+
    iqH                     r   ^ RI HtHtHtHtHtHtHtHtH	t	H
t
HtHtHtHtHtHtHtHtHtHtHtHt ^ RIHt ^ RIHtHtHtHtHtHtH t H!t!H"t"H#t#H$t$H%t%H&t&H't'H(t(H)t)H*t*H+t+H,t,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5H6t6H7t7H8t8H9t9H:t: ^ RIH;t;H<t<H=t=H>t>H?t?H@t@HAtAHBtBHCtCHDtDHEtEHFtFHGtGHHtHHItIHJtJHKtKHLtLHMtMHNtNHOtOHPtPHQtQHRtR ^ RISHTtTHUtU ^ RIVHWtW ^ RIXHYtYHZtZH[t[H\t\H]t]H^t^H_t_ ^ RI`HataHbtbHctcHdtdHeteHftfHgtgHhthHitiHjtjHktkHltl ^ R	ImHntnHotoHptpHqtqHrtr ^ R
IsHtttHutuHvtvHwtwHxtxHytyHztzH{t{H|t|H}t}H~t~HtHtHtHt ^ RIHtHt ]! R4      w  tttR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR tR t]UR 4       tR  tR! tR" tR# tR$ tR% tR& tR' tR( tR) tR* tR+ tR, tR- tR. tR/ tR0 tR1 tR2 tR3 tR4 tR5 tR6 tR7 tR8# )9    )SpioosymbolsFunctionRationalIntegerTupleSymbol
EulerGammaGoldenRatioCatalanLambdaMulPowModEqNeLeLtGtGe)MatrixSolve)!argatan2	bernoullibetaceiling
chebyshevu
chebyshevt	conjugate
DiracDeltaexpexpint	factorialfloorharmonic	HeavisideimlaguerreLambertWlogMaxMin	PiecewisepolylogreRisingFactorialsignsincsqrtzetabinomiallegendredirichlet_eta
riemann_xi)sincostancotseccscasinacosacotatanasecacscsinhcoshtanhcothcschsechasinhacoshatanhacothasechacsch)raisesXFAIL)implemented_function)eyeMatrixMatrixSymbolIdentityHadamardProductSparseMatrixHadamardPower)jnynbesseljbesselybesselibesselkhankel1hankel2airyaiairybiairyaiprimeairybiprime)gamma
lowergamma
uppergammaloggamma	polygamma)ChiCierferfcerfierfcinverfinvfresnelcfresnelsliShiSiLierf2Ei)octave_coder}   zx,y,zc                  r    \        \        ^C4      4      R8X  g   Q h\        \        R4      4      R8X  g   Q hR# )C   67z-1N)mcoder	        ^/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/printing/tests/test_octave.pytest_Integerr   "   s0    %%%%%%r   c                     \        \        ^^4      4      R8X  g   Q h\        \        ^^	4      4      R8X  g   Q h\        \        ^R4      4      R8X  g   Q h\        \        RR4      4      R8X  g   Q h\        \        \        ^^4      ,           4      R8X  g   Q h\        \        ^^4      \        ,          4      R8X  g   Q hR# )	   z3/72z-3/7zx + 3/7z3*x/7Ni)r   r   xr   r   r   test_Rationalr   '   s    !Q E)))"a!S(((!R!V+++"b!"e+++Xa^#$	111!Q!"g---r   c                     \        \        \        \        4      4      R 8X  g   Q h\        \	        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q hR# )zx == yzx != yzx <= yzx < yzx > yzx >= yN)	r   r   r   yr   r   r   r   r   r   r   r   test_Relationalr   0   s    Aq?h&&&Aq?h&&&Aq?h&&&Aq?g%%%Aq?g%%%Aq?h&&&r   c                     \        \        \        4      \        \        4      ,          4      R 8X  g   Q h\        \	        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        4      4      R	8X  g   Q h\        \        \        4      4      R
8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q hR# )zsin(x).^cos(x)zsign(x)zexp(x)zlog(x)zfactorial(x)zfloor(x)zatan2(y, x)z
beta(x, y)zpolylog(x, y)zharmonic(x)zbernoulli(x)zbernoulli(x, y)zlegendre(x, y)N)r   r;   r   r<   r3   r#   r,   r%   r&   r   r   r   r0   r'   r   r8   r   r   r   test_Functionr   9   s?   Q3q6!"&6666a>Y&&&Q=H$$$Q=H$$$1.000q?j(((q!...a,,,A?222!...1.0001a!%6666!Q $4444r   c                     \        \        \        4      4      R 8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \	        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        \        4      4      R8X  g   Q h\        \        \        4      4      R	8X  g   Q h\        \        \        4      4      R
8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \        \        4      4      R8X  g   Q h\        \!        \        4      4      R8X  g   Q h\        \#        \        4      4      R8X  g   Q h\        \%        \        \        4      4      R8X  g   Q h\        \'        \        \        4      4      R8X  g   Q h\        \)        \        4      4      R8X  g   Q h\        \)        \        ^4      4      R8X  g   Q h\        \+        \        4      4      R8X  g   Q h\        \+        \        \        4      4      R8X  g   Q h\        \-        \        \        4      4      R8X  g   Q h\        \/        \        \        4      4      R8X  g   Q hR# )zabs(x)zceil(x)zangle(x)zimag(x)zreal(x)zconj(x)zchebyshevT(y, x)zchebyshevU(y, x)zlaguerreL(x, y)z
coshint(x)z
sinhint(x)z	cosint(x)z	sinint(x)z	logint(x)z
gammaln(x)z	psi(x, y)zpochhammer(x, y)zdirac(x)zdirac(3, x)zheaviside(x, 1/2)zheaviside(x, y)zbincoeff(x, y)z	mod(x, y)N)r   absr   r   r   r)   r1   r!   r    r   r   r*   rn   rx   ro   ry   rw   rl   rm   r2   r"   r(   r7   r   r   r   r   test_Function_change_namer   I   s'   Q=H$$$	)))Q=J&&&A<9$$$A<9$$$1)+++Aq!"&8888Aq!"&8888!Q $5555Q=L(((Q=\)))A<;&&&A<K'''A<K'''!,...1a![000A&'+====A:---Aq!"m3331"55551a!%6666!Q $4444Q{***r   c                  $   \        \        \        \        4      \	        \        \        4      ,           4      R 8X  g   Q h\        \        \        \        \
        4      4      R8X  g   Q h\        \	        \        \        \
        4      4      R8X  g   Q hR# )zmax(x, y) + min(x, y)zmax(x, max(y, z))zmin(x, min(y, z))N)r   r-   r   r   r.   zr   r   r   test_minmaxr   c   s_    QSAY&'+BBBBQ1"5555Q1"5555r   c                  ~   \        \        ^,          4      R8X  g   Q h\        \        \        ^,          ,          4      R8X  g   Q h\        \        \        ^^4      ,          4      R8X  g   Q h\	        R\        \        ^\        ,          4      4      p \        ^V ! \        4      R,          \        \        \        ,          ,
          ,          ,          \        ^,          \        ,           ,          4      R8X  g   Q h\        \        R\        \        \        \        \        RR7      RRR7      RR7      4      R	8X  g   Q hR
# )r   zx.^3z	x.^(y.^3)zx.^(2/3)gg      @z"(3.5*2*x).^(-x + y.^x)./(x.^2 + y)F)evaluatez-2*x./(y.*y)Nr   )r   r   r   r   rU   r   r   r   )r   s    r   test_Powr   i   s    A;&   QT{***HQN"#z111S&AaC.1AAaDHAqD))1a4!845,- - - RCAa 7eL9>@ ADRS S Sr   c                      \        \        \        ,          4      R 8X  g   Q h\        \        \        ,           4      R8X  g   Q h\        \        \        ,
          4      R8X  g   Q h\        \        ) 4      R8X  g   Q hR# )x.*yzx + yzx - yz-xN)r   r   r   r   r   r   test_basic_opsr   u   sX    1:Q<7"""Q<7"""!9r   c                  X   \        ^\        ,          4      R8X  g   Q h\        \        R,          4      \        \        R	,          4      u;8X  d	   R8X  g   Q h Q h\        ^\        \        4      ,          4      R8X  g   Q h\        \        \        P                  ) ,          4      \        \        R
,          4      u;8X  d	   R8X  g   Q h Q h\        \        \        4      4      R8X  g   Q h\        \        \        P                  ,          4      \        \        R,          4      u;8X  d	   R8X  g   Q h Q h\        ^\
        ,          4      R8X  g   Q h\        \
        R,          4      \        \
        R	,          4      u;8X  d	   R8X  g   Q h Q h\        \
        R
,          4      R8X  g   Q hR# )   z1./xz
1./sqrt(x)g      ?zsqrt(x)z1/piz
1/sqrt(pi)Nr   g      g      )r   r   r5   r   Halfr   r   r   r   test_1_over_x_and_sqrtr   |   s'    1:B<5D>3V3333347|+++QVVGag>,>>>>>a>Y&&&AFFuQV}9	999992;&   R=E"d(O5v55555T?l***r   c                     \        ^\        ,          4      R8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        ^\        ,          4      R8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        \        ^,          4      R8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        ^\        ,          \        ,          4      R8X  g   Q h\        ^\        ,          \        ,          \        ,          4      R	8X  g   Q h\        \        \        ,          4      R
8X  g   Q h\        ^\        ,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        ^\        ,          \        ,          4      R8X  g   Q h\        ^\        ,          \        ,          \        ,          \        ,          4      R8X  g   Q h\        ^\        ,          \        ,          4      R8X  g   Q h\        \        ^4      ^,          4      R8X  g   Q h\        \        ^4      ^,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        \        \        ,           \        ,          4      R8X  g   Q h\        \        \        ,           \        \        ,           ,          4      R8X  g   Q h\        \        \        ,           \        ,          4      R\        P                  ! ^4      ,          8X  g   Q h\        \        ^,          \        ,          4      R8X  g   Q h\        \        ^4      ^,          \        ,          \        ,          \        ,          4      R8X  g   Q hR# )r   z3*xzpi*xz3./xzpi./xzx/3zx/pir   z3*x.*yz	3*pi*x.*yzx./yz3*x./yzx.*y./zzx.*z./yz	1./(x.*y)z2*pi*x./(y.*z)z3*pi./xz3/5z3*x/5z	x./(y.*z)z
(x + y)./zz(x + y)./(x + z)z
(x + y)/%szx/(3*pi)z3*x.*y/(5*pi)N)r   r   r   r   r   r   r   evalfr   r   r   test_mix_number_mult_symbolsr      s   1:A;&   1:A;'!!!1:2;&   1:1Q<8###2a?k)))1:1Q<8###1Q<9$$$1Q<9$$$1Q<;&&&2a! 00002a=I%%%1a=E!!!1a?g%%%1Q<;&&&!A#q>\)))!A#!!3333!A#z!"lZ5E5Eb5I&IIII1R=J&&&1a!B?222r   c                     \        \        ^,          4      R8X  g   Q h\        \        ^,          4      R8X  g   Q h\        \        \        ^,          ,          4      R8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        \        \        \        ,          ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q hR# )r   zpi^3zx.^2z	x.^(pi^3)zx.^yz	x.^(y.^z)z	(x.^y).^zN)r   r   r   r   r   r   r   r   test_mix_number_pow_symbolsr      s    Q<6!!!A;&   RU+++A;&   QT{***!Q${***r   c                  H   \        R 4      p \        V 4      R8X  g   Q h\        ^V ,          4      R8X  g   Q h\        \        ^4      ^,          V ,          4      R8X  g   Q h\        ^^V ,          ,           4      R8X  g   Q h\        \        ^4      V ,          4      R8X  g   Q hR# )I1i5iz3*1i/2z3 + 4iz
sqrt(3)*1iN)r   r   r5   )r   s    r   	test_imagr      s    	#A8t1:!A$q&!(((1Q3<8###a|+++r   c                     \        \        4      R 8X  g   Q h\        \        4      R8X  g   Q h\        \        ) 4      R8X  g   Q h\        \        P                  4      R8X  g   Q h\        \        P
                  4      R8X  g   Q h\        \        P                  4      R8X  g   Q h\        \        ^4      4      R8X  g   Q hR# )r   infz-infNaNzexp(1)N)r   r   r   r   NegativeInfinityr   Exp1r#   r   r   r   test_constantsr      s    99":##$...<5   =H$$$Q=H$$$r   c                      \        ^\        ,          4      R8X  g   Q h\        ^\        ,          4      R\        P                  ! ^4      ,          8X  g   Q h\        ^\        ,          4      R\        P                  ! ^4      ,          8X  g   Q hR# )   z2*(1+sqrt(5))/2z2*%sN)r   r   r   r   r   r   r   r   test_constants_otherr      sf    ;#44447vb(99999:&:+;+;B+?"????r   c                     \        \        \        ,          4      R 8X  g   Q h\        \        \        ,          4      R8X  g   Q h\        \        ( 4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q h\        \        \        ,          \        ,          4      R8X  g   Q hR# )zx & yzx | yz~xz	x & y & zz	x | y | zz	z | x & yzz & (x | y)N)r   r   r   r   r   r   r   test_booleanr      s    Q<7"""Q<7"""!9Q{***Q{***!a%1,,,!a%1...r   c                      ^ RI Hp  \        V ! \        \        4      4      R8X  g   Q h\        V ! \        \        ^,           4      4      R8X  g   Q h\        V ! ^\        ,          \        4      4      R8X  g   Q hR# )r   KroneckerDeltazdouble(x == y)zdouble(x == (y + 1))zdouble((2.^x) == y)N)sympy.functionsr   r   r   r   r   s    r   test_KroneckerDeltar      s^    .1%&*::::1q5)*.DDDD1a()-BBBBr   c            	      T   \        \        ^^^
.4      4      R8X  g   Q h\        ^\        \        ^,          4      \	        \        4      .^ ^\
        .^ \        ^4      \        \        4      ..4      p Rp\        V 4      V8X  g   Q h\        V R	,          4      R8X  g   Q h\        V R
,          4      R8X  g   Q h\        \        ^ ^ . 4      4      R8X  g   Q h\        \        ^ ^. 4      4      R8X  g   Q h\        \        \        \        \        ,
          \        ) ..4      4      R8X  g   Q hR# )r   10z-[1 sin(x/2) abs(x); 0 1 pi; 0 exp(1) ceil(x)]z	[1; 0; 0]z[1 sin(x/2) abs(x)]z[]zzeros(0, 3)z[x x - y -y]N)NNNr   )r   r   )	r   rW   r;   r   r   r   r#   r   r   Aexpecteds     r   test_Matricesr      s   1rd#$,,,C!Hc!f%Ar
CFGAJ') 	*A ?H8x3=K'''3=11111b!"d***1b!"m333!QUQB()*n<<<r   c                      \        ^\        ^\        ,          4      ^\        ,          \        ,          ^,          ..4      p \	        V 4      R8X  g   Q h\	        V P
                  4      R8X  g   Q hR# )r   z[1 sin(2./x) 3*pi./(5*x)]z[1; sin(2./x); 3*pi./(5*x)]N)rW   r;   r   r   r   Tr   s    r   test_vector_entries_hadamardr      sT    C!Had1fQh'()A82222:6666r   c                      \        ^\        ^\        ,          4      ^\        ,          \        ,          ^,          .^^\        \        ,          ..4      p Rp\        V 4      V8X  g   Q hR# )r   z.[1 sin(2/x) 3*pi/(5*x);
1        2        x*y]N)rW   r;   r   r   r   r   r   s     r   "test_Matrices_entries_not_hadamardr      sQ    
 	C!Had1fQh'!Q!56A)H8xr   c                  V   \        R RR7      p \        RW 4      p\        RW 4      p\        W,          4      R8X  g   Q h\        W!,          4      R8X  g   Q h\        ^V,          V,          4      R8X  g   Q h\        V^,          V,          4      R8X  g   Q h\        W^\        V 4      ,          ,           ,          4      R	8X  g   Q h\        V\        ^,          ,          4      R
8X  g   Q h\        V^,          4      R8X  g   Q h\        V\
        P                  ,          4      R8X  g   Q hR# )nTintegerr   BzA*BzB*Az2*A*Bz2*B*AzA*(3*eye(n) + B)zA^(x.^2)zA^3zA^(1/2)N)r   rX   r   rY   r   r   r   )r   r   r   s      r   test_MatrixSymbolr      s    sD!AS!AS!A::1Q<7"""1Q<7"""(1+%&'+====QTz)))A;%AFFy(((r   c                      \        R RR7      p \        RW 4      p\        RV ^4      p\        \        W4      4      R8X  g   Q hR# )r   Tr   r   r   zA \ xN)r   rX   r   r   )r   r   r   s      r   test_MatrixSolver   	  s@    sD!AS!AS!QAQ"#x///r   c                  J    \        ^\        ^4      ,          4      R8X  g   Q hR# )   z6*eye(3)N)r   rY   r   r   r   test_special_matricesr     s    8A;:---r   c            	         \        ^^^^^^^..^^	^
.^.4      R8X  g   Q h\        R4      R8X  g   Q h\        ^.4      R8X  g   Q h\        R	4      R8X  g   Q h\        \        . R
O!  4      R8X  g   Q h\        ^\        \        ,          ^\        ^,          334      R8X  g   Q h\        ^\	        ^4      \        ^ ^ . 4      . 34      R8X  g   Q hR# )r   z){1, 2, 3, {4, 5, {6, 7}}, 8, {9, 10}, 11}z{1, 2, {3, 4}}z{1}z	{1, 2, 3}z{1, x.*y, {3, x.^2}}z"{1, [1 0 0; 0 1 0; 0 0 1], [], {}}N)r   r   )r      )r   r   r   r   )r   r
   r   r   rV   rW   r   r   r   test_containersr     s    !QAq1a&>1q"gr:;34 4 4 $4444!:;%	"#{222!QqS1ad)$%)????!SVVAq"-r237[[[[r   c                      \        \        \        ,           \        ,          R RR7      p R\        P                  ! ^4      ,          pW8X  g   Q hR# )meF	assign_toinlinez#Catalan = %s;
me = (x + y)/Catalan;N)r   r   r   r   r   )sourcer   s     r   test_octave_noninliner     s>    AaC=D?F	 bH r   c                    a \        \        \        ^8  3\        ^,          R34      o\        S4      R8X  g   Q h\        SRR7      R8X  g   Q h\        SRRR7      R8X  g   Q h\        \        ^,          \        ^8  3\        ^,          \        ^8  3\        ^,          \        ^8  3\        ^,          R34      oR	p \        S4      V 8X  g   Q h\        SRR7      R
V ,           R,           8X  g   Q h\        SRRR7      R8X  g   Q h\        \        \        ^8  3\        ^,          \        ^8  3\        \        4      \        ^ 8  34      o\	        \
        V3R l4       R# )r   Tz#((x < 1).*(x) + (~(x < 1)).*(x.^2))rr   z(r = ((x < 1).*(x) + (~(x < 1)).*(x.^2));Fr   z(if (x < 1)
  r = x;
else
  r = x.^2;
endzp((x < 1).*(x.^2) + (~(x < 1)).*( ...
(x < 2).*(x.^3) + (~(x < 2)).*( ...
(x < 3).*(x.^4) + (~(x < 3)).*(x.^5))))zr = ;zaif (x < 1)
  r = x.^2;
elseif (x < 2)
  r = x.^3;
elseif (x < 3)
  r = x.^4;
else
  r = x.^5;
endc                     < \        S 4      # )Nr   )exprs   r   <lambda>'test_octave_piecewise.<locals>.<lambda>E  s	    uT{r   N)r/   r   r   r;   rS   
ValueError)r   r   s    @r   test_octave_piecewiser   (  sA   aQZ!Q$.D;????%24 4 4U3	   adAE]QT1q5MAqD!a%=1a4,OD:H ;("""%():S)@@@@U3		 	 	 aQZ!Q$AQQ@D
:*+r   c                  @   \        \        \        ^8  3\        ^,          R34      p \        ^V ,          4      R8X  g   Q h\        V \        ,          4      R8X  g   Q h\        V \        \        ,          ,          4      R8X  g   Q h\        V ^,          4      R8X  g   Q hR# )r   Tz%2*((x < 1).*(x) + (~(x < 1)).*(x.^2))z&((x < 1).*(x) + (~(x < 1)).*(x.^2))./xz+((x < 1).*(x) + (~(x < 1)).*(x.^2))./(x.*y)z%((x < 1).*(x) + (~(x < 1)).*(x.^2))/3N)r/   r   r   r   )pws    r   !test_octave_piecewise_times_constr   H  s~    	Aq1u:1d|	,B2;AAAAA;BBBBQqS?KKKKA;AAAAr   c                      \        . RO.4      p \        V RR7      R8X  g   Q h\        ^^.^^..4      p \        V RR7      R8X  g   Q hR# )r   ar   za = [1 2 3];r   zA = [1 2; 3 4];Nr   )rW   r   r   s    r   test_octave_matrix_assign_tor   P  sP    	{Ac"n444AA Ac"&7777r   c                     aa \        . RO.4      o\        R^^4      p \        R^^4      o\        SV R7      R8X  g   Q h\        \        V3R l4       \        \        VV3R l4       R# )	r   r   Cr   zB = [1 2 3];c                  &   < \        S \        R 7      # r   )r   r   r   s   r   r   3test_octave_matrix_assign_to_more.<locals>.<lambda>]  s    uQ!4r   c                     < \        S SR 7      # r   r   r   r   s   r   r   r   ^      uQ!4r   Nr   rW   rX   r   rS   r   r   r   r   s    @@r   !test_octave_matrix_assign_to_morer   W  sV    	{AS!QAS!QAa N222
:45
:45r   c                     aa \        ^..4      o\        R^^4      p \        R^^4      o\        SV R7      R8X  g   Q h\        \        VV3R l4       R# )r   r   r   r   zB = 3;c                     < \        S SR 7      # r   r   r   s   r   r   (test_octave_matrix_1x1.<locals>.<lambda>h  r   r   Nr   r   s    @@r   test_octave_matrix_1x1r   a  sN    uAS!QAS!QAa H,,, :45r   c                     \        \        ^\        \        ,          ..4      p \        V R,          ^,          V R,          ,           V R,          ,           4      R8X  g   Q h\	        R^^4      p \        V 4      R8X  g   Q h\        V R,          ^,          \        V R,          4      ,           V R,          ,           4      R8X  g   Q h\        \        V 4      4      R8X  g   Q hR# )	r   zx.^2 + x.*y + 2AAz&sin(AA(1, 2)) + AA(1, 1).^2 + AA(1, 3)zAA(1, 1) + AA(1, 2) + AA(1, 3)Nr   r   )r   r   )r   r   )rW   r   r   r   rX   r;   sumr   s    r   test_octave_matrix_elementsr  k  s    Aqs}A4!ag%$/04EEEET1a A8t4!c!C&k)AcF2334 4 4Q=<<<<r   c                      \        R 4      R8X  g   Q h\        \        P                  4      R8X  g   Q h\        R4      R8X  g   Q h\        \        P                  4      R8X  g   Q hR# )TtrueFfalseN)r   r   r  r  r   r   r   test_octave_booleanr	  u  sR    ;&   =F"""<7""">W$$$r   c                     \        \        4      ;_uu_ 4        \        \        P                  4       R R R 4       \        R4      p \        V ! \        4      P                  \        4      RR7      R8X  g   Q hR #   + '       g   i     LN; i)NfFstrictz;% Not supported in Octave:
% Derivative
Derivative(f(x), x))rS   NotImplementedErrorr   r   ComplexInfinityr   r   diffr  s    r   test_octave_not_supportedr  |  s]    	#	$	$a  
%A11e,	   
%	$s   A88B	c            	          ^ RI Hp  \        \        4      ;_uu_ 4        \	        V ! \
        \        \        4      4       RRR4       R#   + '       g   i     R# ; i)r   assoc_laguerreN)#sympy.functions.special.polynomialsr  rS   r  r   r   r   r   r  s    r   *test_octave_not_supported_not_on_whitelistr    s1    B	#	$	$nQ1%& 
%	$	$	$s    AA	c                  *   \        \        ^\        4      4      R8X  g   Q h\        \        4      ;_uu_ 4        \        \        ^\        4      4       RRR4       \        \        \
        \        4      RR7      R8X  g   Q hR#   + '       g   i     L8; i)r   z	expint(x)NFr  z0% Not supported in Octave:
% expint
expint(y, x))r   r$   r   rS   r  r   r   r   r   test_octave_expintr    sg    1+---	#	$	$fQl 
%1e,	   
%	$s   BB	c                      \        R 4      p \        R4      p\        V \        ^ 8  3V\        ^8*  3R4      p\        VRR7      R8X  g   Q hR# )endless	elsewhereF)r   z=if (x < 0)
  endless
elseif (x <= 1)
  elsewhere
else
  1
endN)r   T)r   r/   r   r   )t1t2r   s      r   %test_trick_indent_with_end_else_wordsr    sP    	
9B	
;B	BA;Q!Vi	8BE"	  r   c                     \        R ^^4      p \        R^^4      p\        R^^4      p\        R^^4      p\        W4      p\        R4      p\        V4      R8X  g   Q h\        WB,          4      R8X  g   Q h\        W4,          V,          4      R8X  g   Q h\        W@,          4      R8X  g   Q h\        V\        ,          \
        ,          4      R	8X  g   Q h\        \        W4      4      R
8X  g   Q h\        \        V ^V,           4      4      R8X  g   Q h\        \        WP                  ,          ^V,           4      4      R8X  g   Q hR# )r   r   vhr   zA.*Bz(A.*B)*vz
h*(A.*B)*vz(A.*B)*Az(x.*y)*(A.*B)zA.**nzA.**(n + 1)z(A*B.T).**(n + 1)N)rX   rZ   r   r   r   r   r\   r   )r   r   r!  r"  r   r   s         r   test_hadamardr#    s   S!QAS!QAS!QAS!QAAsA8v:###Q<<''':###1Q<?*** q$%000q!A#&'=888quac*+/BBBBr   c                      \        ^^/ 4      p ^
V R&   ^V R&   ^V R&   ^V R&   \        \        ,          V R&   \        V 4      R8X  g   Q hR# )   z:sparse([4 2 3 1 2], [1 3 3 4 4], [x.*y 20 10 30 22], 5, 6)N)r   r   )r   r   )r   r   )r   r   )r   r   )r[   r   r   r   )Ms    r   test_sparser'    sZ    Q2AAdGAdGAdGAdGcAdG8D  r   c                      \        \        \        4      4      R 8X  g   Q h\        \        \        ^,           4      4      R8X  g   Q h\        \        \        \        ^,           ,          4      4      R8X  g   Q hR# )z
sinc(x/pi)zsinc((x + 3)/pi)zsinc(x + 3)N)r   r4   r   r   r   r   r   	test_sincr)    sT    a>\)))a!e!3333b!a%j!"m333r   c                  j   \         \        \        \        \        \
        \        \        \        \        \        \        \        \        \        \        \         \"        \$        \&        \(        \*        \,        \.        3 F4  p \1        V ! \2        4      V P4                  R ,           8H  4      '       d   K4  Q h	  R# )(x)N)r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   r}   r   __name__r  s    r   test_trigfunr-    sf    3S#sD$dD$D$dD%uU 1Q41::#556666r   c                  t   \        R 4      p \        \        \        \        3 F1  p\        V! V \        4      4      VP                  R,           8X  d   K1  Q h	  \        \        \        \        \        \        \        \        3 F0  p\        V! \        4      4      VP                  R,           8X  d   K0  Q h	  \        \!        V \        4      4      R8X  g   Q h\        \#        V \        4      4      R8X  g   Q h\        \%        \        4      4      R8X  g   Q h\        \'        \        4      4      R8X  g   Q h\        \)        \        4      4      R8X  g   Q h\        \+        \        4      4      R8X  g   Q h\        \-        V \        4      4      R	8X  g   Q h\        \/        V \        4      4      R
8X  g   Q h\        \0        \/        V \        4      ,          4      R8X  g   Q h\        \3        V \        4      4      R8X  g   Q h\        \5        V \        4      4      R8X  g   Q h\        \7        \        4      4      R8X  g   Q h\        \7        \        V 4      4      R8X  g   Q h\        \9        \        4      4      R8X  g   Q h\        \;        \        4      4      R8X  g   Q h\        \=        \        4      4      R8X  g   Q hR# )r   z(n, x)r+  zbesselh(n, 1, x)zbesselh(n, 2, x)z
airy(0, x)z
airy(1, x)z
airy(2, x)z
airy(3, x)z#(gammainc(x, n, 'upper').*gamma(n))z(gammainc(x, n).*gamma(n))zz.^(gammainc(x, n).*gamma(n))z2sqrt(2)*sqrt(pi)*sqrt(1./x).*besselj(n + 1/2, x)/2z2sqrt(2)*sqrt(pi)*sqrt(1./x).*bessely(n + 1/2, x)/2zlambertw(x)zlambertw(n, x)z(logint(exp(x)))zA(((x == 1).*(log(2)) + (~(x == 1)).*((1 - 2.^(1 - x)).*zeta(x))))z/(pi.^(-x/2).*x.*(x - 1).*gamma(x/2).*zeta(x)/2)N)r   r_   r`   ra   rb   r}   r   r,  rq   rr   rp   rt   rs   ru   rv   ri   rc   rd   re   rg   rf   rh   rk   rj   r   r]   r^   r+   r|   r9   r:   )r   r  s     r   test_specfunr/    s   sAw11Q7#qzzH'<<<< 2D#vw(EJ1Q4 AJJ$6666 Kwq!}%);;;;wq!}%);;;;vay!\111{1~&,666vay!\111{1~&,666z!Q'(,SSSSz!Q'(,HHHHq*Q**+/NNNNr!Qx $XXXXr!Qx $XXXXx{#}444x1~&*:::: r!u!3333}Q'(,ooooz!}%)ZZZZr   c                  (   \        R ^^4      p \        R^^4      p\        R^^4      p\        V R,          4      R8X  g   Q h\        ^V R,          ,          4      R8X  g   Q hVR,          P                  W V,
          4      p\        V4      R8X  g   Q hR# )r   r   r   zA(1, 1)z	3*A(1, 1)z(A - B)(1, 1)Nr  )rX   r   subs)r   r   r   Fs       r   test_MatrixElement_printingr3    s    S!QAS!QAS!QA4>Y&&&QtW,,,	$QAA8&&&r   c                      \        \        \        4      4      R 8X  g   Q h\        \        4      ;_uu_ 4        \        \        \        \
        4      4       RRR4       R#   + '       g   i     R# ; i)zzeta(x)N)r}   r6   r   rS   r  r   r   r   r   test_zeta_printing_issue_14820r5    sB    tAw9,,,	#	$	$DAJ 
%	$	$	$s   AA0	c                      \        \        \        4      4      R 8X  g   Q h\        \        \        \        4      4      R8X  g   Q hR# )z(logint(x) - logint(2))z(-erf(x) + erf(y))N)r}   rz   r   r{   r   r   r   r   test_automatic_rewriter7    s4    r!u!::::tAqz"&::::r   N)
sympy.corer   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   sympy.codegen.matrix_nodesr   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   sympy.testing.pytestrS   rT   sympy.utilities.lambdifyrU   sympy.matricesrV   rW   rX   rY   rZ   r[   r\   sympy.functions.special.besselr]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   'sympy.functions.special.gamma_functionsri   rj   rk   rl   rm   'sympy.functions.special.error_functionsrn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   sympy.printing.octaver}   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r	  r  r  r  r  r#  r'  r)  r-  r/  r3  r5  r7  r   r   r   <module>rA     s  G G G G G G 3) ) ) ) ) ) ) ) )M M M M M M M / 9J J JN N N N@ @? ? ? ? ? D
'
1a&
.'5 +46	S+36+,%@/C="7    )0.	\,@B866=%'C(	47[4
' ;r   