C  s.   t | ||| jd | j}| dd  |S r@  )rZ   r>  r%  r&  rB  )r+  rF  r~  resultr*  r*  r-  rZ     s   zIPolys.dmp_evalc                 C  s.   t | |||| jd | j}| ||S r@  )r[   r>  r%  r&  r.  rB  )r+  rF  r~  rw  r  r*  r*  r-  r[     s   zIPolys.dmp_eval_inc                 C  s0   t | ||||| jd | j}| ||S r@  )r]   r>  r%  r&  r.  rB  )r+  rF  ry  r~  rw  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 r@  )r\   r>  r%  r&  r:  rl  lenrB  )r+  rF  Ar  r*  r*  r-  r\     s   
zIPolys.dmp_eval_tailc                 C  rM  r)  )rB  r^   r>  r&  r+  rF  pr*  r*  r-  r^     rC  zIPolys.dup_truncc                 C  s0   |  t| || dd  || jd | jS r@  )rB  r_   r>  r%  r&  rY  r*  r*  r-  r_     ra  zIPolys.dmp_truncc                 C  rO  r@  )rB  r`   r>  r%  r&  r  r*  r*  r-  r`     rP  zIPolys.dmp_ground_truncc                 C  rS  r)  )rB  ra   r>  r&  rT  r*  r*  r-  ra     rU  zIPolys.dup_monicc                 C  rV  r@  )rB  rb   r>  r%  r&  rT  r*  r*  r-  rb     rW  zIPolys.dmp_ground_monicc                 C  s6   t | || || j\}}}|| || |fS r)  )rg   r>  r&  rB  r+  rF  rZ  rG  FGr*  r*  r-  rg     s    zIPolys.dup_extractc                 C  s>   t | || || jd | j\}}}|| || |fS r@  )rh   r>  r%  r&  rB  r  r*  r*  r-  rh     s   (zIPolys.dmp_ground_extractc                 C  s4   t | |d | j\}}| || |fS r@  )ri   r=  r.  r>  r&  rB  r+  rF  r  rd  r*  r*  r-  ri     s    zIPolys.dup_real_imagc                 C  rS  r)  )rB  rj   r>  r&  rT  r*  r*  r-  rj     rU  zIPolys.dup_mirrorc                 C  rM  r)  )rB  rk   r>  r&  r}  r*  r*  r-  rk     rC  zIPolys.dup_scalec                 C  rM  r)  )rB  rl   r>  r&  r}  r*  r*  r-  rl     rC  zIPolys.dup_shiftc                 C  rO  r@  )rB  rm   r>  r%  r&  r}  r*  r*  r-  rm     rP  zIPolys.dmp_shiftc                 C  r]  r)  )rB  rn   r>  r&  r  r*  r*  r-  rn     r\  zIPolys.dup_transformc                 C  rX  r)  )rB  ro   r>  r&  rY  r*  r*  r-  ro     rW  zIPolys.dup_composec                 C  r[  r@  )rB  rp   r>  r%  r&  rY  r*  r*  r-  rp     r\  zIPolys.dmp_composec                 C  "   t | || j}tt| j|S r)  )rq   r>  r&  rl  rm  rB  )r+  rF  
componentsr*  r*  r-  rq        zIPolys.dup_decomposec                 C  (   t | || jd | j}|  |S r@  )rr   r>  r%  r&  r2  rB  r+  rF  r  r*  r*  r-  rr         zIPolys.dmp_liftc                 C  ri  r)  )rs   r>  r&  rT  r*  r*  r-  rs   $  rj  zIPolys.dup_sign_variationsFc                 C  sD   t | || j|d\}}|r| j| j d}n| }|||fS )Nconvertr&  )rt   r>  r&  r0  get_ringrB  r+  rF  r  rG  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 )NrA  r  r  )ru   r>  r%  r&  r0  r  rB  r  r*  r*  r-  ru   .  s
   "zIPolys.dmp_clear_denomsc                 C  rM  r)  )rB  rv   r>  r&  rQ  r*  r*  r-  rv   6  rC  zIPolys.dup_revertc                 C  rb  r)  )rw   r>  r&  rB  r+  rF  rZ  sr_  r*  r*  r-  rw   9  rf  zIPolys.dup_half_gcdexc                 C  rg  r@  )rx   r>  r%  r&  rB  r  r*  r*  r-  rx   <  rh  zIPolys.dmp_half_gcdexc                 C  <   t | || || j\}}}| || || |fS r)  )ry   r>  r&  rB  r+  rF  rZ  r  tr_  r*  r*  r-  ry   ?      zIPolys.dup_gcdexc                 C  D   t | || || jd | j\}}}| || || |fS r@  )rz   r>  r%  r&  rB  r  r*  r*  r-  rz   B     (zIPolys.dmp_gcdexc                 C  rX  r)  )rB  r{   r>  r&  rY  r*  r*  r-  r{   F  rW  zIPolys.dup_invertc                 C  r[  r@  )rB  r|   r>  r%  r&  rY  r*  r*  r-  r|   H  r\  zIPolys.dmp_invertc                 C  *   t | || || j}tt| j|S r)  )r}   r>  r&  rl  rm  rB  r+  rF  rZ  prsr*  r*  r-  r}   K     zIPolys.dup_euclidean_prsc                 C  2   t | || || jd | j}tt| j|S r@  )r~   r>  r%  r&  rl  rm  rB  r  r*  r*  r-  r~   N     "zIPolys.dmp_euclidean_prsc                 C  r  r)  )r   r>  r&  rl  rm  rB  r  r*  r*  r-  r   Q  r  zIPolys.dup_primitive_prsc                 C  r  r@  )r   r>  r%  r&  rl  rm  rB  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&  rl  rm  rB  r+  rF  rZ  r  sresr*  r*  r-  r   X  rf  zIPolys.dup_inner_subresultantsc                 C  s:   t | || || jd | j\}}tt| j||fS r@  )r   r>  r%  r&  rl  rm  rB  r  r*  r*  r-  r   [  rh  zIPolys.dmp_inner_subresultantsc                 C  r  r)  )r   r>  r&  rl  rm  rB  r  r*  r*  r-  r   _  r  zIPolys.dup_subresultantsc                 C  r  r@  )r   r>  r%  r&  rl  rm  rB  r  r*  r*  r-  r   b  r  zIPolys.dmp_subresultantsc                 C  s2   t | || || j\}}|tt| j|fS r)  )r   r>  r&  rl  rm  rB  r+  rF  rZ  resr  r*  r*  r-  r   f  rf  zIPolys.dup_prs_resultantc                 C  sH   t | || || jd | j\}}| dd  |tt| j|fS r@  )r   r>  r%  r&  rB  rl  rm  r  r*  r*  r-  r   i  s   &"zIPolys.dmp_prs_resultantc                 C  s<   t | || || || jd | j}| dd  |S r@  )r   r>  r6  r%  r&  rB  )r+  rF  rZ  r  r  r*  r*  r-  r   m  s   *zIPolys.dmp_zz_modular_resultantc                 C  4   t | || || jd | j}| dd  |S r@  )r   r>  r%  r&  rB  r+  rF  rZ  r  r*  r*  r-  r   p     "zIPolys.dmp_zz_collins_resultantc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r   s  r  zIPolys.dmp_qq_collins_resultantc                 C  s   t | || || jS r)  )r   r>  r&  rY  r*  r*  r-  r   w  rC  zIPolys.dup_resultantc                 C  sB   t | || || jd | j}t|tr| dd  |S |S r@  )r   r>  r%  r&  r:  rl  rB  r  r*  r*  r-  r   y  s   "
zIPolys.dmp_resultantc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r     rj  zIPolys.dup_discriminantc                 C  :   t | || jd | j}t|tr| dd  |S |S r@  )r   r>  r%  r&  r:  rl  rB  )r+  rF  Zdiscr*  r*  r-  r        
zIPolys.dmp_discriminantc                 C  r  r)  )r   r>  r&  rB  r+  rF  rZ  Hr  r  r*  r*  r-  r     r  zIPolys.dup_rr_prs_gcdc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_ff_prs_gcdc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_rr_prs_gcdc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_ff_prs_gcdc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_zz_heu_gcdc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_zz_heu_gcdc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_qq_heu_gcdc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_qq_heu_gcdc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_inner_gcdc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_inner_gcdc                 C  $   t | || || j}| |S r)  )r   r>  r&  rB  r+  rF  rZ  r  r*  r*  r-  r        
zIPolys.dup_gcdc                 C  ,   t | || || jd | j}| |S r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r        "
zIPolys.dmp_gcdc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_rr_lcmc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_ff_lcmc                 C  r  r)  )r   r>  r&  rB  r  r*  r*  r-  r     r  zIPolys.dup_lcmc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_rr_lcmc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_ff_lcmc                 C  r  r@  )r   r>  r%  r&  rB  r  r*  r*  r-  r     r  zIPolys.dmp_lcmc                 C  s   t | || j}|S r)  )rc   r>  r&  r+  rF  contr*  r*  r-  rc     s   zIPolys.dup_contentc                 C  s$   t | || j\}}|| |fS r)  )re   r>  r&  rB  r+  rF  r  Zprimr*  r*  r-  re     s   zIPolys.dup_primitivec                 C  r  r@  )r   r>  r%  r&  r:  rl  rB  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 r@  )r   r>  r%  r&  r:  rl  rB  r  r*  r*  r-  r     s   
zIPolys.dmp_primitivec                 C  s   t | || jd | j}|S r@  )rd   r>  r%  r&  r  r*  r*  r-  rd     s   zIPolys.dmp_ground_contentc                 C  s,   t | || jd | j\}}|| |fS r@  )rf   r>  r%  r&  rB  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&  rB  	r+  rF  rZ  r  r  cfZcgr  r  r*  r*  r-  r     s   zIPolys.dup_cancelc           	      C  sj   t | || || jd | j|d}|s'|\}}}}||| || |fS |\}}| || |fS )NrA  r  )r   r>  r%  r&  rB  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*  rB  .0rZ  kr1  r*  r-  
<listcomp>      z-IPolys.dup_trial_division.<locals>.<listcomp>)r   r>  rl  rm  r&  r+  rF  factorsr*  r1  r-  r         zIPolys.dup_trial_divisionc                   s:   t  |tt j| jd  j} fdd|D S )NrA  c                   r  r*  r  r  r1  r*  r-  r    r  z-IPolys.dmp_trial_division.<locals>.<listcomp>)r   r>  rl  rm  r%  r&  r  r*  r1  r-  r     s   (zIPolys.dmp_trial_divisionc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r     rj  zIPolys.dup_zz_mignotte_boundc                 C  rk  r@  )r   r>  r%  r&  rT  r*  r*  r-  r     rC  zIPolys.dmp_zz_mignotte_boundc                 C  s\   | j }t|||||||||||| j\}}	}
}| || |	| |
| |fS r)  )r>  r   r&  rB  )r+  ry  rF  rZ  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   rl  rm  r&  rB  )r+  r  rF  Zf_listlr  ro  r*  r*  r-  r     s    zIPolys.dup_zz_hensel_liftc                   $   t  | j} fdd|D S )Nc                   r  r*  r  r  r1  r*  r-  r    r  z,IPolys.dup_zz_zassenhaus.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r        zIPolys.dup_zz_zassenhausc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r     rj  zIPolys.dup_zz_irreducible_pc                 C  s   t | || j|dS )N)irreducible)r   r>  r&  )r+  rF  r  r*  r*  r-  r     rv  zIPolys.dup_cyclotomic_pc                 C  s   t || j}| |S r)  )r   r&  rB  )r+  rR  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&  rl  rm  rB  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 )NrA  c                   r  r*  )r>  )r  r  r  mvr*  r-  r    r  z2IPolys.dmp_zz_wang_lead_coeffs.<locals>.<listcomp>)rl  rm  r>  r   r%  r&  rB  )
r+  rF  r  r  r  r  r  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   rl  rm  r>  r&  rB  )r+  r  ry  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 r@  )r   rl  rm  r>  r%  r&  rB  )r+  r  rG  r  r7  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 r@  )rl  rm  r>  r   r%  r&  rB  )	r+  rF  r  rs  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 )NrA  )modseedc                      g | ]}  |qS r*  r  r  rZ  r1  r*  r-  r  9      z&IPolys.dmp_zz_wang.<locals>.<listcomp>)r   r>  r%  r&  )r+  rF  r  r  r  r*  r1  r-  r   7  r  zIPolys.dmp_zz_wangc                   ,   t  | j\}}| fdd|D fS )Nc                   r  r*  r  r  r1  r*  r-  r  =  r  z,IPolys.dup_zz_factor_sqf.<locals>.<listcomp>)r   r>  r&  r+  rF  coeffr  r*  r1  r-  r   ;     zIPolys.dup_zz_factor_sqfc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  A  r  z(IPolys.dup_zz_factor.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   ?  r  zIPolys.dup_zz_factorc                   4   t  | jd  j\}}| fdd|D fS )NrA  c                   r  r*  r  r  r1  r*  r-  r  D  r  z(IPolys.dmp_zz_factor.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   B     zIPolys.dmp_zz_factorc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  H  r  z*IPolys.dup_qq_i_factor.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   F  r  zIPolys.dup_qq_i_factorc                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r  K  r  z*IPolys.dmp_qq_i_factor.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   I  r  zIPolys.dmp_qq_i_factorc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  O  r  z*IPolys.dup_zz_i_factor.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   M  r  zIPolys.dup_zz_i_factorc                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r  R  r  z*IPolys.dmp_zz_i_factor.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   P  r  zIPolys.dmp_zz_i_factorc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  V  r  z)IPolys.dup_ext_factor.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   T  r  zIPolys.dup_ext_factorc                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r  Y  r  z)IPolys.dmp_ext_factor.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   W  r  zIPolys.dmp_ext_factorc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  ]  r  z(IPolys.dup_gf_factor.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   [  r  zIPolys.dup_gf_factorc                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r  `  r  z(IPolys.dmp_gf_factor.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   ^  r  zIPolys.dmp_gf_factorc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  d  r  z*IPolys.dup_factor_list.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   b  r  zIPolys.dup_factor_listc                   r  )Nc                   r  r*  r  r  r1  r*  r-  r  g  r  z2IPolys.dup_factor_list_include.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r   e  r  zIPolys.dup_factor_list_includec                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r  k  r  z*IPolys.dmp_factor_list.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   i  r  zIPolys.dmp_factor_listc                   ,   t  | jd  j} fdd|D S )NrA  c                   r  r*  r  r  r1  r*  r-  r  n  r  z2IPolys.dmp_factor_list_include.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r   l     zIPolys.dmp_factor_list_includec                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r   p  rj  zIPolys.dup_irreducible_pc                 C  rk  r@  )r   r>  r%  r&  rT  r*  r*  r-  r   r  rC  zIPolys.dmp_irreducible_pc                 C  r  r)  )r   r>  r&  rl  rm  rB  )r+  rF  seqr*  r*  r-  r   u  r  zIPolys.dup_sturmc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r   y  rj  zIPolys.dup_sqf_pc                 C  rk  r@  )r   r>  r%  r&  rT  r*  r*  r-  r   {  rC  zIPolys.dmp_sqf_pc                 C  r  r@  )r   r>  r%  r&  r2  rB  rQ  r*  r*  r-  r   ~  r  zIPolys.dmp_normc                 C  s2   t | || j\}}}|| ||  |fS r)  )r   r>  r&  rB  r2  r+  rF  r  r  Rr*  r*  r-  r     s   zIPolys.dup_sqf_normc                 C  s:   t | || jd | j\}}}|| ||  |fS r@  )r   r>  r%  r&  rB  r2  r  r*  r*  r-  r     s    zIPolys.dmp_sqf_normc                 C  rS  r)  )rB  r   r>  r&  rT  r*  r*  r-  r     rU  zIPolys.dup_gf_sqf_partc                 C  rS  r)  )rB  r   r>  r&  rT  r*  r*  r-  r     rU  zIPolys.dmp_gf_sqf_partc                 C  rS  r)  )rB  r   r>  r&  rT  r*  r*  r-  r     rU  zIPolys.dup_sqf_partc                 C  rV  r@  )rB  r   r>  r%  r&  rT  r*  r*  r-  r     rW  zIPolys.dmp_sqf_partc                   0   t  | j|d\}}| fdd|D fS )Nallc                   r  r*  r  r  r1  r*  r-  r    r  z*IPolys.dup_gf_sqf_list.<locals>.<listcomp>)r   r>  r&  r+  rF  r  r  r  r*  r1  r-  r        zIPolys.dup_gf_sqf_listc                   8   t  | jd  j|d\}}| fdd|D fS )NrA  r  c                   r  r*  r  r  r1  r*  r-  r    r  z*IPolys.dmp_gf_sqf_list.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r        "zIPolys.dmp_gf_sqf_listc                   r  )Nr  c                   r  r*  r  r  r1  r*  r-  r    r  z'IPolys.dup_sqf_list.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r     r  zIPolys.dup_sqf_listc                   s(   t  | j|d} fdd|D S )Nr  c                   r  r*  r  r  r1  r*  r-  r    r  z/IPolys.dup_sqf_list_include.<locals>.<listcomp>)r   r>  r&  r+  rF  r  r  r*  r1  r-  r     s   zIPolys.dup_sqf_list_includec                   r  )NrA  r  c                   r  r*  r  r  r1  r*  r-  r    r  z'IPolys.dmp_sqf_list.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r     r  zIPolys.dmp_sqf_listc                   s0   t  | jd  j|d} fdd|D S )NrA  r  c                   r  r*  r  r  r1  r*  r-  r    r  z/IPolys.dmp_sqf_list_include.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r     s   zIPolys.dmp_sqf_list_includec                   r  )Nc                   r  r*  r  r  r1  r*  r-  r    r  z'IPolys.dup_gff_list.<locals>.<listcomp>)r   r>  r&  r  r*  r1  r-  r     r  zIPolys.dup_gff_listc                   r  )NrA  c                   r  r*  r  r  r1  r*  r-  r    r  z'IPolys.dmp_gff_list.<locals>.<listcomp>)r   r>  r%  r&  r  r*  r1  r-  r     r  zIPolys.dmp_gff_listc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r     rj  zIPolys.dup_root_upper_boundc                 C  ri  r)  )r   r>  r&  rT  r*  r*  r-  r     rj  zIPolys.dup_root_lower_boundc                 C  s   t | ||| j|dS )N)fast)r   r>  r&  )r+  rF  Mr  r*  r*  r-  r     rU  z IPolys.dup_step_refine_real_rootc              
   C  s    t | ||| j|||||dS )N)epsstepsdisjointr  mobius)r   r>  r&  )r+  rF  r  r  r  r  r  r  r*  r*  r-  r     rW  z!IPolys.dup_inner_refine_real_rootc              
   C      t | |||| j||||dS N)r  r  r  r  )r   r>  r&  r+  rF  r  r  r  r  r  r  r*  r*  r-  r     rW  z!IPolys.dup_outer_refine_real_rootc              
   C  r  r  )r   r>  r&  r  r*  r*  r-  r     rW  zIPolys.dup_refine_real_rootc                 C     t | || j||dS )N)r  r  )r   r>  r&  )r+  rF  r  r  r*  r*  r-  r     rU  z#IPolys.dup_inner_isolate_real_rootsc              	   C     t | || j|||||dS )N)r  infsupr  r  )r   r>  r&  )r+  rF  r  r  r  r  r  r*  r*  r-  r     rp  z'IPolys.dup_inner_isolate_positive_rootsc              	   C  r  )N)r  r  r  r  r  )r   r>  r&  )r+  rF  r  r  r  r  r  r*  r*  r-  r     rp  z'IPolys.dup_inner_isolate_negative_rootsc              	   C  r  N)r  r  r  r  blackbox)r   r>  r&  r+  rF  r  r  r  r  r  r*  r*  r-  r     rp  z!IPolys.dup_isolate_real_roots_sqfc              	   C  r  )N)r  r  r  basisr  )r   r>  r&  )r+  rF  r  r  r  r  r  r*  r*  r-  r     rp  zIPolys.dup_isolate_real_rootsc              
   C  s&   t tt| j|| j||||||dS )N)r  r  r  strictr  r  )r   rl  rm  r>  r&  )r+  ro  r  r  r  r  r  r  r*  r*  r-  r     rq  z"IPolys.dup_isolate_real_roots_listc                 C  r  )N)r  r  )r   r>  r&  )r+  rF  r  r  r*  r*  r-  r     rU  zIPolys.dup_count_real_rootsc                 C  s   t | || j|||dS )N)r  r  exclude)r   r>  r&  )r+  rF  r  r  r  r*  r*  r-  r     rC  zIPolys.dup_count_complex_rootsc                 C     t | || j||||dS )N)r  r  r  r  )r   r>  r&  )r+  rF  r  r  r  r  r*  r*  r-  r     rI  z$IPolys.dup_isolate_complex_roots_sqfc              	   C  r  r  )r   r>  r&  r  r*  r*  r-  r     rp  z IPolys.dup_isolate_all_roots_sqfc                 C  r  )N)r  r  r  r  )r   r>  r&  )r+  rF  r  r  r  r  r*  r*  r-  r     rI  zIPolys.dup_isolate_all_rootsc                 C  *   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_1rA  )sympy.polys.specialpolysr  tuplerm  rB  r%  r&  )r+  r  r*  r*  r-  fateman_poly_F_1     zIPolys.fateman_poly_F_1c                 C  r  )Nr   )dmp_fateman_poly_F_2rA  )r  r  r   rm  rB  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_3rA  )r  r  r   rm  rB  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  rG  r1  r*  r-  r    r  z&IPolys.to_gf_dense.<locals>.<listcomp>)r   r=  r>  r3  r*  r1  r-  to_gf_dense  rW  zIPolys.to_gf_densec                 C  s   |  t|| jd | jjS r@  )r8  rR   r%  r&  r  r3  r*  r*  r-  from_gf_dense  rI  zIPolys.from_gf_densec                 C  ru  r)  )r   r  rT  r*  r*  r-  r     r?  zIPolys.gf_degreec                 C     t | || jjS r)  )r   r  r&  r  rT  r*  r*  r-  r     r  zIPolys.gf_LCc                 C  r
  r)  )r   r  r&  r  rT  r*  r*  r-  r     r  zIPolys.gf_TCc                 C  s   |  t| |S r)  )r	  r   r  rT  r*  r*  r-  r     r  zIPolys.gf_stripc                 C  s   |  t| || jjS r)  )r	  r   r  r&  r  rT  r*  r*  r-  gf_trunc  rC  zIPolys.gf_truncc                 C      |  t| || jj| jjS r)  )r	  r   r  r&  r  r  rT  r*  r*  r-  	gf_normal  rW  zIPolys.gf_normalc                 C     |  t|| jj| jjS r)  )r	  r   r&  r  r  rT  r*  r*  r-  r     rC  zIPolys.gf_from_dictc                 C     t | || jj|dS N)	symmetric)r   r  r&  r  r+  rF  r  r*  r*  r-  r     rU  zIPolys.gf_to_dictc                 C  s   |  t|| jjS r)  )r	  r   r&  r  rT  r*  r*  r-  r     r  zIPolys.gf_from_int_polyc                 C  r  r  )r   r  r&  r  r  r*  r*  r-  r     rU  zIPolys.gf_to_int_polyc                 C  r  r)  )r	  r   r  r&  r  r  rT  r*  r*  r-  r     rW  zIPolys.gf_negc                 C  "   |  t| ||| jj| jjS r)  )r	  r   r  r&  r  r  r}  r*  r*  r-  r     rP  zIPolys.gf_add_groundc                 C  r  r)  )r	  r   r  r&  r  r  r}  r*  r*  r-  r     rP  zIPolys.gf_sub_groundc                 C  r  r)  )r	  r   r  r&  r  r  r}  r*  r*  r-  r     rP  zIPolys.gf_mul_groundc                 C  r  r)  )r	  r   r  r&  r  r  r}  r*  r*  r-  r     rP  zIPolys.gf_quo_groundc                 C  (   |  t| || || jj| jjS r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r     r\  zIPolys.gf_addc                 C  r  r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r     r\  zIPolys.gf_subc                 C  r  r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r   
  r\  zIPolys.gf_mulc                 C  r  r)  )r	  r   r  r&  r  r  rT  r*  r*  r-  r     rW  zIPolys.gf_sqrc                 C  0   |  t| || || || jj| jjS r)  )r	  r   r  r&  r  r  r^  r*  r*  r-  r     ra  zIPolys.gf_add_mulc                 C  r  r)  )r	  r   r  r&  r  r  r^  r*  r*  r-  r     ra  zIPolys.gf_sub_mulc                 C  s&   |  ttt| j|| jj| jjS r)  )r	  r   rl  rm  r  r&  r  r  )r+  r  r*  r*  r-  r     rq  zIPolys.gf_expandc                 C  s:   t | || || jj| jj\}}| || |fS r)  )r   r  r&  r  r  r	  rc  r*  r*  r-  r     rh  zIPolys.gf_divc                 C  r  r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r     r\  zIPolys.gf_remc                 C  r  r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r     r\  zIPolys.gf_quoc                 C  r  r)  )r	  r   r  r&  r  r  rY  r*  r*  r-  r     r\  zIPolys.gf_exquoc                 C     |  t| ||| jjS r)  )r	  r  r  r&  r  rQ  r*  r*  r-  r  !  rI  zIPolys.gf_lshiftc                 C  r  r)  )r	  r  r  r&  r  rQ  r*  r*  r-  r  #  rI  zIPolys.gf_rshiftc                 C  r  r)  )r	  r  r  r&  r  r  rQ  r*  r*  r-  r  &  rP  zIPolys.gf_powc                 C  s*   |  t| ||| || jj| jjS r)  )r	  r  r  r&  r  r  )r+  rF  rR  rZ  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+  rF  rZ  r_  Zcffcfgr*  r*  r-  r  +  r  zIPolys.gf_cofactorsc                 C  r  r)  )r	  r  r  r&  r  r  rY  r*  r*  r-  r  .  r\  zIPolys.gf_gcdc                 C  r  r)  )r	  r  r  r&  r  r  rY  r*  r*  r-  r  0  r\  zIPolys.gf_lcmc                 C  r  r)  )r	  r  r  r&  r  r  rY  r*  r*  r-  r  2  r\  zIPolys.gf_gcdexc                 C  r  r)  )r	  r	  r  r&  r  r  rT  r*  r*  r-  r	  5  rW  zIPolys.gf_monicc                 C  r  r)  )r	  r
  r  r&  r  r  rT  r*  r*  r-  r
  7  rW  zIPolys.gf_diffc                 C     t | ||| jj| jjS r)  )r  r  r&  r  r  r}  r*  r*  r-  r  :  rI  zIPolys.gf_evalc                 C  r  r)  )r  r  r&  r  r  )r+  rF  r  r*  r*  r-  r  <  rI  zIPolys.gf_multi_evalc                 C  r  r)  )r	  r  r  r&  r  r  rY  r*  r*  r-  r  ?  r\  zIPolys.gf_composec                 C  r  r)  )r	  r  r  r&  r  r  )r+  rZ  r_  rF  r*  r*  r-  r  A  ra  zIPolys.gf_compose_modc                 C  s\   |  |}|  |}|  |}|  |}t|||||| jj| jj\}}| || |fS r)  )r  r  r&  r  r  r	  )r+  r~  brG  rR  rF  UVr*  r*  r-  r  D  s   



 zIPolys.gf_trace_mapc                 C  r  r)  )r	  r  r&  r  r  r+  rR  r*  r*  r-  r  L  rC  zIPolys.gf_randomc                 C  r  r)  )r	  r  r&  r  r  r  r*  r*  r-  r  N  rC  zIPolys.gf_irreduciblec                 C     t | || jj| jjS r)  )r  r  r&  r  r  rT  r*  r*  r-  r  Q  rC  zIPolys.gf_irred_p_ben_orc                 C  r  r)  )r  r  r&  r  r  rT  r*  r*  r-  r  S  rC  zIPolys.gf_irred_p_rabinc                 C  r  r)  )r  r  r&  r  r  rT  r*  r*  r-  r  U  rC  zIPolys.gf_irreducible_pc                 C  r  r)  )r  r  r&  r  r  rT  r*  r*  r-  r  W  rC  zIPolys.gf_sqf_pc                 C  r  r)  )r	  r  r  r&  r  r  rT  r*  r*  r-  r  Z  rW  zIPolys.gf_sqf_partc                   s4   t  | jj jj\}}| fdd|D fS )Nc                   r  r*  r	  r  r1  r*  r-  r  ^  r  z&IPolys.gf_sqf_list.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  r-  gf_sqf_list\  r  zIPolys.gf_sqf_listc                 C  r  r)  )r  r  r&  r  r  rT  r*  r*  r-  r  `  rC  zIPolys.gf_Qmatrixc                   ,   t  | jj jj} fdd|D S )Nc                   r  r*  r  r  r1  r*  r-  r  d  r  z'IPolys.gf_berlekamp.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  r-  r  b  r  zIPolys.gf_berlekampc                   r   )Nc                   r  r*  r  r  r1  r*  r-  r  h  r  z,IPolys.gf_ddf_zassenhaus.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  r-  r  f  r  zIPolys.gf_ddf_zassenhausc                   ,   t  | jj jj} fdd|D S )Nc                   r  r*  r  r  r1  r*  r-  r  k  r  z,IPolys.gf_edf_zassenhaus.<locals>.<listcomp>)r  r  r&  r  r  r+  rF  rR  r  r*  r1  r-  r  i  r  zIPolys.gf_edf_zassenhausc                   r   )Nc                   r  r*  r  r  r1  r*  r-  r  o  r  z'IPolys.gf_ddf_shoup.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  r-  r  m  r  zIPolys.gf_ddf_shoupc                   r!  )Nc                   r  r*  r  r  r1  r*  r-  r  r  r  z'IPolys.gf_edf_shoup.<locals>.<listcomp>)r  r  r&  r  r  r"  r*  r1  r-  r  p  r  zIPolys.gf_edf_shoupc                   r   )Nc                   r  r*  r  r  r1  r*  r-  r  v  r  z(IPolys.gf_zassenhaus.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  r-  r  t  r  zIPolys.gf_zassenhausc                   r   )Nc                   r  r*  r  r  r1  r*  r-  r  y  r  z#IPolys.gf_shoup.<locals>.<listcomp>)r  r  r&  r  r  r  r*  r1  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  r1  r*  r-  r  }  r  z(IPolys.gf_factor_sqf.<locals>.<listcomp>)r  r  r&  r  r  )r+  rF  r#  r  r  r*  r1  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  r1  r*  r-  r    r  z$IPolys.gf_factor.<locals>.<listcomp>)r   r  r&  r  r  r  r*  r1  r-  r   ~  r  zIPolys.gf_factor)NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr)  (,  __name__
__module____qualname____annotations__r.  r0  r2  r5  r6  r8  r=  r>  rB  r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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   Zsympy.core.exprr   Zsympy.polys.domains.domainr   Zsympy.polys.orderingsr   r9  r   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/   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   Zsympy.polys.densebasicrI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   Z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   Z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   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 