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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 ddҐlm Z  e G ddԄ dԃZ!dS )z8Compatibility interface between dense and sparse polys.     )dup_add_term)dmp_add_term)dup_sub_term)dmp_sub_term)dup_mul_term)dmp_mul_term)dup_add_ground)dmp_add_ground)dup_sub_ground)dmp_sub_ground)dup_mul_ground)dmp_mul_ground)dup_quo_ground)dmp_quo_ground)dup_exquo_ground)dmp_exquo_ground)
dup_lshift)
dup_rshift)dup_abs)dmp_abs)dup_neg)dmp_neg)dup_add)dmp_add)dup_sub)dmp_sub)dup_add_mul)dmp_add_mul)dup_sub_mul)dmp_sub_mul)dup_mul)dmp_mul)dup_sqr)dmp_sqr)dup_pow)dmp_pow)dup_pdiv)dup_prem)dup_pquo)
dup_pexquo)dmp_pdiv)dmp_prem)dmp_pquo)
dmp_pexquo)
dup_rr_div)
dmp_rr_div)
dup_ff_div)
dmp_ff_div)dup_div)dup_rem)dup_quo)	dup_exquo)dmp_div)dmp_rem)dmp_quo)	dmp_exquo)dup_max_norm)dmp_max_norm)dup_l1_norm)dmp_l1_norm)dup_l2_norm_squared)dmp_l2_norm_squared)
dup_expand)
dmp_expand)dup_LC)dmp_LC)dup_TC)dmp_TC)dmp_ground_LC)dmp_ground_TC)
dup_degree)
dmp_degree)dmp_degree_in)dmp_to_dict)dup_integrate)dmp_integrate)dmp_integrate_in)dup_diff)dmp_diff)dmp_diff_in)dup_eval)dmp_eval)dmp_eval_in)dmp_eval_tail)dmp_diff_eval_in)	dup_trunc)	dmp_trunc)dmp_ground_trunc)	dup_monic)dmp_ground_monic)dup_content)dmp_ground_content)dup_primitive)dmp_ground_primitive)dup_extract)dmp_ground_extract)dup_real_imag)
dup_mirror)	dup_scale)	dup_shift)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dup_sqf_normdmp_sqf_normdup_gf_sqf_partdmp_gf_sqf_partdup_sqf_partdmp_sqf_partdup_gf_sqf_listdmp_gf_sqf_listdup_sqf_listdup_sqf_list_includedmp_sqf_listdmp_sqf_list_includedup_gff_listdmp_gff_list)8	gf_degreegf_LCgf_TCgf_stripgf_from_dict
gf_to_dictgf_from_int_polygf_to_int_polygf_neggf_add_groundgf_sub_groundgf_mul_groundgf_quo_groundgf_addgf_subgf_mulgf_sqr
gf_add_mul
gf_sub_mul	gf_expandgf_divgf_remgf_quogf_exquo	gf_lshift	gf_rshiftgf_pow
gf_pow_modgf_gcdgf_lcmgf_cofactorsgf_gcdexgf_monicgf_diffgf_evalgf_multi_eval
gf_composegf_compose_modgf_trace_map	gf_randomgf_irreduciblegf_irred_p_ben_orgf_irred_p_rabingf_irreducible_pgf_sqf_pgf_sqf_part
gf_Qmatrixgf_berlekampgf_ddf_zassenhausgf_edf_zassenhausgf_ddf_shoupgf_edf_shoupgf_zassenhausgf_shoupgf_factor_sqf	gf_factor)publicc                   @   s  e Zd ZdZdZdZdZdZdd ZdPddZ	dd Z
dd	 Zd
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 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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Zd?d@ ZdAdB ZdSdDdEZdTdFdGZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdUdXdYZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg ZdVdhdiZdjdk Zdldm Zdndo Zdpdq Zdrds Zdtdu Zdvdw Zdxdy Zdzd{ ZÐd|d} ZĐd~d ZŐdd ZƐdd Zǐdd ZȐdd Zɐdd Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZӐdd ZԐdWddZՐdXddZ֐dYddZאdZddZؐd[ddZِd\ddZڐdd Zېdd Zܐdd Zݐdd Zސd]ddZߐd^ddZd_ddZd`ddZdaddZdbddZdcddZddddZdeddÄZdfdĐdńZdgdƐdǄZdhdȐdɄZdidʐd˄Zdjd̐d̈́ZdkdΐdτZdАdф ZdҐdӄ ZdԐdՄ Zd֐dׄ Zdؐdل Zdڐdۄ Zdܐd݄ Zdސd߄ Zdd Zdd Zdd Zdd ZdlddZdd ZdmddZdd Zdd Zdd Zdd Z dd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Z	dd	 Z
d
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$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"dnd:d;Z#d<d= Z$d>d? Z%d@dA Z&dBdC Z'dDdE Z(dFdG Z)dHdI Z*dJdK Z+dodLdMZ,dNdO Z-dS (p  IPolysNc                 C   s   d S N )selfgenr  r  i/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/polys/compatibility.pydrop   s    zIPolys.dropc                 C   s   d S r  r  )r  symbolsdomainorderr  r  r  clone   s    zIPolys.clonec                 C   s   d S r  r  r  r  r  r  	to_ground   s    zIPolys.to_groundc                 C   s   d S r  r  r  elementr  r  r  
ground_new   s    zIPolys.ground_newc                 C   s   d S r  r  r&  r  r  r  
domain_new   s    zIPolys.domain_newc                 C   s   d S r  r  )r  dr  r  r  	from_dict   s    zIPolys.from_dictc                 C   s<   ddl m} t||r.|j| kr$|S tdn
| |S d S )Nr   )PolyElementzdomain conversions)Zsympy.polys.ringsr,  
isinstanceringNotImplementedErrorr(  )r  r'  r,  r  r  r  wrap   s    


zIPolys.wrapc                 C   s   |  | S r  )r0  to_denser&  r  r  r  r1  	  s    zIPolys.to_densec                 C   s   |  t|| jd | jS N   )r+  rK   ngensr!  r&  r  r  r  
from_dense  s    zIPolys.from_densec                 C   s   |  t| |||| jS r  )r5  r   r1  r!  r  fcir  r  r  r     s    zIPolys.dup_add_termc                 C   s4   |  t| || |d || jd | jS Nr   r3  )r5  r   r1  r0  r  r4  r!  r6  r  r  r  r     s    zIPolys.dmp_add_termc                 C   s   |  t| |||| jS r  )r5  r   r1  r!  r6  r  r  r  r     s    zIPolys.dup_sub_termc                 C   s4   |  t| || |d || jd | jS r:  )r5  r   r1  r0  r  r4  r!  r6  r  r  r  r     s    zIPolys.dmp_sub_termc                 C   s   |  t| |||| jS r  )r5  r   r1  r!  r6  r  r  r  r     s    zIPolys.dup_mul_termc                 C   s4   |  t| || |d || jd | jS r:  )r5  r   r1  r0  r  r4  r!  r6  r  r  r  r     s    zIPolys.dmp_mul_termc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r  r7  r8  r  r  r  r     s    zIPolys.dup_add_groundc                 C   s"   |  t| ||| jd | jS r2  )r5  r	   r1  r4  r!  r;  r  r  r  r	     s    zIPolys.dmp_add_groundc                 C   s   |  t| ||| jS r  )r5  r
   r1  r!  r;  r  r  r  r
      s    zIPolys.dup_sub_groundc                 C   s"   |  t| ||| jd | jS r2  )r5  r   r1  r4  r!  r;  r  r  r  r   "  s    zIPolys.dmp_sub_groundc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r;  r  r  r  r   $  s    zIPolys.dup_mul_groundc                 C   s"   |  t| ||| jd | jS r2  )r5  r   r1  r4  r!  r;  r  r  r  r   &  s    zIPolys.dmp_mul_groundc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r;  r  r  r  r   (  s    zIPolys.dup_quo_groundc                 C   s"   |  t| ||| jd | jS r2  )r5  r   r1  r4  r!  r;  r  r  r  r   *  s    zIPolys.dmp_quo_groundc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r;  r  r  r  r   ,  s    zIPolys.dup_exquo_groundc                 C   s"   |  t| ||| jd | jS r2  )r5  r   r1  r4  r!  r;  r  r  r  r   .  s    zIPolys.dmp_exquo_groundc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r  r7  nr  r  r  r   1  s    zIPolys.dup_lshiftc                 C   s   |  t| ||| jS r  )r5  r   r1  r!  r<  r  r  r  r   3  s    zIPolys.dup_rshiftc                 C   s   |  t| || jS r  )r5  r   r1  r!  r  r7  r  r  r  r   6  s    zIPolys.dup_absc                 C   s    |  t| || jd | jS r2  )r5  r   r1  r4  r!  r>  r  r  r  r   8  s    zIPolys.dmp_absc                 C   s   |  t| || jS r  )r5  r   r1  r!  r>  r  r  r  r   ;  s    zIPolys.dup_negc                 C   s    |  t| || jd | jS r2  )r5  r   r1  r4  r!  r>  r  r  r  r   =  s    zIPolys.dmp_negc                 C   s    |  t| || || jS r  )r5  r   r1  r!  r  r7  gr  r  r  r   @  s    zIPolys.dup_addc                 C   s(   |  t| || || jd | jS r2  )r5  r   r1  r4  r!  r?  r  r  r  r   B  s    zIPolys.dmp_addc                 C   s    |  t| || || jS r  )r5  r   r1  r!  r?  r  r  r  r   E  s    zIPolys.dup_subc                 C   s(   |  t| || || jd | jS r2  )r5  r   r1  r4  r!  r?  r  r  r  r   G  s    zIPolys.dmp_subc                 C   s(   |  t| || || || jS r  )r5  r   r1  r!  r  r7  r@  hr  r  r  r   J  s    zIPolys.dup_add_mulc                 C   s0   |  t| || || || jd | jS r2  )r5  r   r1  r4  r!  rA  r  r  r  r   L  s    zIPolys.dmp_add_mulc                 C   s(   |  t| || || || jS r  )r5  r   r1  r!  rA  r  r  r  r   N  s    zIPolys.dup_sub_mulc                 C   s0   |  t| || || || jd | jS r2  )r5  r   r1  r4  r!  rA  r  r  r  r   P  s    zIPolys.dmp_sub_mulc                 C   s    |  t| || || jS r  )r5  r    r1  r!  r?  r  r  r  r    S  s    zIPolys.dup_mulc                 C   s(   |  t| || || jd | jS r2  )r5  r!   r1  r4  r!  r?  r  r  r  r!   U  s    zIPolys.dmp_mulc                 C   s   |  t| || jS r  )r5  r"   r1  r!  r>  r  r  r  r"   X  s    zIPolys.dup_sqrc                 C   s    |  t| || jd | jS r2  )r5  r#   r1  r4  r!  r>  r  r  r  r#   Z  s    zIPolys.dmp_sqrc                 C   s   |  t| ||| jS r  )r5  r$   r1  r!  r<  r  r  r  r$   \  s    zIPolys.dup_powc                 C   s"   |  t| ||| jd | jS r2  )r5  r%   r1  r4  r!  r<  r  r  r  r%   ^  s    zIPolys.dmp_powc                 C   s2   t | || || j\}}| || |fS r  )r&   r1  r!  r5  r  r7  r@  qrr  r  r  r&   a  s    zIPolys.dup_pdivc                 C   s    |  t| || || jS r  )r5  r'   r1  r!  r?  r  r  r  r'   d  s    zIPolys.dup_premc                 C   s    |  t| || || jS r  )r5  r(   r1  r!  r?  r  r  r  r(   f  s    zIPolys.dup_pquoc                 C   s    |  t| || || jS r  )r5  r)   r1  r!  r?  r  r  r  r)   h  s    zIPolys.dup_pexquoc                 C   s:   t | || || jd | j\}}| || |fS r2  )r*   r1  r4  r!  r5  rC  r  r  r  r*   k  s    &zIPolys.dmp_pdivc                 C   s(   |  t| || || jd | jS r2  )r5  r+   r1  r4  r!  r?  r  r  r  r+   n  s    zIPolys.dmp_premc                 C   s(   |  t| || || jd | jS r2  )r5  r,   r1  r4  r!  r?  r  r  r  r,   p  s    zIPolys.dmp_pquoc                 C   s(   |  t| || || jd | jS r2  )r5  r-   r1  r4  r!  r?  r  r  r  r-   r  s    zIPolys.dmp_pexquoc                 C   s2   t | || || j\}}| || |fS r  )r.   r1  r!  r5  rC  r  r  r  r.   u  s    zIPolys.dup_rr_divc                 C   s:   t | || || jd | j\}}| || |fS r2  )r/   r1  r4  r!  r5  rC  r  r  r  r/   x  s    &zIPolys.dmp_rr_divc                 C   s2   t | || || j\}}| || |fS r  )r0   r1  r!  r5  rC  r  r  r  r0   {  s    zIPolys.dup_ff_divc                 C   s:   t | || || jd | j\}}| || |fS r2  )r1   r1  r4  r!  r5  rC  r  r  r  r1   ~  s    &zIPolys.dmp_ff_divc                 C   s2   t | || || j\}}| || |fS r  )r2   r1  r!  r5  rC  r  r  r  r2     s    zIPolys.dup_divc                 C   s    |  t| || || jS r  )r5  r3   r1  r!  r?  r  r  r  r3     s    zIPolys.dup_remc                 C   s    |  t| || || jS r  )r5  r4   r1  r!  r?  r  r  r  r4     s    zIPolys.dup_quoc                 C   s    |  t| || || jS r  )r5  r5   r1  r!  r?  r  r  r  r5     s    zIPolys.dup_exquoc                 C   s:   t | || || jd | j\}}| || |fS r2  )r6   r1  r4  r!  r5  rC  r  r  r  r6     s    &zIPolys.dmp_divc                 C   s(   |  t| || || jd | jS r2  )r5  r7   r1  r4  r!  r?  r  r  r  r7     s    zIPolys.dmp_remc                 C   s(   |  t| || || jd | jS r2  )r5  r8   r1  r4  r!  r?  r  r  r  r8     s    zIPolys.dmp_quoc                 C   s(   |  t| || || jd | jS r2  )r5  r9   r1  r4  r!  r?  r  r  r  r9     s    zIPolys.dmp_exquoc                 C   s   t | || jS r  )r:   r1  r!  r>  r  r  r  r:     s    zIPolys.dup_max_normc                 C   s   t | || jd | jS r2  )r;   r1  r4  r!  r>  r  r  r  r;     s    zIPolys.dmp_max_normc                 C   s   t | || jS r  )r<   r1  r!  r>  r  r  r  r<     s    zIPolys.dup_l1_normc                 C   s   t | || jd | jS r2  )r=   r1  r4  r!  r>  r  r  r  r=     s    zIPolys.dmp_l1_normc                 C   s   t | || jS r  )r>   r1  r!  r>  r  r  r  r>     s    zIPolys.dup_l2_norm_squaredc                 C   s   t | || jd | jS r2  )r?   r1  r4  r!  r>  r  r  r  r?     s    zIPolys.dmp_l2_norm_squaredc                 C   s   |  ttt| j|| jS r  )r5  r@   listmapr1  r!  r  polysr  r  r  r@     s    zIPolys.dup_expandc                 C   s&   |  ttt| j|| jd | jS r2  )r5  rA   rF  rG  r1  r4  r!  rH  r  r  r  rA     s    zIPolys.dmp_expandc                 C   s   t | || jS r  )rB   r1  r!  r>  r  r  r  rB     s    zIPolys.dup_LCc                 C   s6   t | || j}t|tr.| dd  |S |S d S r2  )rC   r1  r!  r-  rF  r5  )r  r7  LCr  r  r  rC     s    
zIPolys.dmp_LCc                 C   s   t | || jS r  )rD   r1  r!  r>  r  r  r  rD     s    zIPolys.dup_TCc                 C   s6   t | || j}t|tr.| dd  |S |S d S r2  )rE   r1  r!  r-  rF  r5  )r  r7  ZTCr  r  r  rE     s    
zIPolys.dmp_TCc                 C   s   t | || jd | jS r2  )rF   r1  r4  r!  r>  r  r  r  rF     s    zIPolys.dmp_ground_LCc                 C   s   t | || jd | jS r2  )rG   r1  r4  r!  r>  r  r  r  rG     s    zIPolys.dmp_ground_TCc                 C   s   t | |S r  )rH   r1  r>  r  r  r  rH     s    zIPolys.dup_degreec                 C   s   t | || jd S r2  )rI   r1  r4  r>  r  r  r  rI     s    zIPolys.dmp_degreec                 C   s   t | ||| jd S r2  )rJ   r1  r4  )r  r7  jr  r  r  rJ     s    zIPolys.dmp_degree_inc                 C   s   |  t| ||| jS r  )r5  rL   r1  r!  r  r7  mr  r  r  rL     s    zIPolys.dup_integratec                 C   s"   |  t| ||| jd | jS r2  )r5  rM   r1  r4  r!  rL  r  r  r  rM     s    zIPolys.dmp_integratec                 C   s   |  t| ||| jS r  )r5  rO   r1  r!  rL  r  r  r  rO     s    zIPolys.dup_diffc                 C   s"   |  t| ||| jd | jS r2  )r5  rP   r1  r4  r!  rL  r  r  r  rP     s    zIPolys.dmp_diffc                 C   s$   |  t| |||| jd | jS r2  )r5  rQ   r1  r4  r!  r  r7  rM  rK  r  r  r  rQ     s    zIPolys.dmp_diff_inc                 C   s$   |  t| |||| jd | jS r2  )r5  rN   r1  r4  r!  rN  r  r  r  rN     s    zIPolys.dmp_integrate_inc                 C   s   t | ||| jS r  )rR   r1  r!  r  r7  ar  r  r  rR     s    zIPolys.dup_evalc                 C   s.   t | ||| jd | j}| dd  |S r2  )rS   r1  r4  r!  r5  )r  r7  rP  resultr  r  r  rS     s    zIPolys.dmp_evalc                 C   s.   t | |||| jd | j}| ||S r2  )rT   r1  r4  r!  r  r5  )r  r7  rP  rK  rQ  r  r  r  rT     s    zIPolys.dmp_eval_inc                 C   s0   t | ||||| jd | j}| ||S r2  )rV   r1  r4  r!  r  r5  )r  r7  rM  rP  rK  rQ  r  r  r  rV     s     zIPolys.dmp_diff_eval_inc                 C   sF   t | ||| jd | j}t|tr>| d t|  |S |S d S r2  )rU   r1  r4  r!  r-  rF  lenr5  )r  r7  ArQ  r  r  r  rU     s    
zIPolys.dmp_eval_tailc                 C   s   |  t| ||| jS r  )r5  rW   r1  r!  r  r7  pr  r  r  rW     s    zIPolys.dup_truncc                 C   s0   |  t| || dd  || jd | jS r2  )r5  rX   r1  r4  r!  r?  r  r  r  rX     s    zIPolys.dmp_truncc                 C   s"   |  t| ||| jd | jS r2  )r5  rY   r1  r4  r!  rT  r  r  r  rY     s    zIPolys.dmp_ground_truncc                 C   s   |  t| || jS r  )r5  rZ   r1  r!  r>  r  r  r  rZ     s    zIPolys.dup_monicc                 C   s    |  t| || jd | jS r2  )r5  r[   r1  r4  r!  r>  r  r  r  r[     s    zIPolys.dmp_ground_monicc                 C   s6   t | || || j\}}}|| || |fS r  )r`   r1  r!  r5  r  r7  r@  r8  FGr  r  r  r`     s     zIPolys.dup_extractc                 C   s>   t | || || jd | j\}}}|| || |fS r2  )ra   r1  r4  r!  r5  rV  r  r  r  ra     s    (zIPolys.dmp_ground_extractc                 C   s4   t | |d | j\}}| || |fS r2  )rb   r0  r  r1  r!  r5  r  r7  rU  rD  r  r  r  rb     s     zIPolys.dup_real_imagc                 C   s   |  t| || jS r  )r5  rc   r1  r!  r>  r  r  r  rc      s    zIPolys.dup_mirrorc                 C   s   |  t| ||| jS r  )r5  rd   r1  r!  rO  r  r  r  rd     s    zIPolys.dup_scalec                 C   s   |  t| ||| jS r  )r5  re   r1  r!  rO  r  r  r  re     s    zIPolys.dup_shiftc                 C   s(   |  t| || || || jS r  )r5  rf   r1  r!  rY  r  r  r  rf     s    zIPolys.dup_transformc                 C   s    |  t| || || jS r  )r5  rg   r1  r!  r?  r  r  r  rg   	  s    zIPolys.dup_composec                 C   s(   |  t| || || jd | jS r2  )r5  rh   r1  r4  r!  r?  r  r  r  rh     s    zIPolys.dmp_composec                 C   s"   t | || j}tt| j|S r  )ri   r1  r!  rF  rG  r5  )r  r7  
componentsr  r  r  ri     s    zIPolys.dup_decomposec                 C   s(   t | || jd | j}|  |S r2  )rj   r1  r4  r!  r%  r5  r  r7  rQ  r  r  r  rj     s    zIPolys.dmp_liftc                 C   s   t | || jS r  )rk   r1  r!  r>  r  r  r  rk     s    zIPolys.dup_sign_variationsFc                 C   sD   t | || j|d\}}|r2| j| j d}n| }|||fS )Nconvertr!  )rl   r1  r!  r#  get_ringr5  r  r7  r]  r8  rW  r.  r  r  r  rl     s
    zIPolys.dup_clear_denomsc                 C   sL   t | || jd | j|d\}}|r:| j| j d}n| }|||fS )Nr3  r\  r^  )rm   r1  r4  r!  r#  r_  r5  r`  r  r  r  rm      s
    "zIPolys.dmp_clear_denomsc                 C   s   |  t| ||| jS r  )r5  rn   r1  r!  r<  r  r  r  rn   (  s    zIPolys.dup_revertc                 C   s2   t | || || j\}}| || |fS r  )ro   r1  r!  r5  r  r7  r@  srB  r  r  r  ro   +  s    zIPolys.dup_half_gcdexc                 C   s:   t | || || jd | j\}}| || |fS r2  )rp   r1  r4  r!  r5  ra  r  r  r  rp   .  s    &zIPolys.dmp_half_gcdexc                 C   s<   t | || || j\}}}| || || |fS r  )rq   r1  r!  r5  r  r7  r@  rb  trB  r  r  r  rq   1  s     zIPolys.dup_gcdexc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )rr   r1  r4  r!  r5  rc  r  r  r  rr   4  s    (zIPolys.dmp_gcdexc                 C   s    |  t| || || jS r  )r5  rs   r1  r!  r?  r  r  r  rs   8  s    zIPolys.dup_invertc                 C   s(   |  t| || || jd | jS r2  )r5  rt   r1  r4  r!  r?  r  r  r  rt   :  s    zIPolys.dmp_invertc                 C   s*   t | || || j}tt| j|S r  )ru   r1  r!  rF  rG  r5  r  r7  r@  prsr  r  r  ru   =  s    zIPolys.dup_euclidean_prsc                 C   s2   t | || || jd | j}tt| j|S r2  )rv   r1  r4  r!  rF  rG  r5  re  r  r  r  rv   @  s    "zIPolys.dmp_euclidean_prsc                 C   s*   t | || || j}tt| j|S r  )rw   r1  r!  rF  rG  r5  re  r  r  r  rw   C  s    zIPolys.dup_primitive_prsc                 C   s2   t | || || jd | j}tt| j|S r2  )rx   r1  r4  r!  rF  rG  r5  re  r  r  r  rx   F  s    "zIPolys.dmp_primitive_prsc                 C   s2   t | || || j\}}tt| j||fS r  )ry   r1  r!  rF  rG  r5  r  r7  r@  rf  sresr  r  r  ry   J  s    zIPolys.dup_inner_subresultantsc                 C   s:   t | || || jd | j\}}tt| j||fS r2  )r}   r1  r4  r!  rF  rG  r5  rg  r  r  r  r}   M  s    &zIPolys.dmp_inner_subresultantsc                 C   s*   t | || || j}tt| j|S r  )rz   r1  r!  rF  rG  r5  re  r  r  r  rz   Q  s    zIPolys.dup_subresultantsc                 C   s2   t | || || jd | j}tt| j|S r2  )r~   r1  r4  r!  rF  rG  r5  re  r  r  r  r~   T  s    "zIPolys.dmp_subresultantsc                 C   s2   t | || || j\}}|tt| j|fS r  )r{   r1  r!  rF  rG  r5  r  r7  r@  resrf  r  r  r  r{   X  s    zIPolys.dup_prs_resultantc                 C   sH   t | || || jd | j\}}| dd  |tt| j|fS r2  )r   r1  r4  r!  r5  rF  rG  ri  r  r  r  r   [  s    &zIPolys.dmp_prs_resultantc                 C   s<   t | || || || jd | j}| dd  |S r2  )r   r1  r)  r4  r!  r5  )r  r7  r@  rU  rj  r  r  r  r   _  s    *zIPolys.dmp_zz_modular_resultantc                 C   s4   t | || || jd | j}| dd  |S r2  )r   r1  r4  r!  r5  r  r7  r@  rj  r  r  r  r   b  s    "zIPolys.dmp_zz_collins_resultantc                 C   s4   t | || || jd | j}| dd  |S r2  )r   r1  r4  r!  r5  rk  r  r  r  r   e  s    "zIPolys.dmp_qq_collins_resultantc                 C   s   t | || || jS r  )r|   r1  r!  r?  r  r  r  r|   i  s    zIPolys.dup_resultantc                 C   sF   t | || || jd | j}t|tr>| dd  |S |S d S r2  )r   r1  r4  r!  r-  rF  r5  rk  r  r  r  r   k  s    "
zIPolys.dmp_resultantc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r   r  s    zIPolys.dup_discriminantc                 C   s>   t | || jd | j}t|tr6| dd  |S |S d S r2  )r   r1  r4  r!  r-  rF  r5  )r  r7  Zdiscr  r  r  r   t  s    
zIPolys.dmp_discriminantc                 C   s<   t | || || j\}}}| || || |fS r  )r   r1  r!  r5  r  r7  r@  HrW  rX  r  r  r  r   {  s     zIPolys.dup_rr_prs_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r1  r!  r5  rl  r  r  r  r   ~  s     zIPolys.dup_ff_prs_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )r   r1  r4  r!  r5  rl  r  r  r  r     s    (zIPolys.dmp_rr_prs_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )r   r1  r4  r!  r5  rl  r  r  r  r     s    (zIPolys.dmp_ff_prs_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r1  r!  r5  rl  r  r  r  r     s     zIPolys.dup_zz_heu_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )r   r1  r4  r!  r5  rl  r  r  r  r     s    (zIPolys.dmp_zz_heu_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r1  r!  r5  rl  r  r  r  r     s     zIPolys.dup_qq_heu_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )r   r1  r4  r!  r5  rl  r  r  r  r     s    (zIPolys.dmp_qq_heu_gcdc                 C   s<   t | || || j\}}}| || || |fS r  )r   r1  r!  r5  rl  r  r  r  r     s     zIPolys.dup_inner_gcdc                 C   sD   t | || || jd | j\}}}| || || |fS r2  )r   r1  r4  r!  r5  rl  r  r  r  r     s    (zIPolys.dmp_inner_gcdc                 C   s$   t | || || j}| |S r  )r   r1  r!  r5  r  r7  r@  rm  r  r  r  r     s    zIPolys.dup_gcdc                 C   s,   t | || || jd | j}| |S r2  )r   r1  r4  r!  r5  rn  r  r  r  r     s    "zIPolys.dmp_gcdc                 C   s$   t | || || j}| |S r  )r   r1  r!  r5  rn  r  r  r  r     s    zIPolys.dup_rr_lcmc                 C   s$   t | || || j}| |S r  )r   r1  r!  r5  rn  r  r  r  r     s    zIPolys.dup_ff_lcmc                 C   s$   t | || || j}| |S r  )r   r1  r!  r5  rn  r  r  r  r     s    zIPolys.dup_lcmc                 C   s,   t | || || jd | j}| |S r2  )r   r1  r4  r!  r5  rn  r  r  r  r     s    "zIPolys.dmp_rr_lcmc                 C   s,   t | || || jd | j}| |S r2  )r   r1  r4  r!  r5  rn  r  r  r  r     s    "zIPolys.dmp_ff_lcmc                 C   s,   t | || || jd | j}| |S r2  )r   r1  r4  r!  r5  rn  r  r  r  r     s    "zIPolys.dmp_lcmc                 C   s   t | || j}|S r  )r\   r1  r!  r  r7  contr  r  r  r\     s    zIPolys.dup_contentc                 C   s$   t | || j\}}|| |fS r  )r^   r1  r!  r5  r  r7  rp  Zprimr  r  r  r^     s    zIPolys.dup_primitivec                 C   s>   t | || jd | j}t|tr6| dd  |S |S d S r2  )r   r1  r4  r!  r-  rF  r5  ro  r  r  r  r     s    
zIPolys.dmp_contentc                 C   sV   t | || jd | j\}}t|trD| dd  || |fS || |fS d S r2  )r   r1  r4  r!  r-  rF  r5  rq  r  r  r  r     s    
zIPolys.dmp_primitivec                 C   s   t | || jd | j}|S r2  )r]   r1  r4  r!  ro  r  r  r  r]     s    zIPolys.dmp_ground_contentc                 C   s,   t | || jd | j\}}|| |fS r2  )r_   r1  r4  r!  r5  rq  r  r  r  r_     s    zIPolys.dmp_ground_primitiveTc           	      C   sf   t | || || j|d}|sF|\}}}}||| || |fS |\}}| || |fS d S )Ninclude)r   r1  r!  r5  	r  r7  r@  rs  rQ  cfZcgrW  rX  r  r  r  r     s    zIPolys.dup_cancelc           	      C   sn   t | || || jd | j|d}|sN|\}}}}||| || |fS |\}}| || |fS d S )Nr3  rr  )r   r1  r4  r!  r5  rt  r  r  r  r     s    &zIPolys.dmp_cancelc                    s2   t  |tt j| j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r5  .0r@  kr$  r  r  
<listcomp>      z-IPolys.dup_trial_division.<locals>.<listcomp>)r   r1  rF  rG  r!  r  r7  factorsr  r$  r  r     s     zIPolys.dup_trial_divisionc                    s:   t  |tt j| jd  j} fdd|D S )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z-IPolys.dmp_trial_division.<locals>.<listcomp>)r   r1  rF  rG  r4  r!  r|  r  r$  r  r     s    (zIPolys.dmp_trial_divisionc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r     s    zIPolys.dup_zz_mignotte_boundc                 C   s   t | || jd | jS r2  )r   r1  r4  r!  r>  r  r  r  r     s    zIPolys.dmp_zz_mignotte_boundc                 C   s\   | j }t|||||||||||| j\}}	}
}| || |	| |
| |fS r  )r1  r   r!  r5  )r  rM  r7  r@  rB  rb  rd  DrX  rm  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  )r1  r   rF  rG  r!  r5  )r  rU  r7  Zf_listlr~  rI  r  r  r  r     s     zIPolys.dup_zz_hensel_liftc                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z,IPolys.dup_zz_zassenhaus.<locals>.<listcomp>)r   r1  r!  r|  r  r$  r  r     s    zIPolys.dup_zz_zassenhausc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r     s    zIPolys.dup_zz_irreducible_pc                 C   s   t | || j|dS )N)irreducible)r   r1  r!  )r  r7  r  r  r  r  r     s    zIPolys.dup_cyclotomic_pc                 C   s   t || j}| |S r  )r   r!  r5  )r  r=  rW  r  r  r  r     s    zIPolys.dup_zz_cyclotomic_polyc                 C   s2   t | || j}|d u r|S tt| j|S d S r  )r   r1  r!  rF  rG  r5  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 )Nr3  c                    s   g | ]\}}  ||fqS r  )r1  )rx  rd  ry  mvr  r  rz    r{  z2IPolys.dmp_zz_wang_lead_coeffs.<locals>.<listcomp>)rF  rG  r1  r   r4  r!  r5  )
r  r7  r  r  r  rm  rS  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   rF  rG  r1  r!  r5  )r  rW  rM  rU  rQ  r  r  r  r     s    zIPolys.dup_zz_diophantinec                 C   s>   t tt| j|| ||||| jd | j}tt| j|S r2  )r   rF  rG  r1  r4  r!  r5  )r  rW  r8  rS  r*  rU  rQ  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 r2  )rF  rG  r1  r   r4  r!  r5  )	r  r7  rm  rJ  rS  rU  r  r  rQ  r  r  r  r   !  s    "z!IPolys.dmp_zz_wang_hensel_liftingc                    s2   t  | jd  j||d} fdd|D S )Nr3  )modseedc                    s   g | ]}  |qS r  rv  rx  r@  r$  r  r  rz  +  r{  z&IPolys.dmp_zz_wang.<locals>.<listcomp>)r   r1  r4  r!  )r  r7  r  r  r}  r  r$  r  r   )  s     zIPolys.dmp_zz_wangc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]}  |qS r  rv  r  r$  r  r  rz  /  r{  z,IPolys.dup_zz_factor_sqf.<locals>.<listcomp>)r   r1  r!  r  r7  coeffr}  r  r$  r  r   -  s    zIPolys.dup_zz_factor_sqfc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  3  r{  z(IPolys.dup_zz_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   1  s    zIPolys.dup_zz_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  6  r{  z(IPolys.dmp_zz_factor.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   4  s    zIPolys.dmp_zz_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  :  r{  z*IPolys.dup_qq_i_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   8  s    zIPolys.dup_qq_i_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  =  r{  z*IPolys.dmp_qq_i_factor.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   ;  s    zIPolys.dmp_qq_i_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  A  r{  z*IPolys.dup_zz_i_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   ?  s    zIPolys.dup_zz_i_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  D  r{  z*IPolys.dmp_zz_i_factor.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   B  s    zIPolys.dmp_zz_i_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  H  r{  z)IPolys.dup_ext_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   F  s    zIPolys.dup_ext_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  K  r{  z)IPolys.dmp_ext_factor.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   I  s    zIPolys.dmp_ext_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  O  r{  z(IPolys.dup_gf_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   M  s    zIPolys.dup_gf_factorc                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  R  r{  z(IPolys.dmp_gf_factor.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   P  s    zIPolys.dmp_gf_factorc                    s,   t  | j\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  V  r{  z*IPolys.dup_factor_list.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   T  s    zIPolys.dup_factor_listc                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  Y  r{  z2IPolys.dup_factor_list_include.<locals>.<listcomp>)r   r1  r!  r|  r  r$  r  r   W  s    zIPolys.dup_factor_list_includec                    s4   t  | jd  j\}}| fdd|D fS )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  ]  r{  z*IPolys.dmp_factor_list.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r   [  s    zIPolys.dmp_factor_listc                    s,   t  | jd  j} fdd|D S )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz  `  r{  z2IPolys.dmp_factor_list_include.<locals>.<listcomp>)r   r1  r4  r!  r|  r  r$  r  r   ^  s    zIPolys.dmp_factor_list_includec                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r   b  s    zIPolys.dup_irreducible_pc                 C   s   t | || jd | jS r2  )r   r1  r4  r!  r>  r  r  r  r   d  s    zIPolys.dmp_irreducible_pc                 C   s"   t | || j}tt| j|S r  )r   r1  r!  rF  rG  r5  )r  r7  seqr  r  r  r   g  s    zIPolys.dup_sturmc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r   k  s    zIPolys.dup_sqf_pc                 C   s   t | || jd | jS r2  )r   r1  r4  r!  r>  r  r  r  r   m  s    zIPolys.dmp_sqf_pc                 C   s2   t | || j\}}}|| ||  |fS r  )r   r1  r!  r5  r%  r  r7  rb  rW  Rr  r  r  r   p  s    zIPolys.dup_sqf_normc                 C   s:   t | || jd | j\}}}|| ||  |fS r2  )r   r1  r4  r!  r5  r%  r  r  r  r  r   s  s     zIPolys.dmp_sqf_normc                 C   s   |  t| || jS r  )r5  r   r1  r!  r>  r  r  r  r   w  s    zIPolys.dup_gf_sqf_partc                 C   s   |  t| || jS r  )r5  r   r1  r!  r>  r  r  r  r   y  s    zIPolys.dmp_gf_sqf_partc                 C   s   |  t| || jS r  )r5  r   r1  r!  r>  r  r  r  r   {  s    zIPolys.dup_sqf_partc                 C   s    |  t| || jd | jS r2  )r5  r   r1  r4  r!  r>  r  r  r  r   }  s    zIPolys.dmp_sqf_partc                    s0   t  | j|d\}}| fdd|D fS )Nallc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z*IPolys.dup_gf_sqf_list.<locals>.<listcomp>)r   r1  r!  r  r7  r  r  r}  r  r$  r  r     s    zIPolys.dup_gf_sqf_listc                    s8   t  | jd  j|d\}}| fdd|D fS )Nr3  r  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z*IPolys.dmp_gf_sqf_list.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r     s    "zIPolys.dmp_gf_sqf_listc                    s0   t  | j|d\}}| fdd|D fS )Nr  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z'IPolys.dup_sqf_list.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r     s    zIPolys.dup_sqf_listc                    s(   t  | j|d} fdd|D S )Nr  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z/IPolys.dup_sqf_list_include.<locals>.<listcomp>)r   r1  r!  r  r7  r  r}  r  r$  r  r     s    zIPolys.dup_sqf_list_includec                    s8   t  | jd  j|d\}}| fdd|D fS )Nr3  r  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z'IPolys.dmp_sqf_list.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r     s    "zIPolys.dmp_sqf_listc                    s0   t  | jd  j|d} fdd|D S )Nr3  r  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z/IPolys.dmp_sqf_list_include.<locals>.<listcomp>)r   r1  r4  r!  r  r  r$  r  r     s    zIPolys.dmp_sqf_list_includec                    s$   t  | j} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z'IPolys.dup_gff_list.<locals>.<listcomp>)r   r1  r!  r|  r  r$  r  r     s    zIPolys.dup_gff_listc                    s,   t  | jd  j} fdd|D S )Nr3  c                    s   g | ]\}}  ||fqS r  rv  rw  r$  r  r  rz    r{  z'IPolys.dmp_gff_list.<locals>.<listcomp>)r   r1  r4  r!  r|  r  r$  r  r     s    zIPolys.dmp_gff_listc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r     s    zIPolys.dup_root_upper_boundc                 C   s   t | || jS r  )r   r1  r!  r>  r  r  r  r     s    zIPolys.dup_root_lower_boundc                 C   s   t | ||| j|dS )N)fast)r   r1  r!  )r  r7  Mr  r  r  r  r     s    z IPolys.dup_step_refine_real_rootc              
   C   s    t | ||| j|||||dS )N)epsstepsdisjointr  mobius)r   r1  r!  )r  r7  r  r  r  r  r  r  r  r  r  r     s    z!IPolys.dup_inner_refine_real_rootc              
   C   s    t | |||| j||||dS N)r  r  r  r  )r   r1  r!  r  r7  rb  rd  r  r  r  r  r  r  r  r     s    z!IPolys.dup_outer_refine_real_rootc              
   C   s    t | |||| j||||dS r  )r   r1  r!  r  r  r  r  r     s    zIPolys.dup_refine_real_rootc                 C   s   t | || j||dS )N)r  r  )r   r1  r!  )r  r7  r  r  r  r  r  r     s    z#IPolys.dup_inner_isolate_real_rootsc              	   C   s   t | || j|||||dS )N)r  infsupr  r  )r   r1  r!  )r  r7  r  r  r  r  r  r  r  r  r     s    z'IPolys.dup_inner_isolate_positive_rootsc              	   C   s   t | || j|||||dS )N)r  r  r  r  r  )r   r1  r!  )r  r7  r  r  r  r  r  r  r  r  r     s    z'IPolys.dup_inner_isolate_negative_rootsc              	   C   s   t | || j|||||dS N)r  r  r  r  blackbox)r   r1  r!  r  r7  r  r  r  r  r  r  r  r  r     s    z!IPolys.dup_isolate_real_roots_sqfc              	   C   s   t | || j|||||dS )N)r  r  r  basisr  )r   r1  r!  )r  r7  r  r  r  r  r  r  r  r  r     s    zIPolys.dup_isolate_real_rootsc              
   C   s&   t tt| j|| j||||||dS )N)r  r  r  strictr  r  )r   rF  rG  r1  r!  )r  rI  r  r  r  r  r  r  r  r  r  r     s    z"IPolys.dup_isolate_real_roots_listc                 C   s   t | || j||dS )N)r  r  )r   r1  r!  )r  r7  r  r  r  r  r  r     s    zIPolys.dup_count_real_rootsc                 C   s   t | || j|||dS )N)r  r  exclude)r   r1  r!  )r  r7  r  r  r  r  r  r  r     s    zIPolys.dup_count_complex_rootsc                 C   s   t | || j||||dS )N)r  r  r  r  )r   r1  r!  )r  r7  r  r  r  r  r  r  r  r     s    z$IPolys.dup_isolate_complex_roots_sqfc              	   C   s   t | || j|||||dS r  )r   r1  r!  r  r  r  r  r     s    z IPolys.dup_isolate_all_roots_sqfc                 C   s   t | || j||||dS )N)r  r  r  r  )r   r1  r!  )r  r7  r  r  r  r  r  r  r  r     s    zIPolys.dup_isolate_all_rootsc                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_1r3  )sympy.polys.specialpolysr  tuplerG  r5  r4  r!  )r  r  r  r  r  fateman_poly_F_1  s    zIPolys.fateman_poly_F_1c                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_2r3  )r  r  r  rG  r5  r4  r!  )r  r  r  r  r  fateman_poly_F_2  s    zIPolys.fateman_poly_F_2c                 C   s*   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_3r3  )r  r  r  rG  r5  r4  r!  )r  r  r  r  r  fateman_poly_F_3  s    zIPolys.fateman_poly_F_3c                    s    t  fdd | D S )Nc                    s   g | ]} j j| j qS r  )r!  domr]  )rx  r8  r$  r  r  rz    r{  z&IPolys.to_gf_dense.<locals>.<listcomp>)r   r0  r1  r&  r  r$  r  to_gf_dense  s    zIPolys.to_gf_densec                 C   s   |  t|| jd | jjS r2  )r+  rK   r4  r!  r  r&  r  r  r  from_gf_dense  s    zIPolys.from_gf_densec                 C   s   t | |S r  )r   r  r>  r  r  r  r     s    zIPolys.gf_degreec                 C   s   t | || jjS r  )r   r  r!  r  r>  r  r  r  r     s    zIPolys.gf_LCc                 C   s   t | || jjS r  )r   r  r!  r  r>  r  r  r  r     s    zIPolys.gf_TCc                 C   s   |  t| |S r  )r  r   r  r>  r  r  r  r     s    zIPolys.gf_stripc                 C   s   |  t| || jjS r  )r  r   r  r!  r  r>  r  r  r  gf_trunc  s    zIPolys.gf_truncc                 C   s    |  t| || jj| jjS r  )r  r   r  r!  r  r  r>  r  r  r  	gf_normal  s    zIPolys.gf_normalc                 C   s   |  t|| jj| jjS r  )r  r   r!  r  r  r>  r  r  r  r     s    zIPolys.gf_from_dictc                 C   s   t | || jj|dS N)	symmetric)r   r  r!  r  r  r7  r  r  r  r  r     s    zIPolys.gf_to_dictc                 C   s   |  t|| jjS r  )r  r   r!  r  r>  r  r  r  r     s    zIPolys.gf_from_int_polyc                 C   s   t | || jj|dS r  )r   r  r!  r  r  r  r  r  r     s    zIPolys.gf_to_int_polyc                 C   s    |  t| || jj| jjS r  )r  r   r  r!  r  r  r>  r  r  r  r     s    zIPolys.gf_negc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  rO  r  r  r  r     s    zIPolys.gf_add_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  rO  r  r  r  r     s    zIPolys.gf_sub_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  rO  r  r  r  r     s    zIPolys.gf_mul_groundc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  rO  r  r  r  r     s    zIPolys.gf_quo_groundc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_addc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_subc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_mulc                 C   s    |  t| || jj| jjS r  )r  r   r  r!  r  r  r>  r  r  r  r     s    zIPolys.gf_sqrc                 C   s0   |  t| || || || jj| jjS r  )r  r   r  r!  r  r  rA  r  r  r  r     s    zIPolys.gf_add_mulc                 C   s0   |  t| || || || jj| jjS r  )r  r   r  r!  r  r  rA  r  r  r  r     s    zIPolys.gf_sub_mulc                 C   s&   |  ttt| j|| jj| jjS r  )r  r   rF  rG  r  r!  r  r  )r  rW  r  r  r  r     s    zIPolys.gf_expandc                 C   s:   t | || || jj| jj\}}| || |fS r  )r   r  r!  r  r  r  rC  r  r  r  r     s    &zIPolys.gf_divc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_remc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r   
  s    zIPolys.gf_quoc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_exquoc                 C   s   |  t| ||| jjS r  )r  r   r  r!  r  r<  r  r  r  r     s    zIPolys.gf_lshiftc                 C   s   |  t| ||| jjS r  )r  r   r  r!  r  r<  r  r  r  r     s    zIPolys.gf_rshiftc                 C   s"   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  r<  r  r  r  r     s    zIPolys.gf_powc                 C   s*   |  t| ||| || jj| jjS r  )r  r   r  r!  r  r  )r  r7  r=  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  r7  r@  rB  Zcffcfgr  r  r  r     s    (zIPolys.gf_cofactorsc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_gcdc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r     s    zIPolys.gf_lcmc                 C   s(   |  t| || || jj| jjS r  )r  r   r  r!  r  r  r?  r  r  r  r      s    zIPolys.gf_gcdexc                 C   s    |  t| || jj| jjS r  )r  r   r  r!  r  r  r>  r  r  r  r   #  s    zIPolys.gf_monicc                 C   s    |  t| || jj| jjS r  )r  r  r  r!  r  r  r>  r  r  r  r  %  s    zIPolys.gf_diffc                 C   s   t | ||| jj| jjS r  )r  r  r!  r  r  rO  r  r  r  r  (  s    zIPolys.gf_evalc                 C   s   t | ||| jj| jjS r  )r  r  r!  r  r  )r  r7  rS  r  r  r  r  *  s    zIPolys.gf_multi_evalc                 C   s(   |  t| || || jj| jjS r  )r  r  r  r!  r  r  r?  r  r  r  r  -  s    zIPolys.gf_composec                 C   s0   |  t| || || || jj| jjS r  )r  r  r  r!  r  r  )r  r@  rB  r7  r  r  r  r  /  s    zIPolys.gf_compose_modc                 C   s\   |  |}|  |}|  |}|  |}t|||||| jj| jj\}}| || |fS r  )r  r  r!  r  r  r  )r  rP  br8  r=  r7  UVr  r  r  r  2  s    



 zIPolys.gf_trace_mapc                 C   s   |  t|| jj| jjS r  )r  r  r!  r  r  r  r=  r  r  r  r  :  s    zIPolys.gf_randomc                 C   s   |  t|| jj| jjS r  )r  r  r!  r  r  r  r  r  r  r  <  s    zIPolys.gf_irreduciblec                 C   s   t | || jj| jjS r  )r	  r  r!  r  r  r>  r  r  r  r	  ?  s    zIPolys.gf_irred_p_ben_orc                 C   s   t | || jj| jjS r  )r
  r  r!  r  r  r>  r  r  r  r
  A  s    zIPolys.gf_irred_p_rabinc                 C   s   t | || jj| jjS r  )r  r  r!  r  r  r>  r  r  r  r  C  s    zIPolys.gf_irreducible_pc                 C   s   t | || jj| jjS r  )r  r  r!  r  r  r>  r  r  r  r  E  s    zIPolys.gf_sqf_pc                 C   s    |  t| || jj| jjS r  )r  r  r  r!  r  r  r>  r  r  r  r  H  s    zIPolys.gf_sqf_partc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  r  rw  r$  r  r  rz  L  r{  z&IPolys.gf_sqf_list.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  gf_sqf_listJ  s    zIPolys.gf_sqf_listc                 C   s   t | || jj| jjS r  )r  r  r!  r  r  r>  r  r  r  r  N  s    zIPolys.gf_Qmatrixc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  R  r{  z'IPolys.gf_berlekamp.<locals>.<listcomp>)r  r  r!  r  r  r|  r  r$  r  r  P  s    zIPolys.gf_berlekampc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r  rw  r$  r  r  rz  V  r{  z,IPolys.gf_ddf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r|  r  r$  r  r  T  s    zIPolys.gf_ddf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  Y  r{  z,IPolys.gf_edf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r  r7  r=  r}  r  r$  r  r  W  s    zIPolys.gf_edf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]\}}  ||fqS r  r  rw  r$  r  r  rz  ]  r{  z'IPolys.gf_ddf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r|  r  r$  r  r  [  s    zIPolys.gf_ddf_shoupc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  `  r{  z'IPolys.gf_edf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  ^  s    zIPolys.gf_edf_shoupc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  d  r{  z(IPolys.gf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r|  r  r$  r  r  b  s    zIPolys.gf_zassenhausc                    s,   t  | jj jj} fdd|D S )Nc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  g  r{  z#IPolys.gf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r|  r  r$  r  r  e  s    zIPolys.gf_shoupc                    s8   t  | jj jj|d\}}| fdd|D fS )N)methodc                    s   g | ]}  |qS r  r  r  r$  r  r  rz  k  r{  z(IPolys.gf_factor_sqf.<locals>.<listcomp>)r  r  r!  r  r  )r  r7  r  r  r}  r  r$  r  r  i  s    "zIPolys.gf_factor_sqfc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    s   g | ]\}}  ||fqS r  r  rw  r$  r  r  rz  n  r{  z$IPolys.gf_factor.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  l  s    zIPolys.gf_factor)NNN)F)F)T)T)F)NN)F)F)F)F)F)F)F)NNNFF)NNNF)NNNF)NF)NNNFF)NNNFF)NNNFF)NNNFF)NNNFFF)NN)NNN)NNNF)NNNFF)NNNF)T)T)F)N(.  __name__
__module____qualname__r   r4  r!  r"  Zgensr  r#  r%  r(  r)  r+  r0  r1  r5  r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rL   rM   rO   rP   rQ   rN   rR   rS   rT   rV   rU   rW   rX   rY   rZ   r[   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   r}   rz   r~   r{   r   r   r   r   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r\   r^   r   r   r]   r_   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r   r   r   r   r  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r     sV  

		r  N("  __doc__Zsympy.polys.densearithr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   Zsympy.polys.densebasicrB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   Zsympy.polys.densetoolsrL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   Zsympy.polys.euclidtoolsro   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   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   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  H e