
    \h~                        S SK Jr  S SKJrJrJrJr  S SKJr  S SK	J
r
Jr  S SKJr  S SKJr  S SKJr  S SKJr  S S	KJr  S S
KJrJr  S SKJr  S SKJr  S SKJrJr  S SK J!r!  \S 5       r"S r#S r$S r%S r&\!S 5       r'S r(S r)S r*S r+S r,g)    )nfloat)FloatIRationalpi)Eq)Symbolsymbols)sqrt)	Piecewise)sin)Integral)Matrix)mnormmpf)nsolve)lambdify)raisesXFAIL)conserve_mpmath_dpsc                      [        S5      n [        U S-  SU -
  -  SSU -  -
  S-  -  S-
  U S5      nUS:  a  US:  d   eg )Nx      d   r   gq=
ףp?gGz?r
   r   r   anss     X/var/www/auris/envauris/lib/python3.13/site-packages/sympy/solvers/tests/test_numeric.pytest_nsolve_failr       sR    A Aq1uq1Q3wl*S0!Q
7C:#*$$*    c                  f    [        S5      n [        U S-  SU -  -   S-   U S-   -  S5      nUS:X  d   eg )Nr   r      g g      r   r   s     r   test_nsolve_denominatorr$      s<    A
!Q$1*q.1q5)4
0C$;;r!   c                    ^^	^
^^ [        S5      m
[        [        T
5      S5      [        R                  " 5       -
  S:  d   e[        [        ST
-  S5      T
S5      [        ST
-  S-
  S5      :X  d   e[        [        U
4S j5        [        [        U
4S j5        [        S5      n [        S5      nS	U S-  -  SUS-  -  -
  S
-
  nU S-  SU -  -
  US-  -   SU-  -   S-
  n[        X#45      R                  m	[        X4T	R                  SS9mS H%  n[        T	X4USS9m
[        T" T
6 S
5      S::  a  M%   e   [        S5      m
[        S5      m[        S5      mT
* ST-  -   nT
S-  T
TS-  S-
  -  -   ST-  -
  T
S-   -  n[        T
S-  TS-  -   5      T-  n[        X#U45      R                  m	[        T
TT4T	R                  SS9mUU	U
UU4S jn[        [        [        U" S5      5      5      / SQ:X  d   e[        [        US5      [        US5      [        US5      /T
TT/S5      (       d   e[        S5      n[!        [        S
SU-   S	-  -  SSU-
  S	-  -  -
  US5      [#        S5      -
  5      S:  d   eg )Nr   r   gV瞯<ic                  4   > [        [        ST -  S5      5      $ )Nr   r   r   r   s   r   <lambda>test_nsolve.<locals>.<lambda>'   s    fR!QZ0r!   c                  :   > [        [        ST -  S5      T SS5      $ )Nr   r   r'   r(   s   r   r)   r*   (   s    fR!QZAq9r!   x1x2r#   r      mpmath)modules))r   )r   )   r3   )r4   :0yE>)tolg|=yzr3   c                 R   > [        TTTT4U 5      n[        T" U6 S5      S::  d   eU$ )Nr   r5   )r   r   )x0rootFfr   r7   r8   s     r   getroottest_nsolve.<locals>.getroot>   s5    a!QB'QXq!U***r!   )r   r   r   )r   r   r   r   agMbP?   g?g333333?z0.31883011387318591)r	   r   r   r   evalfr   r   	TypeErrorr   Tr   r   r   listmaproundabsr   )r,   r-   f1f2r:   f3r>   r@   r<   r=   r   r7   r8   s           @@@@@r   test_nsolverL   !   s   sA#a&!rxxz)E111"QqS!*a%!a)====
901
99:	B	B	
RUQQY		"B	QR"a%	!b&	(1	,BxA"1331A21rh.QUA&((( 3
 	sAsAsA
acB
Q$AqD1H
!
#A	.B	adQTk	1	B|A!QACC2A  E79-./9<<<2
A2q	2b!9&()1ay)= = = =sAvaQ&C!Ga<7C@!"# $&+, , ,r!   c                  f    [        S5      n [        [        X S:  4U S-  S45      U S5      S:X  d   eg )Nr   r   r   Tr   )r	   r   r   r(   s    r   test_issue_6408rN   J   s7    sA)QAJAt5q!<AAAr!   c                  b    [        S5      u  p[        [        X-  U SS45      US5      S:X  d   eg )Nx yr      r   )r
   r   r   r   r7   s     r   test_issue_6408_integralrS   O   s3    5>DA(13Aq	*Aq1Q666r!   c                      SS K n SU R                  l        [        S5      nUS-  [        -
  n[        X!S5      n[        [        [        5      R                  S5      U-
  5      S:  d   eg )Nr      r   r         @睗[%)	r/   mpdpsr	   r   r   rH   r   rB   )r/   r   e1qs       r   test_increased_dpsr\   T   sY     FIIMsA	
ABrcAtBx~~c"Q&'&000r!   c                  x   [        S5      u  p[        U S-  [        -
  U SSS9n[        [	        [        5      R                  S5      U-
  5      S:  d   e[        U[        5      (       d   e[        US-  U -
  U S-  [        -
  4X4SSS9n[        U[        5      (       d   eUR                  S:X  d   e[        [	        [        5      R                  S5      US	   -
  5      S:  d   e[        [	        [	        [        5      5      R                  S5      US
   -
  5      S:  d   e[        S U 5       5      (       d   eg )NrP   r   r#   rU   precrW   )r#   r#   )r   r   r   r   c              3   B   #    U  H  n[        U[        5      v   M     g 7f)N)
isinstancer   ).0is     r   	<genexpr>(test_nsolve_precision.<locals>.<genexpr>j   s     2Tz!U##Ts   )r
   r   r   rH   r   rB   ra   r   r   shapeall)r   r7   solsolss       r   test_nsolve_precisionrj   _   s   5>DA
AAqs
+CtBx~~c"S()F222c5!!!!1a4!8QTBY'!cBDdF####::tBx~~c"T!W,-666tDH~##C(4723f<<<2T22222r!   c                  "   [        S5      u  p[        U S-  S-   S5      [        S5      [        -  :X  d   e[        U S-  S-   [        5      [        S5      [        -  :X  d   e[        U S-  S-   US-  S-   /X/[        [        /5      [	        [        S5      [        -  [        S5      [        -  /5      :X  d   e[        U S-  S-   US-  S-   /X/[        [        /5      [	        [        S5      [        -  [        S5      [        -  /5      :X  d   eg )NrP   r   y              ?       @)r
   r   r   r   r   rR   s     r   test_nsolve_complexrm   l   s    5>DA!Q$(B48A:---!Q$(A$r(1*,,,1a4!8QTAX&A7648A:tTVxXYzBZ;[[[[1a4!8QTAX&A7648A:tTVxXYzBZ;[[[[r!   c                  L   [        S5      u  p[        U S-  S-
  SSS9U [        S5      0/:X  d   e[        U S-  S-   [        SS9U [        S5      [        -  0/:X  d   e[        U S-  US-  -   S-
  U S-  US-  -
  S-   /X/SS/SS9U [        S5      U[        S5      0/:X  d   eg )	NrP   r   r   T)dictrl   rQ   rV   )r
   r   r   r   rR   s     r   test_nsolve_dict_kwargrp   u   s    5>DA!Q$(Ad+
T"X   !Q$(Ad+
T"XaZ   1a4!Q$;?AqD1a4K!O4qfq!fTR
T"Xq$r(	#$% % %r!   c                      [        S5      n [        U [        SS5      -
  SSS9[        SS5      R                  S5      :X  d   eg )Nr   r   r#   r   r   r^   )r
   r   r   rB   r(   s    r   test_nsolve_rationalrr      s>    A!hq!n$ac2hq!n6J6J36OOOOr!   c                      [        [        S5      5      n [        SS/5      nX-   n[        X U5      [        U* 5      :X  d   e[        UR                  U R                  UR                  5      [        U* 5      :X  d   eg )Nzt s      )r   r
   r   r   rD   )r   r:   eqns      r   test_issue_14950rw      si    wu~A	R	B
&C#",,,#%%bdd#vrc{222r!   N)-sympy.core.functionr   sympy.core.numbersr   r   r   r   sympy.core.relationalr   sympy.core.symbolr	   r
   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   (sympy.functions.elementary.trigonometricr   sympy.integrals.integralsr   sympy.matrices.denser   r/   r   r   sympy.solversr   sympy.utilities.lambdifyr   sympy.testing.pytestr   r   sympy.utilities.decoratorr   r    r$   rL   rN   rS   r\   rj   rm   rp   rr   rw    r!   r   <module>r      s    & 7 7 $ / 9 : 8 . '    - . 9% %&,RB
7
 1 13\
%P
3r!   