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lm
Z
 ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ dd lm Z  dd!lm!Z! dd"lm"Z" dd#lm#Z# dd$lm$Z$ dd%lm%Z% dd&lm&Z& dd'lm'Z' dd(lm(Z( dd)lm)Z) dd*lm*Z* dd+lm+Z+ dd,lm,Z, dd-lm-Z- dd.lm.Z. dd/lm/Z/ dd0lm0Z0 dd1lm1Z1 dd2lm2Z2 dd3lm3Z3 dd4lm4Z4 dd5lm5Z5 dd6lm6Z6 dd7lm7Z7 dd8lm8Z8 dd9lm9Z9 dd:lm:Z: dd;lm;Z; dd<lm<Z< dd=lm=Z= dd>lm>Z> dd?lm?Z? dd@l@mAZA ddAl@mBZB ddBl@mCZC ddCl@mDZD ddDl@mEZE ddEl@mFZF ddFl@mGZG ddGl@mHZH ddHl@mIZI ddIl@mJZJ ddJlKmLZL ddKlKmMZM ddLlKmNZN ddMlKmOZO ddNlKmPZP ddOlKmQZQ ddPlKmRZR ddQlKmSZS ddRlKmTZT ddSlKmUZU ddTlKmVZV ddUlKmWZW ddVlKmXZX ddWlKmYZY ddXlKmZZZ ddYlKm[Z[ ddZlKm\Z\ dd[lKm]Z] dd\lKm^Z^ dd]lKm_Z_ dd^lKm`Z` dd_lKmaZa dd`lKmbZb ddalKmcZc ddblKmdZd ddclKmeZe dddlKmfZf ddelKmgZg ddflKmhZh ddglKmiZi ddhlKmjZj ddilKmkZk ddjlKmlZl ddklKmmZm ddllKmnZn ddmlompZp ddnlomqZq ddolomrZr ddplomsZs ddqlomtZt ddrlomuZu ddslomvZv ddtlomwZw ddulomxZx ddvlomyZy ddwlomzZz ddxlom{Z{ ddylom|Z| ddzlom}Z} dd{lom~Z~ dd|lomZ dd}lomZ dd~lomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlomZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZ ddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ ddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZ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dАlmZ eG dd҄ d҃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_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dLd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dNd@dAZdNdBdCZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdMdTdUZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc ZdOdddeZ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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dMddZӐdMddZԐdMddZՐdMddZ֐dMddZאdMddZؐdd Zِdd Zڐdd Zېdd ZܐdMddZݐdPddZސdQddZߐdQddZdRddZdPddZdPddZdPddZdPddZdSddZdOddÄZdLdĐdńZdQdƐdǄZdPdȐdɄZdQdʐd˄Zd̐d̈́ Z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dNddZdd ZdN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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Z dMd6d7Z!d8d9 Z"d:d; Z#d<d= Z$d>d? Z%d@dA Z&dBdC Z'dDdE Z(dFdG Z)dTdHdIZ*dJdK Z+dS (U  IPolysNc                 C      d S N )selfgenr  r  ;/usr/lib/python3/dist-packages/sympy/polys/compatibility.pydrop      zIPolys.dropc                 C   r  r  r  )r  symbolsdomainorderr  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  r&  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   )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       zIPolys.to_densec                 C   s   |  t|| jd | jS N   )r+  rI   ngensr!  r&  r  r  r  
from_dense
     zIPolys.from_densec                 C      |  t| |||| jS r  )r6  r   r1  r!  r  fcir  r  r  r        zIPolys.dup_add_termc                 C   4   |  t| || |d || jd | jS Nr   r4  )r6  r   r1  r0  r  r5  r!  r9  r  r  r  r        4zIPolys.dmp_add_termc                 C   r8  r  )r6  r   r1  r!  r9  r  r  r  r     r=  zIPolys.dup_sub_termc                 C   r>  r?  )r6  r   r1  r0  r  r5  r!  r9  r  r  r  r     r@  zIPolys.dmp_sub_termc                 C   r8  r  )r6  r   r1  r!  r9  r  r  r  r     r=  zIPolys.dup_mul_termc                 C   r>  r?  )r6  r   r1  r0  r  r5  r!  r9  r  r  r  r     r@  zIPolys.dmp_mul_termc                 C      |  t| ||| jS r  )r6  r   r1  r!  r  r:  r;  r  r  r  r     r7  zIPolys.dup_add_groundc                 C   "   |  t| ||| jd | jS r3  )r6  r	   r1  r5  r!  rB  r  r  r  r	        "zIPolys.dmp_add_groundc                 C   rA  r  )r6  r
   r1  r!  rB  r  r  r  r
     r7  zIPolys.dup_sub_groundc                 C   rC  r3  )r6  r   r1  r5  r!  rB  r  r  r  r      rD  zIPolys.dmp_sub_groundc                 C   rA  r  )r6  r   r1  r!  rB  r  r  r  r   "  r7  zIPolys.dup_mul_groundc                 C   rC  r3  )r6  r   r1  r5  r!  rB  r  r  r  r   $  rD  zIPolys.dmp_mul_groundc                 C   rA  r  )r6  r   r1  r!  rB  r  r  r  r   &  r7  zIPolys.dup_quo_groundc                 C   rC  r3  )r6  r   r1  r5  r!  rB  r  r  r  r   (  rD  zIPolys.dmp_quo_groundc                 C   rA  r  )r6  r   r1  r!  rB  r  r  r  r   *  r7  zIPolys.dup_exquo_groundc                 C   rC  r3  )r6  r   r1  r5  r!  rB  r  r  r  r   ,  rD  zIPolys.dmp_exquo_groundc                 C   rA  r  )r6  r   r1  r!  r  r:  nr  r  r  r   /  r7  zIPolys.dup_lshiftc                 C   rA  r  )r6  r   r1  r!  rE  r  r  r  r   1  r7  zIPolys.dup_rshiftc                 C      |  t| || jS r  )r6  r   r1  r!  r  r:  r  r  r  r   4     zIPolys.dup_absc                 C       |  t| || jd | jS r3  )r6  r   r1  r5  r!  rH  r  r  r  r   6      zIPolys.dmp_absc                 C   rG  r  )r6  r   r1  r!  rH  r  r  r  r   9  rI  zIPolys.dup_negc                 C   rJ  r3  )r6  r   r1  r5  r!  rH  r  r  r  r   ;  rK  zIPolys.dmp_negc                 C       |  t| || || jS r  )r6  r   r1  r!  r  r:  gr  r  r  r   >  rK  zIPolys.dup_addc                 C   (   |  t| || || jd | jS r3  )r6  r   r1  r5  r!  rM  r  r  r  r   @     (zIPolys.dmp_addc                 C   rL  r  )r6  r   r1  r!  rM  r  r  r  r   C  rK  zIPolys.dup_subc                 C   rO  r3  )r6  r   r1  r5  r!  rM  r  r  r  r   E  rP  zIPolys.dmp_subc                 C   (   |  t| || || || jS r  )r6  r   r1  r!  r  r:  rN  hr  r  r  r   H  rP  zIPolys.dup_add_mulc                 C   0   |  t| || || || jd | jS r3  )r6  r   r1  r5  r!  rR  r  r  r  r   J     0zIPolys.dmp_add_mulc                 C   rQ  r  )r6  r   r1  r!  rR  r  r  r  r   L  rP  zIPolys.dup_sub_mulc                 C   rT  r3  )r6  r   r1  r5  r!  rR  r  r  r  r   N  rU  zIPolys.dmp_sub_mulc                 C   rL  r  )r6  r    r1  r!  rM  r  r  r  r    Q  rK  zIPolys.dup_mulc                 C   rO  r3  )r6  r!   r1  r5  r!  rM  r  r  r  r!   S  rP  zIPolys.dmp_mulc                 C   rG  r  )r6  r"   r1  r!  rH  r  r  r  r"   V  rI  zIPolys.dup_sqrc                 C   rJ  r3  )r6  r#   r1  r5  r!  rH  r  r  r  r#   X  rK  zIPolys.dmp_sqrc                 C   rA  r  )r6  r$   r1  r!  rE  r  r  r  r$   Z  r7  zIPolys.dup_powc                 C   rC  r3  )r6  r%   r1  r5  r!  rE  r  r  r  r%   \  rD  zIPolys.dmp_powc                 C   2   t | || || j\}}| || |fS r  )r&   r1  r!  r6  r  r:  rN  qrr  r  r  r&   _     zIPolys.dup_pdivc                 C   rL  r  )r6  r'   r1  r!  rM  r  r  r  r'   b  rK  zIPolys.dup_premc                 C   rL  r  )r6  r(   r1  r!  rM  r  r  r  r(   d  rK  zIPolys.dup_pquoc                 C   rL  r  )r6  r)   r1  r!  rM  r  r  r  r)   f  rK  zIPolys.dup_pexquoc                 C   :   t | || || jd | j\}}| || |fS r3  )r*   r1  r5  r!  r6  rW  r  r  r  r*   i     &zIPolys.dmp_pdivc                 C   rO  r3  )r6  r+   r1  r5  r!  rM  r  r  r  r+   l  rP  zIPolys.dmp_premc                 C   rO  r3  )r6  r,   r1  r5  r!  rM  r  r  r  r,   n  rP  zIPolys.dmp_pquoc                 C   rO  r3  )r6  r-   r1  r5  r!  rM  r  r  r  r-   p  rP  zIPolys.dmp_pexquoc                 C   rV  r  )r.   r1  r!  r6  rW  r  r  r  r.   s  rZ  zIPolys.dup_rr_divc                 C   r[  r3  )r/   r1  r5  r!  r6  rW  r  r  r  r/   v  r\  zIPolys.dmp_rr_divc                 C   rV  r  )r0   r1  r!  r6  rW  r  r  r  r0   y  rZ  zIPolys.dup_ff_divc                 C   r[  r3  )r1   r1  r5  r!  r6  rW  r  r  r  r1   |  r\  zIPolys.dmp_ff_divc                 C   rV  r  )r2   r1  r!  r6  rW  r  r  r  r2     rZ  zIPolys.dup_divc                 C   rL  r  )r6  r3   r1  r!  rM  r  r  r  r3     rK  zIPolys.dup_remc                 C   rL  r  )r6  r4   r1  r!  rM  r  r  r  r4     rK  zIPolys.dup_quoc                 C   rL  r  )r6  r5   r1  r!  rM  r  r  r  r5     rK  zIPolys.dup_exquoc                 C   r[  r3  )r6   r1  r5  r!  r6  rW  r  r  r  r6     r\  zIPolys.dmp_divc                 C   rO  r3  )r6  r7   r1  r5  r!  rM  r  r  r  r7     rP  zIPolys.dmp_remc                 C   rO  r3  )r6  r8   r1  r5  r!  rM  r  r  r  r8     rP  zIPolys.dmp_quoc                 C   rO  r3  )r6  r9   r1  r5  r!  rM  r  r  r  r9     rP  zIPolys.dmp_exquoc                 C      t | || jS r  )r:   r1  r!  rH  r  r  r  r:        zIPolys.dup_max_normc                 C      t | || jd | jS r3  )r;   r1  r5  r!  rH  r  r  r  r;     r7  zIPolys.dmp_max_normc                 C   r]  r  )r<   r1  r!  rH  r  r  r  r<     r^  zIPolys.dup_l1_normc                 C   r_  r3  )r=   r1  r5  r!  rH  r  r  r  r=     r7  zIPolys.dmp_l1_normc                 C   s   |  ttt| j|| jS r  )r6  r>   listmapr1  r!  r  polysr  r  r  r>        zIPolys.dup_expandc                 C   s&   |  ttt| j|| jd | jS r3  )r6  r?   r`  ra  r1  r5  r!  rb  r  r  r  r?        &zIPolys.dmp_expandc                 C   r]  r  )r@   r1  r!  rH  r  r  r  r@     r^  zIPolys.dup_LCc                 C   2   t | || j}t|tr| dd  |S |S r3  )rA   r1  r!  r-  r`  r6  )r  r:  LCr  r  r  rA        
zIPolys.dmp_LCc                 C   r]  r  )rB   r1  r!  rH  r  r  r  rB     r^  zIPolys.dup_TCc                 C   rf  r3  )rC   r1  r!  r-  r`  r6  )r  r:  ZTCr  r  r  rC     rh  zIPolys.dmp_TCc                 C   r_  r3  )rD   r1  r5  r!  rH  r  r  r  rD     r7  zIPolys.dmp_ground_LCc                 C   r_  r3  )rE   r1  r5  r!  rH  r  r  r  rE     r7  zIPolys.dmp_ground_TCc                 C      t | |S r  )rF   r1  rH  r  r  r  rF     r2  zIPolys.dup_degreec                 C   s   t | || jd S r3  )rG   r1  r5  rH  r  r  r  rG        zIPolys.dmp_degreec                 C   s   t | ||| jd S r3  )rH   r1  r5  )r  r:  jr  r  r  rH     rI  zIPolys.dmp_degree_inc                 C   rA  r  )r6  rJ   r1  r!  r  r:  mr  r  r  rJ     r7  zIPolys.dup_integratec                 C   rC  r3  )r6  rK   r1  r5  r!  rl  r  r  r  rK     rD  zIPolys.dmp_integratec                 C   rA  r  )r6  rM   r1  r!  rl  r  r  r  rM     r7  zIPolys.dup_diffc                 C   rC  r3  )r6  rN   r1  r5  r!  rl  r  r  r  rN     rD  zIPolys.dmp_diffc                 C   $   |  t| |||| jd | jS r3  )r6  rO   r1  r5  r!  r  r:  rm  rk  r  r  r  rO        $zIPolys.dmp_diff_inc                 C   rn  r3  )r6  rL   r1  r5  r!  ro  r  r  r  rL     rp  zIPolys.dmp_integrate_inc                 C   s   t | ||| jS r  )rP   r1  r!  r  r:  ar  r  r  rP        zIPolys.dup_evalc                 C   s.   t | ||| jd | j}| dd  |S r3  )rQ   r1  r5  r!  r6  )r  r:  rr  resultr  r  r  rQ     s   zIPolys.dmp_evalc                 C   s.   t | |||| jd | j}| ||S r3  )rR   r1  r5  r!  r  r6  )r  r:  rr  rk  rt  r  r  r  rR     s   zIPolys.dmp_eval_inc                 C   s0   t | ||||| jd | j}| ||S r3  )rT   r1  r5  r!  r  r6  )r  r:  rm  rr  rk  rt  r  r  r  rT     s    zIPolys.dmp_diff_eval_inc                 C   sB   t | ||| jd | j}t|tr| d t|  |S |S r3  )rS   r1  r5  r!  r-  r`  lenr6  )r  r:  Art  r  r  r  rS     s   
zIPolys.dmp_eval_tailc                 C   rA  r  )r6  rU   r1  r!  r  r:  pr  r  r  rU     r7  zIPolys.dup_truncc                 C   s0   |  t| || dd  || jd | jS r3  )r6  rV   r1  r5  r!  rM  r  r  r  rV     rU  zIPolys.dmp_truncc                 C   rC  r3  )r6  rW   r1  r5  r!  rw  r  r  r  rW     rD  zIPolys.dmp_ground_truncc                 C   rG  r  )r6  rX   r1  r!  rH  r  r  r  rX     rI  zIPolys.dup_monicc                 C   rJ  r3  )r6  rY   r1  r5  r!  rH  r  r  r  rY     rK  zIPolys.dmp_ground_monicc                 C   s6   t | || || j\}}}|| || |fS r  )r^   r1  r!  r6  r  r:  rN  r;  FGr  r  r  r^     s    zIPolys.dup_extractc                 C   s>   t | || || jd | j\}}}|| || |fS r3  )r_   r1  r5  r!  r6  ry  r  r  r  r_     s   (zIPolys.dmp_ground_extractc                 C   s4   t | |d | j\}}| || |fS r3  )r`   r0  r  r1  r!  r6  r  r:  rx  rX  r  r  r  r`     s    zIPolys.dup_real_imagc                 C   rG  r  )r6  ra   r1  r!  rH  r  r  r  ra     rI  zIPolys.dup_mirrorc                 C   rA  r  )r6  rb   r1  r!  rq  r  r  r  rb     r7  zIPolys.dup_scalec                 C   rA  r  )r6  rc   r1  r!  rq  r  r  r  rc     r7  zIPolys.dup_shiftc                 C   rQ  r  )r6  rd   r1  r!  r|  r  r  r  rd     rP  zIPolys.dup_transformc                 C   rL  r  )r6  re   r1  r!  rM  r  r  r  re     rK  zIPolys.dup_composec                 C   rO  r3  )r6  rf   r1  r5  r!  rM  r  r  r  rf     rP  zIPolys.dmp_composec                 C   "   t | || j}tt| j|S r  )rg   r1  r!  r`  ra  r6  )r  r:  Z
componentsr  r  r  rg        zIPolys.dup_decomposec                 C   s(   t | || jd | j}|  |S r3  )rh   r1  r5  r!  r%  r6  r  r:  rt  r  r  r  rh     s   zIPolys.dmp_liftc                 C   r]  r  )ri   r1  r!  rH  r  r  r  ri     r^  zIPolys.dup_sign_variationsFc                 C   sD   t | || j|d\}}|r| j| j d}n| }|||fS )Nconvertr!  )rj   r1  r!  r#  get_ringr6  r  r:  r  r;  rz  r.  r  r  r  rj     s
   zIPolys.dup_clear_denomsc                 C   sL   t | || jd | j|d\}}|r| j| j d}n| }|||fS )Nr4  r  r  )rk   r1  r5  r!  r#  r  r6  r  r  r  r  rk     s
   "zIPolys.dmp_clear_denomsc                 C   rA  r  )r6  rl   r1  r!  rE  r  r  r  rl   !  r7  zIPolys.dup_revertc                 C   rV  r  )rm   r1  r!  r6  r  r:  rN  srS  r  r  r  rm   $  rZ  zIPolys.dup_half_gcdexc                 C   r[  r3  )rn   r1  r5  r!  r6  r  r  r  r  rn   '  r\  zIPolys.dmp_half_gcdexc                 C   <   t | || || j\}}}| || || |fS r  )ro   r1  r!  r6  r  r:  rN  r  trS  r  r  r  ro   *      zIPolys.dup_gcdexc                 C   D   t | || || jd | j\}}}| || || |fS r3  )rp   r1  r5  r!  r6  r  r  r  r  rp   -     (zIPolys.dmp_gcdexc                 C   rL  r  )r6  rq   r1  r!  rM  r  r  r  rq   1  rK  zIPolys.dup_invertc                 C   rO  r3  )r6  rr   r1  r5  r!  rM  r  r  r  rr   3  rP  zIPolys.dmp_invertc                 C   *   t | || || j}tt| j|S r  )rs   r1  r!  r`  ra  r6  r  r:  rN  prsr  r  r  rs   6     zIPolys.dup_euclidean_prsc                 C   2   t | || || jd | j}tt| j|S r3  )rt   r1  r5  r!  r`  ra  r6  r  r  r  r  rt   9     "zIPolys.dmp_euclidean_prsc                 C   r  r  )ru   r1  r!  r`  ra  r6  r  r  r  r  ru   <  r  zIPolys.dup_primitive_prsc                 C   r  r3  )rv   r1  r5  r!  r`  ra  r6  r  r  r  r  rv   ?  r  zIPolys.dmp_primitive_prsc                 C   s2   t | || || j\}}tt| j||fS r  )rw   r1  r!  r`  ra  r6  r  r:  rN  r  Zsresr  r  r  rw   C  rZ  zIPolys.dup_inner_subresultantsc                 C   s:   t | || || jd | j\}}tt| j||fS r3  )r{   r1  r5  r!  r`  ra  r6  r  r  r  r  r{   F  r\  zIPolys.dmp_inner_subresultantsc                 C   r  r  )rx   r1  r!  r`  ra  r6  r  r  r  r  rx   J  r  zIPolys.dup_subresultantsc                 C   r  r3  )r|   r1  r5  r!  r`  ra  r6  r  r  r  r  r|   M  r  zIPolys.dmp_subresultantsc                 C   s2   t | || || j\}}|tt| j|fS r  )ry   r1  r!  r`  ra  r6  r  r:  rN  resr  r  r  r  ry   Q  rZ  zIPolys.dup_prs_resultantc                 C   sH   t | || || jd | j\}}| dd  |tt| j|fS r3  )r}   r1  r5  r!  r6  r`  ra  r  r  r  r  r}   T  s   &"zIPolys.dmp_prs_resultantc                 C   s<   t | || || || jd | j}| dd  |S r3  )r~   r1  r)  r5  r!  r6  )r  r:  rN  rx  r  r  r  r  r~   X  s   *zIPolys.dmp_zz_modular_resultantc                 C   4   t | || || jd | j}| dd  |S r3  )r   r1  r5  r!  r6  r  r:  rN  r  r  r  r  r   [     "zIPolys.dmp_zz_collins_resultantc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r   ^  r  zIPolys.dmp_qq_collins_resultantc                 C   s   t | || || jS r  )rz   r1  r!  rM  r  r  r  rz   b  r7  zIPolys.dup_resultantc                 C   sB   t | || || jd | j}t|tr| dd  |S |S r3  )r   r1  r5  r!  r-  r`  r6  r  r  r  r  r   d  s   "
zIPolys.dmp_resultantc                 C   r]  r  )r   r1  r!  rH  r  r  r  r   k  r^  zIPolys.dup_discriminantc                 C   :   t | || jd | j}t|tr| dd  |S |S r3  )r   r1  r5  r!  r-  r`  r6  )r  r:  Zdiscr  r  r  r   m     
zIPolys.dmp_discriminantc                 C   r  r  )r   r1  r!  r6  r  r:  rN  Hrz  r{  r  r  r  r   t  r  zIPolys.dup_rr_prs_gcdc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r   w  r  zIPolys.dup_ff_prs_gcdc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r   z  r  zIPolys.dmp_rr_prs_gcdc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r   }  r  zIPolys.dmp_ff_prs_gcdc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_zz_heu_gcdc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_zz_heu_gcdc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_qq_heu_gcdc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_qq_heu_gcdc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_inner_gcdc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_inner_gcdc                 C   $   t | || || j}| |S r  )r   r1  r!  r6  r  r:  rN  r  r  r  r  r        
zIPolys.dup_gcdc                 C   ,   t | || || jd | j}| |S r3  )r   r1  r5  r!  r6  r  r  r  r  r        "
zIPolys.dmp_gcdc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_rr_lcmc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_ff_lcmc                 C   r  r  )r   r1  r!  r6  r  r  r  r  r     r  zIPolys.dup_lcmc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_rr_lcmc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_ff_lcmc                 C   r  r3  )r   r1  r5  r!  r6  r  r  r  r  r     r  zIPolys.dmp_lcmc                 C   s   t | || j}|S r  )rZ   r1  r!  r  r:  contr  r  r  rZ     s   zIPolys.dup_contentc                 C   s$   t | || j\}}|| |fS r  )r\   r1  r!  r6  r  r:  r  Zprimr  r  r  r\     s   zIPolys.dup_primitivec                 C   r  r3  )r   r1  r5  r!  r-  r`  r6  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 r3  )r   r1  r5  r!  r-  r`  r6  r  r  r  r  r     s   
zIPolys.dmp_primitivec                 C   s   t | || jd | j}|S r3  )r[   r1  r5  r!  r  r  r  r  r[     s   zIPolys.dmp_ground_contentc                 C   s,   t | || jd | j\}}|| |fS r3  )r]   r1  r5  r!  r6  r  r  r  r  r]     s   zIPolys.dmp_ground_primitiveTc           	      C   sb   t | || || j|d}|s#|\}}}}||| || |fS |\}}| || |fS )Ninclude)r   r1  r!  r6  	r  r:  rN  r  rt  ZcfZcgrz  r{  r  r  r  r     s   zIPolys.dup_cancelc           	      C   sj   t | || || jd | j|d}|s'|\}}}}||| || |fS |\}}| || |fS )Nr4  r  )r   r1  r5  r!  r6  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  r6  .0rN  kr$  r  r  
<listcomp>      z-IPolys.dup_trial_division.<locals>.<listcomp>)r   r1  r`  ra  r!  r  r:  factorsr  r$  r  r         zIPolys.dup_trial_divisionc                    s:   t  |tt j| jd  j} fdd|D S )Nr4  c                    r  r  r  r  r$  r  r  r    r  z-IPolys.dmp_trial_division.<locals>.<listcomp>)r   r1  r`  ra  r5  r!  r  r  r$  r  r     s   (zIPolys.dmp_trial_divisionc                 C   r]  r  )r   r1  r!  rH  r  r  r  r     r^  zIPolys.dup_zz_mignotte_boundc                 C   r_  r3  )r   r1  r5  r!  rH  r  r  r  r     r7  zIPolys.dmp_zz_mignotte_boundc                 C   s\   | j }t|||||||||||| j\}}	}
}| || |	| |
| |fS r  )r1  r   r!  r6  )r  rm  r:  rN  rS  r  r  Dr{  r  STr  r  r  r     s   2$zIPolys.dup_zz_hensel_stepc                 C   s6   | j }t|||tt|||| j}tt| j|S r  )r1  r   r`  ra  r!  r6  )r  rx  r:  Zf_listlr  rc  r  r  r  r     s    zIPolys.dup_zz_hensel_liftc                    $   t  | j} fdd|D S )Nc                    r  r  r  r  r$  r  r  r    r  z,IPolys.dup_zz_zassenhaus.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r        zIPolys.dup_zz_zassenhausc                 C   r]  r  )r   r1  r!  rH  r  r  r  r     r^  zIPolys.dup_zz_irreducible_pc                 C   s   t | || j|dS )N)irreducible)r   r1  r!  )r  r:  r  r  r  r  r     rj  zIPolys.dup_cyclotomic_pc                 C   s   t || j}| |S r  )r   r!  r6  )r  rF  rz  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   r1  r!  r`  ra  r6  r  r  r  r  r     s   zIPolys.dup_zz_cyclotomic_factorc                 C   s   t |||| jS r  )r   r!  )r  EcsZ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 )Nr4  c                    r  r  )r1  )r  r  r  mvr  r  r  	  r  z2IPolys.dmp_zz_wang_lead_coeffs.<locals>.<listcomp>)r`  ra  r1  r   r5  r!  r6  )
r  r:  r  r  r  r  rv  uvZHHZ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   r`  ra  r1  r!  r6  )r  rz  rm  rx  rt  r  r  r  r     s   zIPolys.dup_zz_diophantinec                 C   s>   t tt| j|| ||||| jd | j}tt| j|S r3  )r   r`  ra  r1  r5  r!  r6  )r  rz  r;  rv  r*  rx  rt  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 r3  )r`  ra  r1  r   r5  r!  r6  )	r  r:  r  rg  rv  rx  r  r  rt  r  r  r  r     s   "z!IPolys.dmp_zz_wang_hensel_liftingc                    s2   t  | jd  j||d} fdd|D S )Nr4  )modseedc                       g | ]}  |qS r  r  r  rN  r$  r  r  r  $      z&IPolys.dmp_zz_wang.<locals>.<listcomp>)r   r1  r5  r!  )r  r:  r  r  r  r  r$  r  r   "  r  zIPolys.dmp_zz_wangc                    ,   t  | j\}}| fdd|D fS )Nc                    r  r  r  r  r$  r  r  r  (  r  z,IPolys.dup_zz_factor_sqf.<locals>.<listcomp>)r   r1  r!  r  r:  coeffr  r  r$  r  r   &     zIPolys.dup_zz_factor_sqfc                    r  )Nc                    r  r  r  r  r$  r  r  r  ,  r  z(IPolys.dup_zz_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   *  r  zIPolys.dup_zz_factorc                    4   t  | jd  j\}}| fdd|D fS )Nr4  c                    r  r  r  r  r$  r  r  r  /  r  z(IPolys.dmp_zz_factor.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   -     zIPolys.dmp_zz_factorc                    r  )Nc                    r  r  r  r  r$  r  r  r  3  r  z*IPolys.dup_qq_i_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   1  r  zIPolys.dup_qq_i_factorc                    r  )Nr4  c                    r  r  r  r  r$  r  r  r  6  r  z*IPolys.dmp_qq_i_factor.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   4  r  zIPolys.dmp_qq_i_factorc                    r  )Nc                    r  r  r  r  r$  r  r  r  :  r  z*IPolys.dup_zz_i_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   8  r  zIPolys.dup_zz_i_factorc                    r  )Nr4  c                    r  r  r  r  r$  r  r  r  =  r  z*IPolys.dmp_zz_i_factor.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   ;  r  zIPolys.dmp_zz_i_factorc                    r  )Nc                    r  r  r  r  r$  r  r  r  A  r  z)IPolys.dup_ext_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   ?  r  zIPolys.dup_ext_factorc                    r  )Nr4  c                    r  r  r  r  r$  r  r  r  D  r  z)IPolys.dmp_ext_factor.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   B  r  zIPolys.dmp_ext_factorc                    r  )Nc                    r  r  r  r  r$  r  r  r  H  r  z(IPolys.dup_gf_factor.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   F  r  zIPolys.dup_gf_factorc                    r  )Nr4  c                    r  r  r  r  r$  r  r  r  K  r  z(IPolys.dmp_gf_factor.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   I  r  zIPolys.dmp_gf_factorc                    r  )Nc                    r  r  r  r  r$  r  r  r  O  r  z*IPolys.dup_factor_list.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   M  r  zIPolys.dup_factor_listc                    r  )Nc                    r  r  r  r  r$  r  r  r  R  r  z2IPolys.dup_factor_list_include.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r   P  r  zIPolys.dup_factor_list_includec                    r  )Nr4  c                    r  r  r  r  r$  r  r  r  V  r  z*IPolys.dmp_factor_list.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   T  r  zIPolys.dmp_factor_listc                    ,   t  | jd  j} fdd|D S )Nr4  c                    r  r  r  r  r$  r  r  r  Y  r  z2IPolys.dmp_factor_list_include.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   W     zIPolys.dmp_factor_list_includec                 C   r]  r  )r   r1  r!  rH  r  r  r  r   [  r^  zIPolys.dup_irreducible_pc                 C   r_  r3  )r   r1  r5  r!  rH  r  r  r  r   ]  r7  zIPolys.dmp_irreducible_pc                 C   r}  r  )r   r1  r!  r`  ra  r6  )r  r:  seqr  r  r  r   `  r~  zIPolys.dup_sturmc                 C   r]  r  )r   r1  r!  rH  r  r  r  r   d  r^  zIPolys.dup_sqf_pc                 C   r_  r3  )r   r1  r5  r!  rH  r  r  r  r   f  r7  zIPolys.dmp_sqf_pc                 C   s2   t | || j\}}}|| ||  |fS r  )r   r1  r!  r6  r%  r  r:  r  rz  Rr  r  r  r   i  s   zIPolys.dup_sqf_normc                 C   s:   t | || jd | j\}}}|| ||  |fS r3  )r   r1  r5  r!  r6  r%  r  r  r  r  r   l  s    zIPolys.dmp_sqf_normc                 C   rG  r  )r6  r   r1  r!  rH  r  r  r  r   p  rI  zIPolys.dup_gf_sqf_partc                 C   rG  r  )r6  r   r1  r!  rH  r  r  r  r   r  rI  zIPolys.dmp_gf_sqf_partc                 C   rG  r  )r6  r   r1  r!  rH  r  r  r  r   t  rI  zIPolys.dup_sqf_partc                 C   rJ  r3  )r6  r   r1  r5  r!  rH  r  r  r  r   v  rK  zIPolys.dmp_sqf_partc                    0   t  | j|d\}}| fdd|D fS )Nallc                    r  r  r  r  r$  r  r  r  {  r  z*IPolys.dup_gf_sqf_list.<locals>.<listcomp>)r   r1  r!  r  r:  r  r  r  r  r$  r  r   y     zIPolys.dup_gf_sqf_listc                    8   t  | jd  j|d\}}| fdd|D fS )Nr4  r  c                    r  r  r  r  r$  r  r  r  ~  r  z*IPolys.dmp_gf_sqf_list.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r   |     "zIPolys.dmp_gf_sqf_listc                    r  )Nr  c                    r  r  r  r  r$  r  r  r    r  z'IPolys.dup_sqf_list.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r     r  zIPolys.dup_sqf_listc                    s(   t  | j|d} fdd|D S )Nr  c                    r  r  r  r  r$  r  r  r    r  z/IPolys.dup_sqf_list_include.<locals>.<listcomp>)r   r1  r!  r  r:  r  r  r  r$  r  r     s   zIPolys.dup_sqf_list_includec                    r  )Nr4  r  c                    r  r  r  r  r$  r  r  r    r  z'IPolys.dmp_sqf_list.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r     r  zIPolys.dmp_sqf_listc                    s0   t  | jd  j|d} fdd|D S )Nr4  r  c                    r  r  r  r  r$  r  r  r    r  z/IPolys.dmp_sqf_list_include.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r     s   zIPolys.dmp_sqf_list_includec                    r  )Nc                    r  r  r  r  r$  r  r  r    r  z'IPolys.dup_gff_list.<locals>.<listcomp>)r   r1  r!  r  r  r$  r  r     r  zIPolys.dup_gff_listc                    r  )Nr4  c                    r  r  r  r  r$  r  r  r    r  z'IPolys.dmp_gff_list.<locals>.<listcomp>)r   r1  r5  r!  r  r  r$  r  r     r  zIPolys.dmp_gff_listc                 C   r]  r  )r   r1  r!  rH  r  r  r  r     r^  zIPolys.dup_root_upper_boundc                 C   r]  r  )r   r1  r!  rH  r  r  r  r     r^  zIPolys.dup_root_lower_boundc                 C   s   t | ||| j|dS )N)fast)r   r1  r!  )r  r:  Mr  r  r  r  r     rI  z IPolys.dup_step_refine_real_rootc              
   C   s    t | ||| j|||||dS )N)epsstepsdisjointr  mobius)r   r1  r!  )r  r:  r  r  r  r  r  r  r  r  r  r     rK  z!IPolys.dup_inner_refine_real_rootc              
   C       t | |||| j||||dS N)r  r  r  r  )r   r1  r!  r  r:  r  r  r  r  r  r  r  r  r  r     rK  z!IPolys.dup_outer_refine_real_rootc              
   C   r  r  )r   r1  r!  r  r  r  r  r     rK  zIPolys.dup_refine_real_rootc                 C      t | || j||dS )N)r  r  )r   r1  r!  )r  r:  r  r  r  r  r  r     rI  z#IPolys.dup_inner_isolate_real_rootsc              	   C      t | || j|||||dS )N)r  infsupr  r  )r   r1  r!  )r  r:  r  r  r  r  r  r  r  r  r     rd  z'IPolys.dup_inner_isolate_positive_rootsc              	   C   r  )N)r  r  r  r  r  )r   r1  r!  )r  r:  r  r  r  r  r  r  r  r  r     rd  z'IPolys.dup_inner_isolate_negative_rootsc              	   C   r  N)r  r  r  r  blackbox)r   r1  r!  r  r:  r  r  r  r  r  r  r  r  r     rd  z!IPolys.dup_isolate_real_roots_sqfc              	   C   r  )N)r  r  r  basisr  )r   r1  r!  )r  r:  r  r  r  r  r  r  r  r  r     rd  zIPolys.dup_isolate_real_rootsc              
   C   s&   t tt| j|| j||||||dS )N)r  r  r  strictr  r  )r   r`  ra  r1  r!  )r  rc  r  r  r  r  r  r  r  r  r  r     re  z"IPolys.dup_isolate_real_roots_listc                 C   r  )N)r  r  )r   r1  r!  )r  r:  r  r  r  r  r  r     rI  zIPolys.dup_count_real_rootsc                 C   s   t | || j|||dS )N)r  r  exclude)r   r1  r!  )r  r:  r  r  r  r  r  r  r     r7  zIPolys.dup_count_complex_rootsc                 C      t | || j||||dS )N)r  r  r  r  )r   r1  r!  )r  r:  r  r  r  r  r  r  r  r     r=  z$IPolys.dup_isolate_complex_roots_sqfc              	   C   r  r  )r   r1  r!  r  r  r  r  r     rd  z IPolys.dup_isolate_all_roots_sqfc                 C   r  )N)r  r  r  r  )r   r1  r!  )r  r:  r  r  r  r  r  r  r  r     r=  zIPolys.dup_isolate_all_rootsc                 C   *   ddl m} tt| j|| jd | jS )Nr   )dmp_fateman_poly_F_1r4  )sympy.polys.specialpolysr  tuplera  r6  r5  r!  )r  r  r  r  r  fateman_poly_F_1     zIPolys.fateman_poly_F_1c                 C   r  )Nr   )dmp_fateman_poly_F_2r4  )r  r  r  ra  r6  r5  r!  )r  r  r  r  r  fateman_poly_F_2  r  zIPolys.fateman_poly_F_2c                 C   r  )Nr   )dmp_fateman_poly_F_3r4  )r  r  r  ra  r6  r5  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  r;  r$  r  r  r    r  z&IPolys.to_gf_dense.<locals>.<listcomp>)r   r0  r1  r&  r  r$  r  to_gf_dense  rK  zIPolys.to_gf_densec                 C   s   |  t|| jd | jjS r3  )r+  rI   r5  r!  r  r&  r  r  r  from_gf_dense  r=  zIPolys.from_gf_densec                 C   ri  r  )r   r  rH  r  r  r  r     r2  zIPolys.gf_degreec                 C      t | || jjS r  )r   r  r!  r  rH  r  r  r  r     rs  zIPolys.gf_LCc                 C   r  r  )r   r  r!  r  rH  r  r  r  r     rs  zIPolys.gf_TCc                 C   s   |  t| |S r  )r  r   r  rH  r  r  r  r     rs  zIPolys.gf_stripc                 C   s   |  t| || jjS r  )r  r   r  r!  r  rH  r  r  r  gf_trunc  r7  zIPolys.gf_truncc                 C       |  t| || jj| jjS r  )r  r   r  r!  r  r  rH  r  r  r  	gf_normal  rK  zIPolys.gf_normalc                 C      |  t|| jj| jjS r  )r  r   r!  r  r  rH  r  r  r  r     r7  zIPolys.gf_from_dictc                 C      t | || jj|dS N)	symmetric)r   r  r!  r  r  r:  r  r  r  r  r     rI  zIPolys.gf_to_dictc                 C   s   |  t|| jjS r  )r  r   r!  r  rH  r  r  r  r     rs  zIPolys.gf_from_int_polyc                 C   r  r  )r   r  r!  r  r  r  r  r  r     rI  zIPolys.gf_to_int_polyc                 C   r  r  )r  r   r  r!  r  r  rH  r  r  r  r     rK  zIPolys.gf_negc                 C   "   |  t| ||| jj| jjS r  )r  r   r  r!  r  r  rq  r  r  r  r     rD  zIPolys.gf_add_groundc                 C   r   r  )r  r   r  r!  r  r  rq  r  r  r  r     rD  zIPolys.gf_sub_groundc                 C   r   r  )r  r   r  r!  r  r  rq  r  r  r  r     rD  zIPolys.gf_mul_groundc                 C   r   r  )r  r   r  r!  r  r  rq  r  r  r  r     rD  zIPolys.gf_quo_groundc                 C   (   |  t| || || jj| jjS r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_addc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_subc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_mulc                 C   r  r  )r  r   r  r!  r  r  rH  r  r  r  r     rK  zIPolys.gf_sqrc                 C   0   |  t| || || || jj| jjS r  )r  r   r  r!  r  r  rR  r  r  r  r     rU  zIPolys.gf_add_mulc                 C   r  r  )r  r   r  r!  r  r  rR  r  r  r  r     rU  zIPolys.gf_sub_mulc                 C   s&   |  ttt| j|| jj| jjS r  )r  r   r`  ra  r  r!  r  r  )r  rz  r  r  r  r     re  zIPolys.gf_expandc                 C   s:   t | || || jj| jj\}}| || |fS r  )r   r  r!  r  r  r  rW  r  r  r  r     r\  zIPolys.gf_divc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_remc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_quoc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_exquoc                 C      |  t| ||| jjS r  )r  r   r  r!  r  rE  r  r  r  r     r=  zIPolys.gf_lshiftc                 C   r  r  )r  r   r  r!  r  rE  r  r  r  r   
  r=  zIPolys.gf_rshiftc                 C   r   r  )r  r   r  r!  r  r  rE  r  r  r  r     rD  zIPolys.gf_powc                 C   s*   |  t| ||| || jj| jjS r  )r  r   r  r!  r  r  )r  r:  rF  rN  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  r:  rN  rS  ZcffZcfgr  r  r  r     r  zIPolys.gf_cofactorsc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_gcdc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_lcmc                 C   r  r  )r  r   r  r!  r  r  rM  r  r  r  r     rP  zIPolys.gf_gcdexc                 C   r  r  )r  r   r  r!  r  r  rH  r  r  r  r     rK  zIPolys.gf_monicc                 C   r  r  )r  r   r  r!  r  r  rH  r  r  r  r     rK  zIPolys.gf_diffc                 C      t | ||| jj| jjS r  )r   r  r!  r  r  rq  r  r  r  r   !  r=  zIPolys.gf_evalc                 C   r  r  )r  r  r!  r  r  )r  r:  rv  r  r  r  r  #  r=  zIPolys.gf_multi_evalc                 C   r  r  )r  r  r  r!  r  r  rM  r  r  r  r  &  rP  zIPolys.gf_composec                 C   r  r  )r  r  r  r!  r  r  )r  rN  rS  r:  r  r  r  r  (  rU  zIPolys.gf_compose_modc                 C   s\   |  |}|  |}|  |}|  |}t|||||| jj| jj\}}| || |fS r  )r  r  r!  r  r  r  )r  rr  br;  rF  r:  UVr  r  r  r  +  s   



 zIPolys.gf_trace_mapc                 C   r  r  )r  r  r!  r  r  r  rF  r  r  r  r  3  r7  zIPolys.gf_randomc                 C   r  r  )r  r  r!  r  r  r  r  r  r  r  5  r7  zIPolys.gf_irreduciblec                 C      t | || jj| jjS r  )r  r  r!  r  r  rH  r  r  r  r  8  r7  zIPolys.gf_irred_p_ben_orc                 C   r	  r  )r  r  r!  r  r  rH  r  r  r  r  :  r7  zIPolys.gf_irred_p_rabinc                 C   r	  r  )r	  r  r!  r  r  rH  r  r  r  r	  <  r7  zIPolys.gf_irreducible_pc                 C   r	  r  )r
  r  r!  r  r  rH  r  r  r  r
  >  r7  zIPolys.gf_sqf_pc                 C   r  r  )r  r  r  r!  r  r  rH  r  r  r  r  A  rK  zIPolys.gf_sqf_partc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    r  r  r  r  r$  r  r  r  E  r  z&IPolys.gf_sqf_list.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  gf_sqf_listC  r  zIPolys.gf_sqf_listc                 C   r	  r  )r  r  r!  r  r  rH  r  r  r  r  G  r7  zIPolys.gf_Qmatrixc                    ,   t  | jj jj} fdd|D S )Nc                    r  r  r
  r  r$  r  r  r  K  r  z'IPolys.gf_berlekamp.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  I  r  zIPolys.gf_berlekampc                    r  )Nc                    r  r  r
  r  r$  r  r  r  O  r  z,IPolys.gf_ddf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  M  r  zIPolys.gf_ddf_zassenhausc                    ,   t  | jj jj} fdd|D S )Nc                    r  r  r
  r  r$  r  r  r  R  r  z,IPolys.gf_edf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r  r:  rF  r  r  r$  r  r  P  r  zIPolys.gf_edf_zassenhausc                    r  )Nc                    r  r  r
  r  r$  r  r  r  V  r  z'IPolys.gf_ddf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  T  r  zIPolys.gf_ddf_shoupc                    r  )Nc                    r  r  r
  r  r$  r  r  r  Y  r  z'IPolys.gf_edf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  W  r  zIPolys.gf_edf_shoupc                    r  )Nc                    r  r  r
  r  r$  r  r  r  ]  r  z(IPolys.gf_zassenhaus.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  [  r  zIPolys.gf_zassenhausc                    r  )Nc                    r  r  r
  r  r$  r  r  r  `  r  z#IPolys.gf_shoup.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  ^  r  zIPolys.gf_shoupc                    s8   t  | jj jj|d\}}| fdd|D fS )N)methodc                    r  r  r
  r  r$  r  r  r  d  r  z(IPolys.gf_factor_sqf.<locals>.<listcomp>)r  r  r!  r  r  )r  r:  r  r  r  r  r$  r  r  b  r  zIPolys.gf_factor_sqfc                    s4   t  | jj jj\}}| fdd|D fS )Nc                    r  r  r
  r  r$  r  r  r  g  r  z$IPolys.gf_factor.<locals>.<listcomp>)r  r  r!  r  r  r  r  r$  r  r  e  r  zIPolys.gf_factor)NNN)F)T)NN)NNNFF)NNNF)NF)NNNFFFr  (,  __name__
__module____qualname__r   r5  r!  r"  Zgensr  r#  r%  r(  r)  r+  r0  r1  r6  r   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   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   rJ   rK   rM   rN   rO   rL   rP   rQ   rR   rT   rS   rU   rV   rW   rX   rY   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   rw   r{   rx   r|   ry   r}   r~   r   r   rz   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   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     sT   

		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?   Zsympy.polys.densebasicr@   rA   rB   rC   rD   rE   rF   rG   rH   rI   Zsympy.polys.densetoolsrJ   rK   rL   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   Zsympy.polys.euclidtoolsrm   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   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^ 