+
    i-                        ^ RI Ht ^ RIHt ^ RIHtHt ^ RIHt ^ RI	H
t
 ^ RIHt ^ RIHt ^ RIHtHt ^ R	IHt ^ R
IHt ^ RIHt ^ RIHt ^ RIHt ^ RIHtHtHt ^ RI H!t!H"t"H#t#H$t$H%t%H&t&H't' ^ RI(H)t) ^ RI*H+t+ ^ RI,H-t-H.t. ^ RI/H0t0H1t1H2t2H3t3H4t4H5t5H6t6 ^ RI7H8t8 ^ RI9H:t:H;t;H<t<H=t= ^ RI>H?t?H@t@HAtAHBtBHCtCHDtD ^ RIEHFtF ^ RIGHHtHHItI ^ RIJHKtK ]K! R4      tL]K! R4      tM]L'       d7   ]LP                  ]LP                  . 4      P                  4      tQ]QP                  tSR tTR tUR tVR tWR  tXR! tYR" tZR# t[R$ t\R% t]R& t^R' t_R( t`R) taR* tbR+ tcR, tdR- teR. tfR/ tgR0 thR1 tiR2 tjR3 tkR4 tlR5 tmR6 tnR7# )8    )Sum)Mod)Equality
Unequality)Symbol)sqrt)	Piecewise)	polygamma)SiCi)Matrix)BlockMatrix)MatrixSymbol)Identity)lambdify)symbolsMinMax)xijabcd)Pow)MatrixSolve)	logaddexp
logaddexp2)log1pexpm1hypotlog10exp2log2Sqrt)Array)ArrayTensorProductArrayAddPermuteDimsArrayDiagonal)NumPyPrinterSciPyPrinter_numpy_known_constants_numpy_known_functions_scipy_known_constants_scipy_known_functions)convert_matrix_to_array)skipraises)import_modulenumpyjaxc                     \        4       p \        ^\        ^ 8  3R4      pV P                  V4      R8X  g   Q hV P                  R0 Rm/8X  g   Q hR# )z
NumPyPrinter needs to print Piecewise()'s choicelist as a list to avoid
breaking compatibility with numpy 1.8. This is not necessary in numpy 1.9+.
See gh-9747 and gh-9749 for details.
z?numpy.select([numpy.less(x, 0),True], [1,0], default=numpy.nan)r6   N)r   T>   nanlessselect)r,   r	   r   doprintmodule_imports)printerps     ]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/printing/tests/test_numpy.pytest_numpy_piecewise_regressionrA   &   sZ     nG1a!e*i(A??1IJ J J!!g/H%IIII    c                      \        \        \        4      p \        4       P	                  V 4      R 8X  g   Q h\        \        \        4      p\        4       P	                  V4      R8X  g   Q hR# )znumpy.logaddexp(a, b)znumpy.logaddexp2(a, b)N)r   r   r   r,   r<   r   )laelae2s     r@   test_numpy_logaddexprF   2   sQ    
Aq/C>!!#&*AAAAaD>!!$'+CCCCrB   c                    a \         '       g   \        R 4       \        \        \        ,          \        \
        \        34      p \        \
        \        \        3V R4      p^ ^
r2\         P                  R^^
4      o\         P                  V! W#S4      \        V3R l\        W#^,           4       4       4      4      '       g   Q h\        \        \        ,          \        \
        \        34      p \        \
        \        \        3V R4      p^ ^
r2\         P                  R^^
4      o\         P                  V! W#S4      \        V3R l\        W#^,           4       4       4      4      '       g   Q hR# )NumPy not installedr6   c              3   6   <"   T F  pSV,          x  K  	  R # 5iN .0i_x_s   & r@   	<genexpr>test_sum.<locals>.<genexpr>B   s     )O=Nr"((=Ns   c              3   4   <"   T F  qS,          x  K  	  R # 5irJ   rK   rL   s   & r@   rP   rQ   I   s     )N<Mbr''<Ms   N)npr3   r   r   r   r   r   r   linspaceallclosesumrange)sfa_b_rO   s       @r@   test_sumr]   9   s    2"#AFQ1IA!QAw'A	RR	 B;;q}c)OU2Av=N)O&OPPPPAEAq!9A!QAw'A	RR	 B;;q}c)NE"1f<M)N&NOOOOrB   c                    aaa \         '       g   \        R 4       \        \        \        ,           \
        ,          \
        \        \        3\        \        \        34      p \        \        \        \        \        \        3V R4      p^ ^
r2^^uoo\         P                  R^^
4      o\         P                  V! W#SSS4      \        VVV3R l\        W#^,           4       4       4      4      '       g   Q hR# )rH   r6   c              3   x   <"   T F/  p\        SS^,           4       F  pSV,           V,          x  K  	  K1  	  R# 5i)   N)rX   )rM   rN   j_c_d_rO   s   &  r@   rP   %test_multiple_sums.<locals>.<genexpr>W   s6     b4EbPUVXZ\_`Z`Pa"BGr>>Pa>4Es   7:NrS   )rT   r3   r   r   r   r   r   r   r   r   r   rU   rV   rW   rX   )rY   rZ   r[   r\   rb   rc   rO   s       @@@r@   test_multiple_sumsre   L   s    2"#QUaK!QQ1I.A!Q1a!W-AFB	RR	 B;;qR,bE"1f4Ebbd d d drB   c                  z   \         '       g   \        R 4       \        R^^4      p \        R^^4      p\        W,          4      p\	        W3VR4      p\         P                  ^^.^^..4      p\         P                  ^R.R^..4      pV! WE4      \         P                  WE4      8H  P                  4       '       g   Q hR# )rH   MNr6   NrS   )rT   r3   r   r2   r   arraymatmulall)rg   rh   cgrZ   mambs         r@   test_codegen_einsumrp   Z   s    2"#S!QAS!QA	 	'B!W%A	Aq6Aq6"	#B	Ab6B7#	$BbI2**//1111rB   c            
      0   \         '       g   \        R 4       \        R^^4      p \        R^^4      p\        R^^4      p\        R^^4      p\         P                  ^^.^^..4      p\         P                  ^R.R	^..4      p\         P                  ^^ .^^..4      p\         P                  ^R	.^^..4      p\	        W4      p\        W3VR4      p	V	! WE4      \         P                  V^ ^.V^^.4      8H  P                  4       '       g   Q h\        W4      p\        W3VR4      p	V	! WE4      WE,           8H  P                  4       '       g   Q h\        WV4      p\        WV3VR4      p	V	! WEV4      WE,           V,           8H  P                  4       '       g   Q h\        WW#4      p\        WW#3VR4      p	V	! WEWg4      WE,           V,           V,           8H  P                  4       '       g   Q h\        V ^^ .4      p\        V 3VR4      p	V	! V4      VP                  8H  P                  4       '       g   Q h\        \	        W4      . R
O4      p\        W3VR4      p	V	! WE4      \         P                  \         P                  V^ ^.V^^.4      R
4      8H  P                  4       '       g   Q h\        \	        W4      R4      p\        W3VR4      p	V	! WE4      \         P                  \         P                  V^ ^.V^^.4      ^^R7      8H  P                  4       '       g   Q hR# )rH   rg   rh   PQr6   )axis1axis2Nri   rS   )r`         r   )r`   rv   )rT   r3   r   rj   r(   r   einsumrl   r)   r*   T	transposer+   diagonal)
rg   rh   rr   rs   rn   ro   mcmdrm   rZ   s
             r@   test_codegen_extrar~   i   s   2"#S!QAS!QAS!QAS!QA	Aq6Aq6"	#B	Ab6B7#	$B	Aq6Aq6"	#B	Ab6Aq6"	#B	A	!B!W%AbI21vrAq6::??AAAA	!B!W%AbI##%%%%	!	B!B(AbbMRU2X%**,,,,	!	B!r7+Abbr",113333	QA	B!r7#AbERTTM    	'-|	<B!W%AbIbiiQFBA&GVV[[]]]]	)!/	8B!W%AbIRYYrAq621v%FaWXYY^^````rB   c                  d   \         '       g   \        R 4       \        \        ^4      p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q h\        \        ^4      p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q h\        ^8  p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q h\        ^8*  p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q h\        ^8  p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q h\        ^8  p \	        \        3V 4      p\         P                  . RO4      p\         P                  V! V4      . RO4      '       g   Q hR# )	rH   N)r   r`   rv   )FTF)TFT)TFF)TTF)FFT)FTT)rT   r3   r   r   r   rj   array_equalr   )erZ   rO   s      r@   test_relationalr      s   2"#AA!qA	)	B>>!B%!566661aA!qA	)	B>>!B%!45555	
QA!qA	)	B>>!B%!56666	
aA!qA	)	B>>!B%!45555	
QA!qA	)	B>>!B%!56666	
aA!qA	)	B>>!B%!45555rB   c                  V   \         '       g   \        R 4       \        \        \        4      p \        \        \        3V 4      p\         P                  . RO4      p^p\         P                  V! W#4      . RO4      '       g   Q h\         P                  . RO4      p\         P                  . RO4      p\         P                  V! W#4      . RO4      '       g   Q h\         P                  . RO4      p\         P                  . RO4      p\         P                  V! W#4      . RO4      '       g   Q hR# )rH   N)r   r`   rv   rw   )r   r`   r   r`   )rv   rv   rv   rv   )rv   rw         )r   r   r   r   )rT   r3   r   r   r   r   rj   r   )r   rZ   r[   r\   s       r@   test_modr      s    2"#Aq	A!QA	,	B	
B>>!B)\2222	,	B	,	B>>!B)\2222	,	B	,	B>>!B)\2222rB   c                      \         '       g   \        R 4       \        ^RRR7      p \        . V R4      pV! 4       R8X  g   Q hR# )rH   F)evaluater6   g      ?NrS   )rT   r3   r   r   )exprrZ   s     r@   test_powr      s:    2"#q"u%DT7#A3#::rB   c                      \         '       g   \        R 4       \        \        3\	        \        4      R4      p \        V ! R4      R,
          R,
          4      R\        ,          8:  g   Q hR# )rH   r6   g|=g#B;N)rT   r3   r   r   r!   absNUMPY_DEFAULT_EPSILONrZ   s    r@   
test_expm1r      sK    2"#!uQx)Aqx%%'(E4I,IIIIrB   c                      \         '       g   \        R 4       \        \        3\	        \        4      R4      p \        V ! R4      R,
          4      R\        ,          8:  g   Q hR# )rH   r6   g>N}a+N)rT   r3   r   r   r    r   r   r   s    r@   
test_log1pr      sF    2"#!uQx)Aqx% E,A$AAAArB   c            	          \         '       g   \        R 4       \        \        \        \
        3\        \        \
        4      R4      ! ^^4      ^,
          4      \        8:  g   Q hR# rH   r6   N)rT   r3   r   r   r   r   r"   r   rK   rB   r@   
test_hypotr      sC    2"#xAaW5a;a?@DYYYYrB   c                      \         '       g   \        R 4       \        \        \        3\        \        4      R4      ! ^d4      ^,
          4      \        8:  g   Q hR# r   )rT   r3   r   r   r   r#   r   rK   rB   r@   
test_log10r      s=    2"#xeAh059:>SSSSrB   c                      \         '       g   \        R 4       \        \        \        3\        \        4      R4      ! ^4      ^ ,
          4      \        8:  g   Q hR# r   )rT   r3   r   r   r   r$   r   rK   rB   r@   	test_exp2r      s=    2"#xd1gw/2R78<QQQQrB   c                      \         '       g   \        R 4       \        \        \        3\        \        4      R4      ! R4      ^,
          4      \        8:  g   Q hR# )rH   r6      N)rT   r3   r   r   r   r%   r   rK   rB   r@   	test_log2r      s=    2"#xd1gw/4q89=RRRRrB   c                      \         '       g   \        R 4       \        \        \        3\        \        4      R4      ! ^4      ^,
          4      \        8:  g   Q hR# r   )rT   r3   r   r   r   r&   r   rK   rB   r@   	test_Sqrtr      =    2"#xd1gw/2Q67;PPPPrB   c                      \         '       g   \        R 4       \        \        \        3\        \        4      R4      ! ^4      ^,
          4      \        8:  g   Q hR# r   )rT   r3   r   r   r   r   r   rK   rB   r@   	test_sqrtr     r   rB   c                     \         '       g   \        R 4       \        R^^4      p \        R^^4      pV R,          V,          V,           p\        W4      V,           p\	        W3V4      p\	        W3V4      p\         P                  . RO. RO. RO.4      p\         P                  P                  V4      ^8X  g   Q h\         P                  . RO4      p\         P                  V! Wg4      V! Wg4      4      '       g   Q hR# )	rH   rg   r   NrS   r`   rv   rw   )rw   rv   r   )r         )rw   r   r   )	rT   r3   r   r   r   rj   linalgmatrix_rankrV   )rg   r   r   matsolve_exprrZ   
f_matsolvem0x0s           r@   test_matsolver     s    2"#S!QAS!QAr7Q;?D%)M!A1&-0J	9i3	4B99  $)))	)	B;;z")1R95555rB   c                  $   \         '       g   \        R 4       \        R^
^4      p \        R^
^4      p\        R^
^4      p\        R^
^4      p\        W.W#..4      pVP                  R8X  g   Q h\        4       pVP                  V4      R8X  g   Q hR# )rH   a_1a_2a_3a_4z%numpy.block([[a_1, a_2], [a_3, a_4]])N)   r   )rT   r3   r   r   shaper,   r<   )r   r   r   r   Ar>   s         r@   
test_16857r      s    2"#
ub!
$C
ub!
$C
ub!
$C
ub!
$CcZ#,-A77gnG??1!HHHHrB   c                    aa \         '       g   \        R 4       \        R^^4      p \        W \	        ^4      ,           4      p\         P                  ^^.^^..4      p\         P                  ^^.^^..4      pV! V4      V8H  P                  4       '       g   Q h^ RIHp V! RRR7      o\        RSS4      o\        \        VV3R l4       R# )rH   rg   )r   nT)integerc                  <   < \        S S \        S4      ,           4      # rJ   )r   r   )rh   r   s   r@   <lambda>"test_issue_17006.<locals>.<lambda>>  s    AO(DrB   N)rT   r3   r   r   r   rj   rl   sympy.core.symbolr   r4   NotImplementedError)rg   rZ   rn   mrr   rh   r   s        @@r@   test_issue_17006r   /  s    2"#S!QAO$A	Aq6Aq6"	#B	Aq6Aq6"	#BbERK)T"AS!QA
 DErB   c                     \         '       g   \        R 4       \        R4      w  rp\        WV4      \	        WV4      ,           p\        WV3VR4      pRRre\         P                  P                  V4      \         P                  P                  V4      r\        P                  V! V!  V! V!  4      '       g   Q h\        P                  V! V!  V! V!  4      '       g   Q hR# )zJax not installedzx y zr7   Nr   )r   r   r   )
r7   r3   r   r   r   r   r6   asarrayrT   rV   )	r   yzr   funcinput_tuple1input_tuple2input_array1input_array2s	            r@   test_jax_tuple_compatibilityr   @  s    3 !gGA!qQ<#aA,&DQ1ItU+D!*I,!$!2!2<!@#))BSBST`Ba,;;t\*D,,?@@@@;;t\*D,,?@@@@rB   c                  N   \        4       p V P                  \        ^^.^^..4      4      R8X  g   Q hV P                  \        ^^.4      4      R8X  g   Q hV P                  \        . R
O..4      4      R8X  g   Q hV P                  \        . R4      4      R8X  g   Q hV P                  \        . R4      4      R8X  g   Q hV P                  \        . R4      4      R8X  g   Q hV P                  \        . R4      4      R8X  g   Q hV P                  \        ^.R4      4      R8X  g   Q hR	# )r`   numpy.array([[1, 2], [3, 5]])znumpy.array([1, 2])znumpy.array([[[1, 2, 3]]])znumpy.zeros((0,))numpy.zeros((0, 0))numpy.zeros((0, 1))numpy.zeros((1, 0))znumpy.array(1)Nr   )r   )r   r   )r   r`   )r`   r   rK   )r,   r<   r'   r?   s    r@   test_numpy_arrayr   L  s   A99UQFQF+,-1PPPP99UAq6]#'<<<<99UYK=)*.JJJJ99U2t_%)<<<<99U2v&'+@@@@99U2v&'+@@@@99U2v&'+@@@@99UA3^$(8888rB   c                     \        4       p V P                  \        ^^.^^..4      4      R8X  g   Q hV P                  \        ^^.4      4      R8X  g   Q hV P                  \        ^ ^ . 4      4      R8X  g   Q hV P                  \        ^ ^. 4      4      R8X  g   Q hV P                  \        ^^ . 4      4      R8X  g   Q hR# )r`   r   znumpy.array([[1], [2]])r   r   r   N)r,   r<   r   r   s    r@   test_numpy_matrixr   W  s    A99VaVaV,-.2QQQQ99VQF^$(AAAA99VAq"%&*????99VAq"%&*????99VAq"%&*????rB   c                      \         R ,          R8X  g   Q h\         R,          R8X  g   Q h\        R,          R8X  g   Q h\        R,          R8X  g   Q hR# )	NaNz	numpy.nan
EulerGammaznumpy.euler_gammaacosznumpy.arccoslogz	numpy.logN)r.   r/   rK   rB   r@   test_numpy_known_funcs_constsr   _  sO    !%(K777!,/3FFFF!&)^;;;!%(K777rB   c                      \         R ,          R8X  g   Q h\         R,          R8X  g   Q h\        R,          R8X  g   Q h\        R,          R8X  g   Q hR# )	GoldenRatiozscipy.constants.golden_ratioPizscipy.constants.pierfzscipy.special.erf	factorialzscipy.special.factorialN)r0   r1   rK   rB   r@   test_scipy_known_funcs_constsr   f  sR    !-04RRRR!$'+????!%(,????!+.2KKKKrB   c                  j    \        4       p \        V R 4      '       g   Q h\        V R4      '       g   Q hR# )_print_acos
_print_logN)r,   hasattr)prntrs    r@   test_numpy_print_methodsr   m  s/    NE5-((((5,''''rB   c                     \        4       p \        V R 4      '       g   Q h\        V R4      '       g   Q h\        V R4      '       g   Q h\        V R4      '       g   Q h\        V R4      '       g   Q h\        RRRR7      p\        RRR	7      pV P                  \	        W4      4      R
8X  g   Q hV P                  \        V4      4      R8X  g   Q hV P                  \        V4      4      R8X  g   Q hR# )r   r   
_print_erf_print_factorial_print_chebyshevtkT)r   nonnegativer   )realzscipy.special.polygamma(k, x)zscipy.special.sici(x)[0]zscipy.special.sici(x)[1]N)r-   r   r   r<   r
   r   r   )r   r   r   s      r@   test_scipy_print_methodsr   r  s    NE5-((((5,''''5,''''5,----5-....sDd3AsA==1)-LLLL==A#======A#====rB   N)osympy.concrete.summationsr   sympy.core.modr   sympy.core.relationalr   r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser	   'sympy.functions.special.gamma_functionsr
   'sympy.functions.special.error_functionsr   r   sympy.matricesr   &sympy.matrices.expressions.blockmatrixr   "sympy.matrices.expressions.matexprr   "sympy.matrices.expressions.specialr   sympy.utilities.lambdifyr   sympyr   r   r   	sympy.abcr   r   r   r   r   r   r   
sympy.corer   sympy.codegen.matrix_nodesr   sympy.codegen.numpy_nodesr   r   sympy.codegen.cfunctionsr    r!   r"   r#   r$   r%   r&   sympy.tensor.arrayr'   0sympy.tensor.array.expressions.array_expressionsr(   r)   r*   r+   sympy.printing.numpyr,   r-   r.   r/   r0   r1   3sympy.tensor.array.expressions.from_matrix_to_arrayr2   sympy.testing.pytestr3   r4   sympy.externalr5   rT   r7   finforj   dtypedeafult_float_infoepsr   rA   rF   r]   re   rp   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   rK   rB   r@   <module>r     sJ   )  8 $ 9 : = < ! > ; 7 - # # ) ) )  2 ; Q Q Q $ K K W - (7E"((2,"4"45.22
JDP&d2'aT&6R3(JBZ
TRSQQ6*IF"
A	9@8L(
>rB   