
~9\c           @  s  d  Z  d d l m Z 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 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 m0 Z0 d d/ l m1 Z1 d d0 l m2 Z2 d d1 l m3 Z3 d d2 l m4 Z4 d d3 l m5 Z5 d d4 l m6 Z6 d d5 l m7 Z7 d d6 l m8 Z8 d d7 l m9 Z9 d d8 l m: Z: d d9 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 mA ZA d d@ l mB ZB d dA lC mD ZD d dB lC mE ZE d dC lC mF ZF d dD lC mG ZG d dE lC mH ZH d dF lC mI ZI d dG lC mJ ZJ d dH lC mK ZK d dI lC mL ZL d dJ lC mM ZM d dK lN mO ZO d dL lN mP ZP d dM lN mQ ZQ d dN lN mR ZR d dO lN mS ZS d dP lN mT ZT d dQ lN mU ZU d dR lN mV ZV d dS lN mW ZW d dT lN mX ZX d dU lN mY ZY d dV lN mZ ZZ d dW lN m[ Z[ d dX lN m\ Z\ d dY lN m] Z] d dZ lN m^ Z^ d d[ lN m_ Z_ d d\ lN m` Z` d d] lN ma Za d d^ lN mb Zb d d_ lN mc Zc d d` lN md Zd d da lN me Ze d db lN mf Zf d dc lN mg Zg d dd lN mh Zh d de lN mi Zi d df lN mj Zj d dg lN mk Zk d dh lN ml Zl d di lN mm Zm d dj lN mn Zn d dk lN mo Zo d dl lN mp Zp d dm lN mq Zq d dn lr ms Zs d do lr mt Zt d dp lr mu Zu d dq lr mv Zv d dr lr mw Zw d ds lr mx Zx d dt lr my Zy d du lr mz Zz d dv lr m{ Z{ d dw lr m| Z| d dx lr m} Z} d dy lr m~ Z~ d dz lr m Z d d{ lr m Z d d| lr m Z d d} lr m Z d d~ lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr m Z d d lr 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 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 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 d l m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z mZmZmZmZmZ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 d lmZed ef d     Y Zd S(   s8   Compatibility interface between dense and sparse polys. i(   t   print_functiont   division(   t   dup_add_term(   t   dmp_add_term(   t   dup_sub_term(   t   dmp_sub_term(   t   dup_mul_term(   t   dmp_mul_term(   t   dup_add_ground(   t   dmp_add_ground(   t   dup_sub_ground(   t   dmp_sub_ground(   t   dup_mul_ground(   t   dmp_mul_ground(   t   dup_quo_ground(   t   dmp_quo_ground(   t   dup_exquo_ground(   t   dmp_exquo_ground(   t
   dup_lshift(   t
   dup_rshift(   t   dup_abs(   t   dmp_abs(   t   dup_neg(   t   dmp_neg(   t   dup_add(   t   dmp_add(   t   dup_sub(   t   dmp_sub(   t   dup_add_mul(   t   dmp_add_mul(   t   dup_sub_mul(   t   dmp_sub_mul(   t   dup_mul(   t   dmp_mul(   t   dup_sqr(   t   dmp_sqr(   t   dup_pow(   t   dmp_pow(   t   dup_pdiv(   t   dup_prem(   t   dup_pquo(   t
   dup_pexquo(   t   dmp_pdiv(   t   dmp_prem(   t   dmp_pquo(   t
   dmp_pexquo(   t
   dup_rr_div(   t
   dmp_rr_div(   t
   dup_ff_div(   t
   dmp_ff_div(   t   dup_div(   t   dup_rem(   t   dup_quo(   t	   dup_exquo(   t   dmp_div(   t   dmp_rem(   t   dmp_quo(   t	   dmp_exquo(   t   dup_max_norm(   t   dmp_max_norm(   t   dup_l1_norm(   t   dmp_l1_norm(   t
   dup_expand(   t
   dmp_expand(   t   dup_LC(   t   dmp_LC(   t   dup_TC(   t   dmp_TC(   t   dmp_ground_LC(   t   dmp_ground_TC(   t
   dup_degree(   t
   dmp_degree(   t   dmp_degree_in(   t   dmp_to_dict(   t   dup_integrate(   t   dmp_integrate(   t   dmp_integrate_in(   t   dup_diff(   t   dmp_diff(   t   dmp_diff_in(   t   dup_eval(   t   dmp_eval(   t   dmp_eval_in(   t   dmp_eval_tail(   t   dmp_diff_eval_in(   t	   dup_trunc(   t	   dmp_trunc(   t   dmp_ground_trunc(   t	   dup_monic(   t   dmp_ground_monic(   t   dup_content(   t   dmp_ground_content(   t   dup_primitive(   t   dmp_ground_primitive(   t   dup_extract(   t   dmp_ground_extract(   t   dup_real_imag(   t
   dup_mirror(   t	   dup_scale(   t	   dup_shift(   t   dup_transform(   t   dup_compose(   t   dmp_compose(   t   dup_decompose(   t   dmp_lift(   t   dup_sign_variations(   t   dup_clear_denoms(   t   dmp_clear_denoms(   t
   dup_revert(   t   dup_half_gcdex(   t   dmp_half_gcdex(   t	   dup_gcdex(   t	   dmp_gcdex(   t
   dup_invert(   t
   dmp_invert(   t   dup_euclidean_prs(   t   dmp_euclidean_prs(   t   dup_primitive_prs(   t   dmp_primitive_prs(   t   dup_inner_subresultants(   t   dup_subresultants(   t   dup_prs_resultant(   t   dup_resultant(   t   dmp_inner_subresultants(   t   dmp_subresultants(   t   dmp_prs_resultant(   t   dmp_zz_modular_resultant(   t   dmp_zz_collins_resultant(   t   dmp_qq_collins_resultant(   t   dmp_resultant(   t   dup_discriminant(   t   dmp_discriminant(   t   dup_rr_prs_gcd(   t   dup_ff_prs_gcd(   t   dmp_rr_prs_gcd(   t   dmp_ff_prs_gcd(   t   dup_zz_heu_gcd(   t   dmp_zz_heu_gcd(   t   dup_qq_heu_gcd(   t   dmp_qq_heu_gcd(   t   dup_inner_gcd(   t   dmp_inner_gcd(   t   dup_gcd(   t   dmp_gcd(   t
   dup_rr_lcm(   t
   dup_ff_lcm(   t   dup_lcm(   t
   dmp_rr_lcm(   t
   dmp_ff_lcm(   t   dmp_lcm(   t   dmp_content(   t   dmp_primitive(   t
   dup_cancel(   t
   dmp_cancel(   t   dup_trial_division(   t   dmp_trial_division(   t   dup_zz_mignotte_bound(   t   dmp_zz_mignotte_bound(   t   dup_zz_hensel_step(   t   dup_zz_hensel_lift(   t   dup_zz_zassenhaus(   t   dup_zz_irreducible_p(   t   dup_cyclotomic_p(   t   dup_zz_cyclotomic_poly(   t   dup_zz_cyclotomic_factor(   t   dup_zz_factor_sqf(   t   dup_zz_factor(   t   dmp_zz_wang_non_divisors(   t   dmp_zz_wang_lead_coeffs(   t   dup_zz_diophantine(   t   dmp_zz_diophantine(   t   dmp_zz_wang_hensel_lifting(   t   dmp_zz_wang(   t   dmp_zz_factor(   t   dup_ext_factor(   t   dmp_ext_factor(   t   dup_gf_factor(   t   dmp_gf_factor(   t   dup_factor_list(   t   dup_factor_list_include(   t   dmp_factor_list(   t   dmp_factor_list_include(   t   dup_irreducible_p(   t   dmp_irreducible_p(   t	   dup_sturm(   t   dup_root_upper_bound(   t   dup_root_lower_bound(   t   dup_step_refine_real_root(   t   dup_inner_refine_real_root(   t   dup_outer_refine_real_root(   t   dup_refine_real_root(   t   dup_inner_isolate_real_roots(   t    dup_inner_isolate_positive_roots(   t    dup_inner_isolate_negative_roots(   t   dup_isolate_real_roots_sqf(   t   dup_isolate_real_roots(   t   dup_isolate_real_roots_list(   t   dup_count_real_roots(   t   dup_count_complex_roots(   t   dup_isolate_complex_roots_sqf(   t   dup_isolate_all_roots_sqf(   t   dup_isolate_all_roots(   t	   dup_sqf_pt	   dmp_sqf_pt   dup_sqf_normt   dmp_sqf_normt   dup_gf_sqf_partt   dmp_gf_sqf_partt   dup_sqf_partt   dmp_sqf_partt   dup_gf_sqf_listt   dmp_gf_sqf_listt   dup_sqf_listt   dup_sqf_list_includet   dmp_sqf_listt   dmp_sqf_list_includet   dup_gff_listt   dmp_gff_list(8   t	   gf_degreet   gf_LCt   gf_TCt   gf_stript   gf_from_dictt
   gf_to_dictt   gf_from_int_polyt   gf_to_int_polyt   gf_negt   gf_add_groundt   gf_sub_groundt   gf_mul_groundt   gf_quo_groundt   gf_addt   gf_subt   gf_mult   gf_sqrt
   gf_add_mult
   gf_sub_mult	   gf_expandt   gf_divt   gf_remt   gf_quot   gf_exquot	   gf_lshiftt	   gf_rshiftt   gf_powt
   gf_pow_modt   gf_gcdt   gf_lcmt   gf_cofactorst   gf_gcdext   gf_monict   gf_difft   gf_evalt   gf_multi_evalt
   gf_composet   gf_compose_modt   gf_trace_mapt	   gf_randomt   gf_irreduciblet   gf_irred_p_ben_ort   gf_irred_p_rabint   gf_irreducible_pt   gf_sqf_pt   gf_sqf_partt
   gf_Qmatrixt   gf_berlekampt   gf_ddf_zassenhaust   gf_edf_zassenhaust   gf_ddf_shoupt   gf_edf_shoupt   gf_zassenhaust   gf_shoupt   gf_factor_sqft	   gf_factor(   t   publict   IPolysc           B  s6  e  Z d Z d Z d Z d Z d Z d    Z d d d d  Z	 d   Z
 d   Z d   Z d   Z d   Z d   Z d   Z d	   Z d
   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z  d   Z! d   Z" d   Z# d   Z$ d   Z% d   Z& d   Z' d    Z( d!   Z) d"   Z* d#   Z+ d$   Z, d%   Z- d&   Z. d'   Z/ d(   Z0 d)   Z1 d*   Z2 d+   Z3 d,   Z4 d-   Z5 d.   Z6 d/   Z7 d0   Z8 d1   Z9 d2   Z: d3   Z; d4   Z< d5   Z= d6   Z> d7   Z? d8   Z@ d9   ZA d:   ZB d;   ZC d<   ZD d=   ZE d>   ZF d?   ZG d@   ZH dA   ZI dB   ZJ dC   ZK dD   ZL dE   ZM dF   ZN dG   ZO dH   ZP dI   ZQ dJ   ZR dK   ZS dL   ZT dM   ZU dN   ZV dO   ZW dP   ZX dQ   ZY dR   ZZ dS   Z[ dT   Z\ dU   Z] dV   Z^ dW   Z_ dX   Z` dY   Za dZ   Zb d[   Zc d\   Zd d]   Ze d^   Zf d_   Zg d`   Zh da   Zi db   Zj dc   Zk dd   Zl de   Zm df   Zn dg   Zo dh   Zp di   Zq dj   Zr dk   Zs et dl  Zu et dm  Zv dn   Zw do   Zx dp   Zy dq   Zz dr   Z{ ds   Z| dt   Z} du   Z~ dv   Z dw   Z dx   Z dy   Z dz   Z d{   Z d|   Z d}   Z d~   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z e d  Z e d  Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z et d  Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d d d  Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z et d  Z et d  Z et d  Z et d  Z et d  Z et d  Z d   Z d   Z d   Z d   Z et d  Z d d d et et d  Z d d d et d  Z d d d et d  Z d et d  Z d d d et et d  Z d d d et et d  Z d d d et et d  Z d d d et et d  Z d d d et et et d  Z d d d  Z d d d d  Z d d d et d  Z d d d et et d  Z d d d et d  Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z e d  Z d   Z e d  Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Z d   Zd   Zd   Zd   Zd   Zd   Zd   Zd   Zd   Z	d   Z
d  Zd  Zd  Zd  Zd  Zd  Zd  Zd  Zd	  Zd
  Zd  Zd  Zd  Zd  Zd  Zd  Zd  Zd  Zd  Zd  Zet d Zd  Z d  Z!d  Z"d  Z#d  Z$d  Z%d  Z&d  Z'd d Z(d  Z)RS(!  c         C  s   d  S(   N(    (   t   selft   gen(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   drop   s    c         C  s   d  S(   N(    (   R  t   symbolst   domaint   order(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   clone   s    c         C  s   d  S(   N(    (   R  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt	   to_ground   s    c         C  s   d  S(   N(    (   R  t   element(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt
   ground_new   s    c         C  s   d  S(   N(    (   R  R  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt
   domain_new   s    c         C  s   d  S(   N(    (   R  t   d(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt	   from_dict   s    c         C  sR   d d l  m } t | |  rA | j |  k r2 | St d   n |  j |  Sd  S(   Ni(   t   PolyElements   domain conversions(   t   sympy.polys.ringsR!  t
   isinstancet   ringt   NotImplementedErrorR  (   R  R  R!  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   wrap   s    c         C  s   |  j  |  j   S(   N(   R&  t   to_dense(   R  R  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR'    s    c         C  s#   |  j  t | |  j d |  j   S(   Ni   (   R   RI   t   ngensR  (   R  R  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt
   from_dense  s    c         C  s(   |  j  t |  j |  | | |  j   S(   N(   R)  R   R'  R  (   R  t   ft   ct   i(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   
  s    c         C  sJ   |  j  t |  j |  |  j |  j d  j   | |  j d |  j   S(   Ni    i   (   R)  R   R'  R&  R  R(  R  (   R  R*  R+  R,  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   |  j  t |  j |  | | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  R,  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sJ   |  j  t |  j |  |  j |  j d  j   | |  j d |  j   S(   Ni    i   (   R)  R   R'  R&  R  R(  R  (   R  R*  R+  R,  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   |  j  t |  j |  | | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  R,  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sJ   |  j  t |  j |  |  j |  j d  j   | |  j d |  j   S(   Ni    i   (   R)  R   R'  R&  R  R(  R  (   R  R*  R+  R,  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R	   R'  R(  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR	     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R
   R'  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR
     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   !  s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   #  s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   %  s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   '  s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   )  s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  t   n(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   ,  s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R   R'  R  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   .  s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   1  s    c         C  s,   |  j  t |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   3  s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   6  s    c         C  s,   |  j  t |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   8  s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  t   g(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   ;  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   =  s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   @  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   B  s    c         C  s:   |  j  t |  j |  |  j |  |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  R.  t   h(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   E  s    c         C  sD   |  j  t |  j |  |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R.  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   G  s    c         C  s:   |  j  t |  j |  |  j |  |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  R.  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   I  s    c         C  sD   |  j  t |  j |  |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  R.  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   K  s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R    R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR    N  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R!   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR!   P  s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R"   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR"   S  s    c         C  s,   |  j  t |  j |  |  j d |  j   S(   Ni   (   R)  R#   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR#   U  s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  R$   R'  R  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR$   W  s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  R%   R'  R(  R  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR%   Y  s    c         C  sI   t  |  j |  |  j |  |  j  \ } } |  j |  |  j |  f S(   N(   R&   R'  R  R)  (   R  R*  R.  t   qt   r(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR&   \  s    -c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R'   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR'   _  s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R(   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR(   a  s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R)   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR)   c  s    c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } |  j |  |  j |  f S(   Ni   (   R*   R'  R(  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR*   f  s    7c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R+   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR+   i  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R,   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR,   k  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R-   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR-   m  s    c         C  sI   t  |  j |  |  j |  |  j  \ } } |  j |  |  j |  f S(   N(   R.   R'  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR.   p  s    -c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } |  j |  |  j |  f S(   Ni   (   R/   R'  R(  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR/   s  s    7c         C  sI   t  |  j |  |  j |  |  j  \ } } |  j |  |  j |  f S(   N(   R0   R'  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR0   v  s    -c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } |  j |  |  j |  f S(   Ni   (   R1   R'  R(  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR1   y  s    7c         C  sI   t  |  j |  |  j |  |  j  \ } } |  j |  |  j |  f S(   N(   R2   R'  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR2   }  s    -c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R3   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR3     s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R4   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR4     s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  R5   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR5     s    c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } |  j |  |  j |  f S(   Ni   (   R6   R'  R(  R  R)  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR6     s    7c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R7   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR7     s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R8   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR8     s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  R9   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR9     s    c         C  s   t  |  j |  |  j  S(   N(   R:   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR:     s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   R;   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR;     s    c         C  s   t  |  j |  |  j  S(   N(   R<   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR<     s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   R=   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR=     s    c         C  s+   |  j  t t t |  j |   |  j   S(   N(   R)  R>   t   listt   mapR'  R  (   R  t   polys(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR>     s    c         C  s5   |  j  t t t |  j |   |  j d |  j   S(   Ni   (   R)  R?   R2  R3  R'  R(  R  (   R  R4  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR?     s    c         C  s   t  |  j |  |  j  S(   N(   R@   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR@     s    c         C  sC   t  |  j |  |  j  } t | t  r; |  d j |  S| Sd  S(   Ni   (   RA   R'  R  R#  R2  R)  (   R  R*  t   LC(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRA     s    c         C  s   t  |  j |  |  j  S(   N(   RB   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRB     s    c         C  sC   t  |  j |  |  j  } t | t  r; |  d j |  S| Sd  S(   Ni   (   RC   R'  R  R#  R2  R)  (   R  R*  t   TC(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRC     s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   RD   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRD     s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   RE   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRE     s    c         C  s   t  |  j |   S(   N(   RF   R'  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRF     s    c         C  s   t  |  j |  |  j d  S(   Ni   (   RG   R'  R(  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRG     s    c         C  s    t  |  j |  | |  j d  S(   Ni   (   RH   R'  R(  (   R  R*  t   j(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRH     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  RJ   R'  R  (   R  R*  t   m(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRJ     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  RK   R'  R(  R  (   R  R*  R8  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRK     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  RM   R'  R  (   R  R*  R8  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRM     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  RN   R'  R(  R  (   R  R*  R8  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRN     s    c         C  s2   |  j  t |  j |  | | |  j d |  j   S(   Ni   (   R)  RO   R'  R(  R  (   R  R*  R8  R7  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRO     s    c         C  s2   |  j  t |  j |  | | |  j d |  j   S(   Ni   (   R)  RL   R'  R(  R  (   R  R*  R8  R7  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRL     s    c         C  s   t  |  j |  | |  j  S(   N(   RP   R'  R  (   R  R*  t   a(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRP     s    c         C  s9   t  |  j |  | |  j d |  j  } |  d j |  S(   Ni   (   RQ   R'  R(  R  R)  (   R  R*  R9  t   result(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRQ     s    (c         C  sA   t  |  j |  | | |  j d |  j  } |  j |  j |  S(   Ni   (   RR   R'  R(  R  R  R)  (   R  R*  R9  R7  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRR     s    +c         C  sD   t  |  j |  | | | |  j d |  j  } |  j |  j |  S(   Ni   (   RT   R'  R(  R  R  R)  (   R  R*  R8  R9  R7  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRT     s    .c         C  sW   t  |  j |  | |  j d |  j  } t | t  rO |  t |   j |  S| Sd  S(   Ni   (   RS   R'  R(  R  R#  R2  t   lenR)  (   R  R*  t   AR:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRS     s    (c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  RU   R'  R  (   R  R*  t   p(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRU     s    c         C  s<   |  j  t |  j |  |  d j |  |  j d |  j   S(   Ni   (   R)  RV   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRV     s    c         C  s/   |  j  t |  j |  | |  j d |  j   S(   Ni   (   R)  RW   R'  R(  R  (   R  R*  R=  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRW     s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  RX   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRX     s    c         C  s,   |  j  t |  j |  |  j d |  j   S(   Ni   (   R)  RY   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRY     s    c         C  sO   t  |  j |  |  j |  |  j  \ } } } | |  j |  |  j |  f S(   N(   R^   R'  R  R)  (   R  R*  R.  R+  t   Ft   G(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR^     s    0c         C  sY   t  |  j |  |  j |  |  j d |  j  \ } } } | |  j |  |  j |  f S(   Ni   (   R_   R'  R(  R  R)  (   R  R*  R.  R+  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR_     s    :c         C  sL   t  |  j |  j d  j   |  j  \ } } |  j |  |  j |  f S(   Ni   (   R`   R&  R  R'  R  R)  (   R  R*  R=  R0  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR`     s    0c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  Ra   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRa     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  Rb   R'  R  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRb     s    c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  Rc   R'  R  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRc     s    c         C  s:   |  j  t |  j |  |  j |  |  j |  |  j   S(   N(   R)  Rd   R'  R  (   R  R*  R=  R0  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRd     s    c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  Re   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRe     s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  Rf   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRf     s    c         C  s1   t  |  j |  |  j  } t t |  j |   S(   N(   Rg   R'  R  R2  R3  R)  (   R  R*  t
   components(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRg     s    c         C  s8   t  |  j |  |  j d |  j  } |  j   j |  S(   Ni   (   Rh   R'  R(  R  R  R)  (   R  R*  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRh     s    %c         C  s   t  |  j |  |  j  S(   N(   Ri   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRi     s    c         C  sd   t  |  j |  |  j d | \ } } | rK |  j d |  j j    } n |  } | | j |  f S(   Nt   convertR  (   Rj   R'  R  R  t   get_ringR)  (   R  R*  RA  R+  R>  R$  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRj     s
    'c         C  sn   t  |  j |  |  j d |  j d | \ } } | rU |  j d |  j j    } n |  } | | j |  f S(   Ni   RA  R  (   Rk   R'  R(  R  R  RB  R)  (   R  R*  RA  R+  R>  R$  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRk     s
    1c         C  s%   |  j  t |  j |  | |  j   S(   N(   R)  Rl   R'  R  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRl     s    c         C  sI   t  |  j |  |  j |  |  j  \ } } |  j |  |  j |  f S(   N(   Rm   R'  R  R)  (   R  R*  R.  t   sR/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRm   !  s    -c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } |  j |  |  j |  f S(   Ni   (   Rn   R'  R(  R  R)  (   R  R*  R.  RC  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRn   $  s    7c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   Ro   R'  R  R)  (   R  R*  R.  RC  t   tR/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRo   '  s    0c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   Rp   R'  R(  R  R)  (   R  R*  R.  RC  RD  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRp   *  s    :c         C  s.   |  j  t |  j |  |  j |  |  j   S(   N(   R)  Rq   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRq   .  s    c         C  s8   |  j  t |  j |  |  j |  |  j d |  j   S(   Ni   (   R)  Rr   R'  R(  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRr   0  s    c         C  s=   t  |  j |  |  j |  |  j  } t t |  j |   S(   N(   Rs   R'  R  R2  R3  R)  (   R  R*  R.  t   prs(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRs   3  s    'c         C  sG   t  |  j |  |  j |  |  j d |  j  } t t |  j |   S(   Ni   (   Rt   R'  R(  R  R2  R3  R)  (   R  R*  R.  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRt   6  s    1c         C  s=   t  |  j |  |  j |  |  j  } t t |  j |   S(   N(   Ru   R'  R  R2  R3  R)  (   R  R*  R.  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRu   9  s    'c         C  sG   t  |  j |  |  j |  |  j d |  j  } t t |  j |   S(   Ni   (   Rv   R'  R(  R  R2  R3  R)  (   R  R*  R.  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRv   <  s    1c         C  sI   t  |  j |  |  j |  |  j  \ } } t t |  j |   | f S(   N(   Rw   R'  R  R2  R3  R)  (   R  R*  R.  RE  t   sres(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRw   @  s    -c         C  sS   t  |  j |  |  j |  |  j d |  j  \ } } t t |  j |   | f S(   Ni   (   R{   R'  R(  R  R2  R3  R)  (   R  R*  R.  RE  RF  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR{   C  s    7c         C  s=   t  |  j |  |  j |  |  j  } t t |  j |   S(   N(   Rx   R'  R  R2  R3  R)  (   R  R*  R.  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRx   G  s    'c         C  sG   t  |  j |  |  j |  |  j d |  j  } t t |  j |   S(   Ni   (   R|   R'  R(  R  R2  R3  R)  (   R  R*  R.  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR|   J  s    1c         C  sI   t  |  j |  |  j |  |  j  \ } } | t t |  j |   f S(   N(   Ry   R'  R  R2  R3  R)  (   R  R*  R.  t   resRE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRy   N  s    -c         C  s`   t  |  j |  |  j |  |  j d |  j  \ } } |  d j |  t t |  j |   f S(   Ni   (   R}   R'  R(  R  R)  R2  R3  (   R  R*  R.  RG  RE  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR}   Q  s    7c         C  sN   t  |  j |  |  j |  |  j |  |  j d |  j  } |  d j |  S(   Ni   (   R~   R'  R  R(  R  R)  (   R  R*  R.  R=  RG  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR~   U  s    =c         C  sB   t  |  j |  |  j |  |  j d |  j  } |  d j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RG  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   X  s    1c         C  sB   t  |  j |  |  j |  |  j d |  j  } |  d j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RG  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   [  s    1c         C  s%   t  |  j |  |  j |  |  j  S(   N(   Rz   R'  R  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRz   _  s    c         C  sY   t  |  j |  |  j |  |  j d |  j  } t | t  rQ |  d j |  S| Sd  S(   Ni   (   R   R'  R(  R  R#  R2  R)  (   R  R*  R.  RG  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   a  s    1c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   h  s    c         C  sM   t  |  j |  |  j d |  j  } t | t  rE |  d j |  S| Sd  S(   Ni   (   R   R'  R(  R  R#  R2  R)  (   R  R*  t   disc(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   j  s    %c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   R'  R  R)  (   R  R*  R.  t   HR>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   q  s    0c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   R'  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   t  s    0c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   w  s    :c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   z  s    :c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   R'  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   }  s    0c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    :c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   R'  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    0c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    :c         C  sX   t  |  j |  |  j |  |  j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   R'  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    0c         C  sb   t  |  j |  |  j |  |  j d |  j  \ } } } |  j |  |  j |  |  j |  f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    :c         C  s4   t  |  j |  |  j |  |  j  } |  j |  S(   N(   R   R'  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    'c         C  s>   t  |  j |  |  j |  |  j d |  j  } |  j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    1c         C  s4   t  |  j |  |  j |  |  j  } |  j |  S(   N(   R   R'  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    'c         C  s4   t  |  j |  |  j |  |  j  } |  j |  S(   N(   R   R'  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    'c         C  s4   t  |  j |  |  j |  |  j  } |  j |  S(   N(   R   R'  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    'c         C  s>   t  |  j |  |  j |  |  j d |  j  } |  j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    1c         C  s>   t  |  j |  |  j |  |  j d |  j  } |  j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    1c         C  s>   t  |  j |  |  j |  |  j d |  j  } |  j |  S(   Ni   (   R   R'  R(  R  R)  (   R  R*  R.  RI  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    1c         C  s   t  |  j |  |  j  } | S(   N(   RZ   R'  R  (   R  R*  t   cont(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyRZ     s    c         C  s4   t  |  j |  |  j  \ } } | |  j |  f S(   N(   R\   R'  R  R)  (   R  R*  RJ  t   prim(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR\     s    !c         C  sM   t  |  j |  |  j d |  j  } t | t  rE |  d j |  S| Sd  S(   Ni   (   R   R'  R(  R  R#  R2  R)  (   R  R*  RJ  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    %c         C  sq   t  |  j |  |  j d |  j  \ } } t | t  rZ |  d j |  |  j |  f S| |  j |  f Sd  S(   Ni   (   R   R'  R(  R  R#  R2  R)  (   R  R*  RJ  RK  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    + c         C  s)   t  |  j |  |  j d |  j  } | S(   Ni   (   R[   R'  R(  R  (   R  R*  RJ  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR[     s    %c         C  s>   t  |  j |  |  j d |  j  \ } } | |  j |  f S(   Ni   (   R]   R'  R(  R  R)  (   R  R*  RJ  RK  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR]     s    +c   	      C  s   t  |  j |  |  j |  |  j d | } | sg | \ } } } } | | |  j |  |  j |  f S| \ } } |  j |  |  j |  f Sd  S(   Nt   include(   R   R'  R  R)  (	   R  R*  R.  RL  R:  t   cft   cgR>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    -"c   	      C  s   t  |  j |  |  j |  |  j d |  j d | } | sq | \ } } } } | | |  j |  |  j |  f S| \ } } |  j |  |  j |  f Sd  S(   Ni   RL  (   R   R'  R(  R  R)  (	   R  R*  R.  RL  R:  RM  RN  R>  R?  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    7"c         C  s\   t  |  j |  t t |  j |   |  j  } g  | D]! \ } } |  j |  | f ^ q7 S(   N(   R   R'  R2  R3  R  R)  (   R  R*  t   factorsR.  t   k(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    0c         C  sf   t  |  j |  t t |  j |   |  j d |  j  } g  | D]! \ } } |  j |  | f ^ qA S(   Ni   (   R   R'  R2  R3  R(  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    :c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   |  j  } t | | |  | |  | |  | |  | |  |  j  \ } }	 }
 } |  j |  |  j |	  |  j |
  |  j |  f S(   N(   R'  R   R  R)  (   R  R8  R*  R.  R/  RC  RD  t   DR?  RI  t   St   T(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    	Kc         C  sO   |  j  } t | | |  t t | |   | |  j  } t t |  j |   S(   N(   R'  R   R2  R3  R  R)  (   R  R=  R*  t   f_listt   lRQ  R4  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    	0c         C  sG   t  |  j |  |  j  } g  | D]! \ } } |  j |  | f ^ q" S(   N(   R   R'  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  |  j |  |  j d | S(   Nt   irreducible(   R   R'  R  (   R  R*  RV  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  | |  j  } |  j |  S(   N(   R   R  R)  (   R  R-  R>  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sE   t  |  j |  |  j  } | d  k r+ | St t |  j |   Sd  S(   N(   R   R'  R  t   NoneR2  R3  R)  (   R  R*  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  | | | |  j  S(   N(   R   R  (   R  t   Et   cst   ct(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c      	   C  s   |  d } g  | D]! \ } }	 | j  |  |	 f ^ q } |  d  }
 t t |
 j  |   } t |  j  |  | | | | | |  j d |  j  \ } } } |  j |  t t |
 j |   t t | j |   f S(   Ni   (   R'  R2  R3  R   R(  R  R)  (   R  R*  RS  RY  RX  RI  R<  t   mvRD  RP  t   uvt   HHt   CC(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    
.
=c         C  s@   t  t t |  j |   | | |  j  } t t |  j |   S(   N(   R   R2  R3  R'  R  R)  (   R  R>  R8  R=  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    *c         C  sY   t  t t |  j |   |  j |  | | | |  j d |  j  } t t |  j |   S(   Ni   (   R   R2  R3  R'  R(  R  R)  (   R  R>  R+  R<  R  R=  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    Cc   	      C  s   |  d  } |  d } t  t | j |   } t  t | j |   } t |  j |  | | | | |  j d |  j  } t  t |  j |   S(   Ni   (   R2  R3  R'  R   R(  R  R)  (	   R  R*  RI  R5  R<  R=  R\  R[  R:  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    

1c         C  sQ   t  |  j |  |  j d |  j d | d | } g  | D] } |  j |  ^ q8 S(   Ni   t   modt   seed(   R   R'  R(  R  R)  (   R  R*  R_  R`  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    1c         C  sG   t  |  j |  |  j  \ } } | g  | D] } |  j |  ^ q+ f S(   N(   R   R'  R  R)  (   R  R*  t   coeffRO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   #  s    !c         C  sS   t  |  j |  |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q+ f S(   N(   R   R'  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   '  s    !c         C  s]   t  |  j |  |  j d |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q5 f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   *  s    +c         C  sS   t  |  j |  |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q+ f S(   N(   R   R'  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   .  s    !c         C  s]   t  |  j |  |  j d |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q5 f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   1  s    +c         C  sS   t  |  j |  |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q+ f S(   N(   R   R'  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   5  s    !c         C  s]   t  |  j |  |  j d |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q5 f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   8  s    +c         C  sS   t  |  j |  |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q+ f S(   N(   R   R'  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   <  s    !c         C  sG   t  |  j |  |  j  } g  | D]! \ } } |  j |  | f ^ q" S(   N(   R   R'  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   ?  s    c         C  s]   t  |  j |  |  j d |  j  \ } } | g  | D]! \ } } |  j |  | f ^ q5 f S(   Ni   (   R   R'  R(  R  R)  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   C  s    +c         C  sQ   t  |  j |  |  j d |  j  } g  | D]! \ } } |  j |  | f ^ q, S(   Ni   (   R   R'  R(  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   F  s    %c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   J  s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   L  s    c         C  s1   t  |  j |  |  j  } t t |  j |   S(   N(   R   R'  R  R2  R3  R)  (   R  R*  t   seq(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   O  s    c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   S  s    c         C  s#   t  |  j |  |  j d |  j  S(   Ni   (   R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   U  s    c         C  sI   t  |  j |  |  j  \ } } } | |  j |  |  j   j |  f S(   N(   R   R'  R  R)  R  (   R  R*  RC  R>  t   R(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   X  s    $c         C  sS   t  |  j |  |  j d |  j  \ } } } | |  j |  |  j   j |  f S(   Ni   (   R   R'  R(  R  R)  R  (   R  R*  RC  R>  Rc  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   [  s    .c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   _  s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   a  s    c         C  s"   |  j  t |  j |  |  j   S(   N(   R)  R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   c  s    c         C  s,   |  j  t |  j |  |  j d |  j   S(   Ni   (   R)  R   R'  R(  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   e  s    c         C  sY   t  |  j |  |  j d | \ } } | g  | D]! \ } } |  j |  | f ^ q1 f S(   Nt   all(   R   R'  R  R)  (   R  R*  Rd  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   h  s    'c         C  sc   t  |  j |  |  j d |  j d | \ } } | g  | D]! \ } } |  j |  | f ^ q; f S(   Ni   Rd  (   R   R'  R(  R  R)  (   R  R*  Rd  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   k  s    1c         C  sY   t  |  j |  |  j d | \ } } | g  | D]! \ } } |  j |  | f ^ q1 f S(   NRd  (   R   R'  R  R)  (   R  R*  Rd  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   o  s    'c         C  sM   t  |  j |  |  j d | } g  | D]! \ } } |  j |  | f ^ q( S(   NRd  (   R   R'  R  R)  (   R  R*  Rd  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   r  s    !c         C  sc   t  |  j |  |  j d |  j d | \ } } | g  | D]! \ } } |  j |  | f ^ q; f S(   Ni   Rd  (   R   R'  R(  R  R)  (   R  R*  Rd  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   u  s    1c         C  sW   t  |  j |  |  j d |  j d | } g  | D]! \ } } |  j |  | f ^ q2 S(   Ni   Rd  (   R   R'  R(  R  R)  (   R  R*  Rd  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   x  s    +c         C  sG   t  |  j |  |  j  } g  | D]! \ } } |  j |  | f ^ q" S(   N(   R   R'  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR   |  s    c         C  sQ   t  |  j |  |  j d |  j  } g  | D]! \ } } |  j |  | f ^ q, S(   Ni   (   R   R'  R(  R  R)  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    %c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  |  j |  |  j  S(   N(   R   R'  R  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s"   t  |  j |  | |  j d | S(   Nt   fast(   R   R'  R  (   R  R*  t   MRe  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   t  |  j |  | |  j d | d | d | d | d | S(   Nt   epst   stepst   disjointRe  t   mobius(   R   R'  R  (   R  R*  Rf  Rg  Rh  Ri  Re  Rj  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  | | |  j d | d | d | d | S(   NRg  Rh  Ri  Re  (   R   R'  R  (   R  R*  RC  RD  Rg  Rh  Ri  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  | | |  j d | d | d | d | S(   NRg  Rh  Ri  Re  (   R   R'  R  (   R  R*  RC  RD  Rg  Rh  Ri  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s%   t  |  j |  |  j d | d | S(   NRg  Re  (   R   R'  R  (   R  R*  Rg  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  |  j d | d | d | d | d | S(   NRg  t   inft   supRe  Rj  (   R   R'  R  (   R  R*  Rg  Rk  Rl  Re  Rj  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  |  j d | d | d | d | d | S(   NRk  Rl  Rg  Re  Rj  (   R   R'  R  (   R  R*  Rk  Rl  Rg  Re  Rj  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  |  j d | d | d | d | d | S(   NRg  Rk  Rl  Re  t   blackbox(   R   R'  R  (   R  R*  Rg  Rk  Rl  Re  Rm  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  |  j d | d | d | d | d | S(   NRg  Rk  Rl  t   basisRe  (   R   R'  R  (   R  R*  Rg  Rk  Rl  Rn  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sF   t  t t |  j |   |  j d | d | d | d | d | d | S(   NRg  Rk  Rl  t   strictRn  Re  (   R   R2  R3  R'  R  (   R  R4  Rg  Rk  Rl  Ro  Rn  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s%   t  |  j |  |  j d | d | S(   NRk  Rl  (   R   R'  R  (   R  R*  Rk  Rl  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c      	   C  s+   t  |  j |  |  j d | d | d | S(   NRk  Rl  t   exclude(   R   R'  R  (   R  R*  Rk  Rl  Rp  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   t  |  j |  |  j d | d | d | d | S(   NRg  Rk  Rl  Rm  (   R   R'  R  (   R  R*  Rg  Rk  Rl  Rm  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   t  |  j |  |  j d | d | d | d | d | S(   NRg  Rk  Rl  Re  Rm  (   R   R'  R  (   R  R*  Rg  Rk  Rl  Re  Rm  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   t  |  j |  |  j d | d | d | d | S(   NRg  Rk  Rl  Re  (   R   R'  R  (   R  R*  Rg  Rk  Rl  Re  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s9   d d l  m } t t |  j | |  j d |  j    S(   Ni(   t   dmp_fateman_poly_F_1i   (   t   sympy.polys.specialpolysRq  t   tupleR3  R)  R(  R  (   R  Rq  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   fateman_poly_F_1  s    c         C  s9   d d l  m } t t |  j | |  j d |  j    S(   Ni(   t   dmp_fateman_poly_F_2i   (   Rr  Ru  Rs  R3  R)  R(  R  (   R  Ru  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   fateman_poly_F_2  s    c         C  s9   d d l  m } t t |  j | |  j d |  j    S(   Ni(   t   dmp_fateman_poly_F_3i   (   Rr  Rw  Rs  R3  R)  R(  R  (   R  Rw  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   fateman_poly_F_3  s    c         C  sA   t  g  |  j |  j   D]! } |  j j j | |  j  ^ q  S(   N(   R   R&  R'  R  t   domRA  (   R  R  R+  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   to_gf_dense  s    c         C  s&   |  j  t | |  j d |  j j   S(   Ni   (   R   RI   R(  R  Ry  (   R  R  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   from_gf_dense  s    c         C  s   t  |  j |   S(   N(   R   Rz  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  |  j |  |  j j  S(   N(   R   Rz  R  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   t  |  j |  |  j j  S(   N(   R   Rz  R  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   |  j  t |  j |    S(   N(   R{  R   Rz  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s%   |  j  t |  j |  |  j j   S(   N(   R{  R   Rz  R  R_  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   gf_trunc  s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt	   gf_normal  s    c         C  s%   |  j  t | |  j j |  j j   S(   N(   R{  R   R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s"   t  |  j |  |  j j d | S(   Nt	   symmetric(   R   Rz  R  R_  (   R  R*  R~  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   |  j  t | |  j j   S(   N(   R{  R   R  R_  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s"   t  |  j |  |  j j d | S(   NR~  (   R   Rz  R  R_  (   R  R*  R~  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   |  j  t |  j |  | |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   |  j  t |  j |  | |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   |  j  t |  j |  | |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   |  j  t |  j |  | |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sF   |  j  t |  j |  |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sF   |  j  t |  j |  |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  R/  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s7   |  j  t t t |  j |   |  j j |  j j   S(   N(   R{  R   R2  R3  Rz  R  R_  Ry  (   R  R>  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sU   t  |  j |  |  j |  |  j j |  j j  \ } } |  j |  |  j |  f S(   N(   R   Rz  R  R_  Ry  R{  (   R  R*  R.  R0  R1  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    9c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   |  j  t |  j |  | |  j j   S(   N(   R{  R   Rz  R  Ry  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   |  j  t |  j |  | |  j j   S(   N(   R{  R   Rz  R  Ry  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s1   |  j  t |  j |  | |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s=   |  j  t |  j |  | |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R-  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sd   t  |  j |  |  j |  |  j j |  j j  \ } } } |  j |  |  j |  |  j |  f S(   N(   R   Rz  R  R_  Ry  R{  (   R  R*  R.  R/  t   cfft   cfg(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    <c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   t  |  j |  | |  j j |  j j  S(   N(   R   Rz  R  R_  Ry  (   R  R*  R9  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s(   t  |  j |  | |  j j |  j j  S(   N(   R   Rz  R  R_  Ry  (   R  R*  R<  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s:   |  j  t |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R*  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  sF   |  j  t |  j |  |  j |  |  j |  |  j j |  j j   S(   N(   R{  R   Rz  R  R_  Ry  (   R  R.  R/  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    c         C  s   |  j  |  } |  j  |  } |  j  |  } |  j  |  } t | | | | | |  j j |  j j  \ } } |  j |  |  j |  f S(   N(   Rz  R   R  R_  Ry  R{  (   R  R9  t   bR+  R-  R*  t   Ut   V(    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     s    0c         C  s%   |  j  t | |  j j |  j j   S(   N(   R{  R  R  R_  Ry  (   R  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  "  s    c         C  s%   |  j  t | |  j j |  j j   S(   N(   R{  R  R  R_  Ry  (   R  R-  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  $  s    c         C  s%   t  |  j |  |  j j |  j j  S(   N(   R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  '  s    c         C  s%   t  |  j |  |  j j |  j j  S(   N(   R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  )  s    c         C  s%   t  |  j |  |  j j |  j j  S(   N(   R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  +  s    c         C  s%   t  |  j |  |  j j |  j j  S(   N(   R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  -  s    c         C  s.   |  j  t |  j |  |  j j |  j j   S(   N(   R{  R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  0  s    c         C  se   t  |  j |  |  j j |  j j d | \ } } | g  | D]! \ } } |  j |  | f ^ q= f S(   NRd  (   R  Rz  R  R_  Ry  R{  (   R  R*  Rd  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   gf_sqf_list2  s    3c         C  s%   t  |  j |  |  j j |  j j  S(   N(   R  Rz  R  R_  Ry  (   R  R*  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  6  s    c         C  sG   t  |  j |  |  j j |  j j  } g  | D] } |  j |  ^ q. S(   N(   R	  Rz  R  R_  Ry  R{  (   R  R*  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR	  8  s    'c         C  sS   t  |  j |  |  j j |  j j  } g  | D]! \ } } |  j |  | f ^ q. S(   N(   R
  Rz  R  R_  Ry  R{  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR
  <  s    'c         C  sG   t  |  j |  |  j j |  j j  } g  | D] } |  j |  ^ q. S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  R-  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  ?  s    'c         C  sS   t  |  j |  |  j j |  j j  } g  | D]! \ } } |  j |  | f ^ q. S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  C  s    'c         C  sG   t  |  j |  |  j j |  j j  } g  | D] } |  j |  ^ q. S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  R-  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  F  s    'c         C  sG   t  |  j |  |  j j |  j j  } g  | D] } |  j |  ^ q. S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  J  s    'c         C  sG   t  |  j |  |  j j |  j j  } g  | D] } |  j |  ^ q. S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  M  s    'c         C  sY   t  |  j |  |  j j |  j j d | \ } } | g  | D] } |  j |  ^ q= f S(   Nt   method(   R  Rz  R  R_  Ry  R{  (   R  R*  R  Ra  RO  R.  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  Q  s    3c         C  s_   t  |  j |  |  j j |  j j  \ } } | g  | D]! \ } } |  j |  | f ^ q7 f S(   N(   R  Rz  R  R_  Ry  R{  (   R  R*  Ra  RO  R.  RP  (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR  T  s    -N(*  t   __name__t
   __module__RW  R  R(  R  R  t   gensR  R  R  R  R  R   R&  R'  R)  R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   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   t   FalseRj   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]   t   TrueR   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   Rt  Rv  Rx  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  (    (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyR     sJ  						
																																																																																																																																																																																																																																																											N(   t   __doc__t
   __future__R    R   t   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?   t   sympy.polys.densebasicR@   RA   RB   RC   RD   RE   RF   RG   RH   RI   t   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   t   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   t   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   t   sympy.polys.rootisolationR   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   t   sympy.polys.sqfreetoolsR   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   t   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  t   sympy.utilitiesR  t   objectR  (    (    (    s8   lib/python2.7/site-packages/sympy/polys/compatibility.pyt   <module>   s  j [