+
    iM                         ^ RI Ht ^ RIHtHt ^ RIHt ^ RIHt ^ RI	H
t
Ht ^ RIHtHt ^ RIHtHt ^ RIHt ^ R	IHtHtHtHtHt ^ R
IHt ^ RIHt R tR tR t R t!R t"R t#R t$R t%R# )    )x)IRational)S)sqrt)Polycyclotomic_poly)FFQQ)DomainMatrixDM)DMRankError)AlgIntPowerscoeff_search extract_fundamental_discriminantisolatesupplement_a_subspace)IntervalPrinter)raisesc                    aaa \        \        ^4      4      p \        V 4      o\        \        V3R l4       \        ^
4       F  pV^,          oS^8  dp   SV,          oSS,          ^8X  dU   \        ;QJ d)    VV3R l\        ^4       4       F  '       d   K   RM	  RM! VV3R l\        ^4       4       4      '       g   Q hK  SV,          R.^,          8X  d   K  Q h	  R# )   c                     < S R,          # )    )zeta_pows   k/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/polys/numberfields/tests/test_utilities.py<lambda>&test_AlgIntPowers_01.<locals>.<lambda>   s	    x|    c              3   L   <"   T F  qS8w  g   K  SV,          ^ 8H  x  K  	  R# 5i)r   Nr   ).0iacs   & r   	<genexpr>'test_AlgIntPowers_01.<locals>.<genexpr>   s     $K1FYQqTQYs   $$FTNr   )r   r	   r   r   
ValueErrorrangeall)Ter$   r%   r   s     @@@r   test_AlgIntPowers_01r-      s    _Q AAH
:+,2YEq5AQ419$Ka$K$Ka$K!K!KKK!KA;2$(*** r    c                     \        \        ^,          ^\        ^,          ,          ,           ^\        ,          ,           ^,           4      p ^p\        W4      p\        ^
4       F  pW#,          p\        \        4      V,          V ,          \        \        ^,          4      ,           P                  P                  4       R,          p\        V4       Uu. uF  qfV,          NK  	  ppWG8X  d   K  Q h	  R# u upi )   :r   NNN)r   r   r   r)   repto_listreversed)r+   m	theta_powr,   computedcoeffsr%   expecteds           r   test_AlgIntPowers_02r8      s    QTAadF]QqS 1$%A	AQ"I2Y<q'1*q.41:-22::<R@#+F#34#3aEE#34###	  5s   C1c                      . p \        ^^4      p\        V4       F  w  r#V P                  V4       V^8X  g   K   M	  V ^^.^^ .^R.^ ^.^^.^^.^^ .^R.^R.^^.^R.^ ^.^^..8X  g   Q hR# )   Nr   )r   	enumerateappend)Csearchr#   r%   s       r   test_coeff_searchr@   )   s    
A!QF&!	7 " !Q!Q!R1a&1a&1a&1a&1b'TUWYSZ]^`a\befhjdknoqrmsvwyzu{||||r    c                  (   \        \        R  4       \        \        R 4       ^ / ^ ^/3^/ / 3^^^// 3R^^R^// 3^^^^^// 3^$/ ^^^^/3^-^^/^^/3^0^^^^/^^/3R^^/^^^^/33	p V  F#  w  rp\        V4      w  rEWB8X  g   Q hWS8X  d   K#  Q h	  R# )c                      \        ^4      # )r:   r   r   r    r   r   7test_extract_fundamental_discriminant.<locals>.<lambda>5   
    ?Br    c                      \        ^4      # )r/   rC   r   r    r   r   rD   6   rE   r    ie  Nir   )r   r(   r   )casesr$   
D_expected
F_expectedDFs         r   %test_extract_fundamental_discriminantrL   3   s    
:BC
:BC 
BA	
B	
QFB	aB]B	aAq\2	R!Q1	aVaV	aAq\Aq6"	1v1a|$
E &+!z/2 &+r    c                     \        . RO. RO.\        4      P                  4       p \        V 4      pVR,          V 8X  g   Q hVR,          \        P
                  ! ^\        4      P                  4       R,          8X  g   Q hV P                  \        ^4      4      p \        V 4      pVR,          V 8X  g   Q hVR,          \        P
                  ! ^\        ^4      4      P                  4       R,          8X  g   Q hR# )r   N)r      r   )r:   r/      )NNN:Nr:   N)rP   r:   )rP   r   )rP   r   )	r   r   	transposer   r   eyeto_dense
convert_tor
   )MBs     r   test_supplement_a_subspace_1rW   I   s    
Iy!2&002A 	a AU8q==T7l&&q"-668>>>> 	
RUAa AU8q== T7l&&q"Q%099;DAAAAr    c                      \        . RO. RO.\        4      P                  4       p \        \        4      ;_uu_ 4        \        V 4       RRR4       R#   + '       g   i     R# ; i)r   N)r   r   r   )r:   r   r   )r   r   rQ   r   r   r   )rU   s    r   test_supplement_a_subspace_2rY   [   s>    
Iy!2&002A			a  
			s   AA#	c                      \        4       p V P                  \        \        ^^4      ,          4      R8X  g   Q hV P                  \	        \        4      4      R8X  g   Q hR# )r   zx**(mpi('1/3'))zx**(mpi('1/2'))N)r   doprintr   r   r   )ips    r   test_IntervalPrinterr]   a   sI    		B::a!Q'(,====::d1g"3333r    c                  ,   \        ^4      R8X  g   Q h\        \        P                  4      \        P                  \        P                  38X  g   Q h\        \        ^4      4      R8X  g   Q h\        \        ^4      ) 4      R8X  g   Q h\        \        ^4      \	        ^^d4      R7      \	        ^^4      \	        ^^4      38X  g   Q h\        \        ^4      ) \	        ^^d4      R7      \	        R^4      \	        R^4      38X  g   Q h\        \        R 4       R# )	r   )epsc                       \        \        4      # )N)r   r   r   r    r   r   test_isolate.<locals>.<lambda>q   s    
r    N)r   r   )r   r:   )r;   r   ii)r   r   Halfr   r   r   NotImplementedErrorr   r    r   test_isolaterd   g   s    1:166?qvvqvv....47v%%%DG8(((47C 01hr26FQSUWHX5YYYYDG8!S!12xR7H(SVXZJ[6\\\\
 23r    N)&	sympy.abcr   sympy.core.numbersr   r   sympy.core.singletonr   (sympy.functions.elementary.miscellaneousr   sympy.polysr   r	   sympy.polys.domainsr
   r   sympy.polys.matricesr   r   sympy.polys.matrices.exceptionsr   "sympy.polys.numberfields.utilitiesr   r   r   r   r   sympy.printing.lambdareprr   sympy.testing.pytestr   r-   r8   r@   rL   rW   rY   r]   rd   r   r    r   <module>rp      sY     , " 9 - & 1 7  6 '
+$},B$!4
4r    