+
    ‰°³jqf  ã                   óâ   € R t ^ RIt^ RIt^ RIt^ RI5 ]3R lt]! ^ 4      t]! ^4      t]	! R4      t
]	! R4      t]	! R4      tR tR tR	 tR
 tR tR tR tR tR tR tR tR tR tR tR tR# )a�  
Limited tests of the elliptic functions module.  A full suite of
extensive testing can be found in elliptic_torture_tests.py

Author of the first version: M.T. Taschuk

References:

[1] Abramowitz & Stegun. 'Handbook of Mathematical Functions, 9th Ed.',
    (Dover duplicate of 1972 edition)
[2] Whittaker 'A Course of Modern Analysis, 4th Ed.', 1946,
    Cambridge University Press

N)Ú*c                 óÊ   € R pT;'       d'    V P                   P                  VP                   V4      pT;'       d'    V P                  P                  VP                  V4      pV# )T)ÚrealÚaeÚimag)ÚaÚbÚepsÚress   &&& Ú[/home/luca/screen-checking/.venv/lib/python3.14/site-packages/mpmath/tests/test_elliptic.pyÚmpc_aer      sL   € Ø
€CØ
×
(Ð
(�!—&‘&—)‘)˜AŸF™F CÓ(€CØ
×
(Ð
(�!—&‘&—)‘)˜AŸF™F CÓ(€CØ€Jó    ÚsnÚcnÚdnc                 ó   € \        V R 7      # )©Úk)Úqfromr   s   &r   Ú<lambda>r   #   s   € œ5 1�:r   c                  óD  € ^\         n        \        R^ ^ 4      ^8X  g   Q h\        R^ ^ 4      ^8X  g   Q h\        R^ ^ 4      ^8X  g   Q h\        R^ ^ 4      ^8X  g   Q h\        RR^ 4      P                  \	        R4      4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  ^4      '       g   Q h\        R	R^ 4      P                  \        R4      4      '       g   Q h\        R
R^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  ^4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  \	        R4      4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^ 4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        R	R^4      P                  \        R4      4      '       g   Q h\        R
R^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  ^4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RR^4      P                  ^4      '       g   Q h\        RR^4      P                  \        R4      4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        R	RR4      P                  R4      '       g   Q h\        R
RR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q h\        RRR4      P                  R4      '       g   Q hR# ) é   ÚssÚccÚddÚnnr   ç      Ð?r   r   ÚnsÚncÚndÚscÚsdÚcdÚcsÚdcÚdsç      à?g@p4ü(‚Ï?gTiÍ$íï?gý>x¤ò‚ï?gô(ÔÌæ?@gZx:Ç	‚ð?g Ï~?ð?gbUaåAÐ?g]`w73ÿÏ?g’Þòkï?g)– Ì@g
oüì†Að?g¡Óff @N)ÚmpÚdpsÚellipfunr   ÚsinÚcosÚcscÚsecÚtanÚcotÚtanhÚsechÚcothÚcoshÚsinhÚcsch© r   r   Útest_ellipfunr7   %   sA  € Ø„B„FÜ�D˜!˜QÓ 1Ô$Ð$Ð$Ü�D˜!˜QÓ 1Ô$Ð$Ð$Ü�D˜!˜QÓ 1Ô$Ð$Ð$Ü�D˜!˜QÓ 1Ô$Ð$Ð$Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ% a×(Ò(Ð(Ð(Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ% a×(Ò(Ð(Ð(Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤c¨$£i×0Ò0Ð0Ð0Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ% a×(Ò(Ð(Ð(Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó"×%Ñ% a×(Ò(Ð(Ð(Ü�D˜$ Ó"×%Ñ%¤d¨4£j×1Ò1Ð1Ð1Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ð>Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ð>Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ð>Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(>×?Ò?Ð?Ð?Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ð>Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ð>Ü�D˜$ Ó$×'Ñ'Ð(=×>Ò>Ð>Ò>r   c                  ó@  € ^d\         n        \        \        4      p V \        8X  g   Q h^\         n        \	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^4      ^
,          \	        R4      3\	        ^	4      ^
,          \	        R	4      3\	        ^	4      ^
,          \	        R	4      3.
pV F@  pV^ ,          p\        \        V4      4      p V P                  V^,          4      '       d   K@  Q h	  ^\         n        R
# )éd   z0.006584651553858370274473060z0.01394285727531826872146409z0.02227743615715350822901627z0.03188334731336317755064299z0.04321391826377224977441774z0.05702025781460967637754953z0.07468994353717944761143751z0.09927369733882489703607378z0.1401731269542615524091055N)r'   r(   Úcalculate_nomeÚzeroÚmpfÚsqrtr   )ÚqÚmath1ÚiÚms       r   Útest_calculate_nomerB   S   sK  € Ø„B„Fä”tÓ€AØ”Œ9Ðˆ9à„B„Fä�!‹f�R�iœÐ<Ó=Ð>Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ;Ó<Ð=Ü�!‹f�R�iœÐ:Ó;Ð<Ü�!‹f�R�iœÐ:Ó;Ð<ð	>€Eó ˆØˆa�DˆÜœ4 ›7Ó#ˆØ�t‰t�A�a•D�zŒzÐˆzñ ð
 „B†Fr   c                  ó>  aaa	€ ^\         n        \        ;o	o\        ^^4       F'  o\	        SS	S4      p V S^,
          ^,          8X  d   K'  Q h	  \
        \        ^4      3 F7  o\        ^^4       F$  o\        P                  ! \        VVV	3R l4       K&  	  K9  	  \
        ^
,          o	\
        ^,          o\        R4      p\	        ^S	S4      pVP                  V4      '       g   Q h\        R4      p\	        ^S	S4      pVP                  V4      '       g   Q h\        R4      p\	        ^S	S4      pVP                  V4      '       g   Q h\        R4      p\	        ^S	S4      pVP                  V4      '       g   Q h\        p\        ^,          p\        ^
4       Fx  p\        \        P                  ! 4       4      p\        V4      o\	        ^VS4      pVP                  ^ 4      '       g   Q h\	        ^VS4      pVP                  ^ 4      '       d   Kx  Q h	  ^\         n        R# )é   c                  ó   <€ \        S SS4      # ©N©Újtheta)Únr>   Úzs   €€€r   r   Útest_jtheta.<locals>.<lambda>w   s   ø€ ¬f°Q¸¸1¬or   z0.1069552990104042681962096z1.101385760258855791140606z1.178319743354331061795905z0.8219318954665153577314573N)r'   r(   r;   ÚrangerH   Úoner<   ÚpytestÚraisesÚ
ValueErrorr   ÚpiÚstrÚrandom)
Úvaluer
   ÚresultÚz1Úz2r@   ÚqstringrI   r>   rJ   s
          @@@r   Útest_jthetarY   m   s½  ú€ Ø„B„Fä€L€AˆÜ�1�QŽZˆÜ�q˜!˜Q“ˆØ˜˜1�˜q�Ö Ð!Ð ñ ô ”3�q“6‹]ˆÜ�q˜–ˆAÜ�MŠMœ*Ö&=Ö>ó ñ ô 	ˆB�€AÜˆB�€Aô Ð+Ó
,€CÜ�A�q˜!‹_€FØ�9‰9�S�>Š>Ðˆ>ô Ð*Ó
+€CÜ�A�q˜!‹_€FØ�9‰9�S�>Š>Ðˆ>ô Ð*Ó
+€CÜ�A�q˜!‹_€FØ�9‰9�S�>Š>Ðˆ>ô Ð+Ó
,€CÜ�A�q˜!‹_€FØ�9‰9�S�>Š>Ðˆ>ô 
€BÜ	ˆA�€BÜ�2ŽYˆÜ”f—m’m“oÓ&ˆÜ�‹LˆÜ˜˜2˜qÓ!ˆØ�y‰y˜�|Š|Ðˆ|Ü˜˜2˜qÓ!ˆØ�y‰y˜�|Œ|Ðˆ|ñ ð „B†Fr   c                  ó¶  a€ ^\         n        \         ;P                  ^,          un        \        ^4      ^
,          \        R,          ,
          \        ^4      ^
,          \        ,          ,
          o\         ;P                  ^,          un        \        R4      \        R4      \        ,          ,           p \        ^^S4      p\         ;P                  ^,          un        \        ^4      ^
,          \        R,          ,
          \        ^4      ^
,          \        ,          ,
          o\         ;P                  ^,          un        \        P                  ! \        V3R l4       ^d\         n        ^\        ,           ^,          p\        R4      R,          \        R4      R,          \        ,          ,           o\        R4      \        R4      \        ,          ,           p ^\         n        \        ^VS4      pVP                  V 4      '       g   Q h^P\         n        ^^\        ,          ,           pRR\        ,          ,           o\        ^VS4      p^\         n        \        ^VS4      pVP                  V4      '       g   Q h^P\         n        ^\        ,           p\        \        ^,          4      p\        ^^4       FZ  p^P\         n        V^\        ^4      ^
V,          ,          ,
          ,          o\        ^VS4      p^\         n        \        ^VS4      pK\  	  VP                  V4      '       g   Q h^\         n        \        ^R	R
^	4      P                  R4      '       g   Q h\        ^R	R
^24      P                  R4      '       g   Q h^2\         n        \        ^R	R
^	4      pVP                  R4      '       g   Q h\        ^R	R
^24      pVP                  R4      '       g   Q hR# )é   z32.0031009628901652627099524264z16.6153027998236087899308935624c                  ó   <€ \        ^^S 4      # )é   rG   )r>   s   €r   r   Ú&test_jtheta_issue_79.<locals>.<lambda>°   s   ø€ ¤f¨Q°°1¤or   l   ³'e[>
 l   tQüh z$2.4439389177990737589761828991467471z$0.5446453005688226915290954851851490r&   g      @r   gîlÞ2<•@z21359.048926806828939547859396600218966947753213803z4-6148327726309051673317975084654262.4119215720343656Ni@B i€–˜ l     �Iú5 g‹3må,òòÆ)r'   r(   r<   rM   ÚjrH   rN   rO   rP   r   ÚexprL   )	r
   rU   rJ   Úr1Úr2Úq1rI   Úrr>   s	           @r   Útest_jtheta_issue_79re   ž   sÁ  ø€ ð „B„FÜ‡F‚Fˆb…L…FÜˆA‹ˆr�	”C˜•IÕ¤ A£ r¥	¬A¥Õ-€AÜ‡F‚Fˆb…L…Fô
 Ð/Ó
0Ü
Ð/Ó
0´1Õ
4õ5€Cä�A�q˜!‹_€Fä‡F‚Fˆb…L…FÜˆA‹ˆr�	”C˜•IÕ¤ A£ r¥	¬A¥Õ-€AÜ‡F‚Fˆb…L…FÜ
‡M‚M”*Ô5Ô6ð „B„FØ	
Œ1�ˆa�€AÜˆOÓ˜VÕ#¤c¨/Ó&:¸6Õ&AÄAÕ&EÕE€Aä
Ð4Ó
5Ü
Ð4Ó
5´qÕ
8õ9€Cà„B„FÜ�A�q˜!‹_€FØ�9‰9�S�>Š>Ðˆ>Ø„B„FØ	ˆAŒa�C�€AØˆc”!�e�€AÜ	��1�a‹€BØ„B„FÜ	��1�a‹€BØ�5‰5��9Š9Ðˆ9Ø„B„FØ	ŒA�€AÜ	ŒQˆq�S‹€Bô �1�aŽ[ˆØŒŒØ�”C˜“F˜2˜q�5•LÕ Õ!ˆÜ�A�q˜!‹_ˆØŒŒÜ�A�q˜!‹_Šñ ð �5‰5��9Š9Ðˆ9Ø„B„Fä�!�S˜$ Ó"×%Ñ%Ð&6×7Ò7Ð7Ð7Ü�!�S˜$ Ó#×&Ñ&Ð'<×=Ò=Ð=Ð=Ø„B„FÜˆq�#�t˜QÓ€AØ�4‰4ÐD×EÒEÐEÐEÜˆq�#�t˜RÓ €AØ�4‰4ÐF×GÒGÐGÒGr   c                 ó6  € ^n\         n        \        \        ^4      p \	        ^
4       EFâ  p\        \        P                  ! 4       4      p\        V4      p\        ^
\        P                  ! 4       ,          4      p\        V4      p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          pWg,
          V,           p	V	P                  ^ V 4      '       g   Q h\        ^d\        P                  ! 4       ,          4      p\        V4      p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          pWg,
          V,           p	V	P                  ^ V 4      '       g   Q h\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          pWg,
          V,           p	V	P                  ^ V 4      '       g   Q h\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          p\        ^WS4      ^,          \        ^\        V4      ^,          ,          pWg,
          V,           p	V	P                  ^ V 4      '       g   Q h\        ^\        V4      ^,          p\        ^\        V4      ^,          p\        ^\        V4      ^,          pWg,           V,
          p	V	P                  ^ V 4      '       d   EKã  Q h	  ^\         n        R# )z�
Tests the some of the jacobi identidies found in Abramowitz,
Sec. 16.28, Pg. 576. The identities are tested to 1 part in 10^98.
N)r'   r(   Úldexpr	   rL   rR   rS   r<   rH   r;   r   )
Úeps1r@   rX   r>   ÚzstringrJ   Úterm1Úterm2Úterm3Úequalitys
             r   Útest_jtheta_identitiesrn   Ù   s  € ð
 „B„FÜ”�b‹>€Dä�2�YˆÜ”f—m’m“oÓ&ˆÜ�‹Lˆä�bœŸš›Õ(Ó)ˆÜ�‹Lˆô ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆØ•= 5Õ(ˆØ�{‰{˜1˜d×#Ò#Ð$Ð#ä�cœ&Ÿ-š-›/Õ)Ó*ˆÜ�‹Lˆô ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆØ•= 5Õ(ˆØ�{‰{˜1˜d×#Ò#Ð$Ð#ô
 ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆØ•= 5Õ(ˆØ�{‰{˜1˜d×#Ò#Ð$Ð#ô
 ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆÜ˜˜1“ !Õ#¬¨q´$¸Ó(:¸AÕ(=Õ>ˆØ•= 5Õ(ˆØ�{‰{˜1˜d×#Ò#Ð$Ð#ô ˜œ4 Ó# aÕ'ˆÜ˜œ4 Ó# aÕ'ˆÜ˜œ4 Ó# aÕ'ˆØ•= 5Õ(ˆØ�{‰{˜1˜d×#Õ#Ð$Ð#ñe ðf „B†Fr   c            	      óŒ  € ^\         n        \        ^4      ^,          \        ^,          ,           p \        ^4      ^,          \        ^,          ,           p\        R4      \        R4      \        ,          ,           p\	        ^W4      p\        W24      '       g   Q h\        R4      \        R4      \        ,          ,           p\	        ^W4      p\        W24      '       g   Q h\        R4      \        R4      \        ,          ,           p\	        ^W4      p\        W24      '       g   Q h\        R4      \        R4      \        ,          ,
          p\	        ^W4      p\        W24      '       g   Q h^d\         n        \        ^4      ^,          \        ^,          ,           p \        ^4      ^,          \        ^,          ,           p\         ;P                  ^
,          un        ^ ^ \	        ^^ V4      \	        ^^ V4      \	        ^^ V4      .p^ \	        ^W4      \	        ^W4      \	        ^W4      \	        ^W4      .pV^,          V^,          ,          ^,          V^,          V^,          ,          ^,          ,
          V^,          V^,          ,          ^,          ,           V^,          V^,          ,          ^,          V^,          V^,          ,          ^,          ,
          V^,          V^,          ,          ^,          ,           V^,          V^,          ,          ^,          V^,          V^,          ,          ^,          ,
          V^,          V^,          ,          ^,          ,           V^,          V^,          ,          ^,          V^,          V^,          ,          ^,          ,
          V^,          V^,          ,          ^,          ,           V^,          ^,          V^,          ^,          ,           V^,          ^,          ,
          .p\         ;P                  ^
,          un        V F   p\        V\        ^ 4      4      '       d   K   Q h	  ^\         n        R	# )
r[   z%0.31618034835986160705729105731678285z%0.07542013825835103435142515194358975z$1.6530986428239765928634711417951828z$0.2015344864707197230526742145361455z$1.6520564411784228184326012700348340z$0.1998129119671271328684690067401823z%0.37619082382228348252047624089973824z%0.15623022130983652972686227200681074N)r'   r(   r<   r_   rH   r   ÚdosÚmpc)rJ   r>   r
   rd   r   ÚtÚxs          r   Útest_jtheta_complexrt     sü  € Ø„B„FÜˆA‹ˆq�”1�Q•3�€AÜˆA‹ˆq�”1�Q•3�€Aä
Ð5Ó
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:õ;€Cäˆq�!‹€AÜ�!�>Š>Ðˆ>ô Ð4Ó
5Ü
Ð4Ó
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9õ:€Cäˆq�!‹€AÜ�!�>Š>Ðˆ>ô Ð4Ó
5Ü
Ð4Ó
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9õ:€Cäˆq�!‹€AÜ�!�>Š>Ðˆ>ô Ð5Ó
6Ü
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:õ;€Cäˆq�!‹€AÜ�!�>Š>Ðˆ>ð „B„FÜˆA‹ˆq�”1�Q•3�€AÜˆA‹ˆq�”1�Q•3�€AÜ‡F‚Fˆb…L…FØ	
ˆ1Œf�Q˜˜1‹oœv a¨¨A›´°q¸!¸Q³Ð@€AØ	
ŒF�1�a‹OœV A q›_¬f°Q¸«o¼vÀaÈ»ÐO€AØ
ˆA�$ˆq��t�)�a�˜1˜Q�4  !¥�9 q�.Õ	(¨A¨a­D°!°Aµ$­J¸­?Õ	:Ø	
ˆ1�ˆa��d��Q�˜!˜A�$˜q �t�) a�Õ'¨1¨Q­4°°1µ­:¸­/Õ9Ø	
ˆ1�ˆa��d��Q�˜!˜A�$˜q �t�) a�Õ'¨1¨Q­4°°1µ­:¸­/Õ9Ø	
ˆ1�ˆa��d��Q�˜!˜A�$˜q �t�) a�Õ'¨1¨Q­4°°1µ­:¸­/Õ9Ø	ˆ!�ˆa��!�A•$˜•'Õ˜A˜a�D !�GÕ#ð		%€Aô
 ‡F‚Fˆb…L…FÛˆÜ�aœ˜Q›× Ô Ð!Ð ñ à„B†Fr   c                  óH  a	a
€ ^\         n        \        ^,          \        ^,          ,           p \        ^,          \        ^,          ,           o
\	        R4      \	        R4      \        ,          ,
          p\        ^V S
^4      p\        W!4      '       g   Q h\	        R4      \	        R4      \        ,          ,
          p\        ^V S
^4      p\        W!4      '       g   Q h\	        R4      \	        R4      \        ,          ,
          p\        ^V S
^4      p\        W!4      '       g   Q h\	        R4      \	        R4      \        ,          ,           p\        ^V S
^4      p\        W!4      '       g   Q h\        ^
4       F§  p\        \        P                  ! 4       ,          \        \        P                  ! 4       ,          ,           ^,          o
\        ^^ S
^4      p\        ^^ S
4      \        ^^ S
4      ,          \        ^^ S
4      ,          pVP                  V4      '       d   K§  Q h	  ^\         n        \        ^,          \        ^,          3\        ^,          \        ^,          ,           \        ^,          3\        ^,          \        ^,          \        ^,          ,           3\        ^,          \        ^,          ,           \        ^,          \        ^,          ,           33 Fƒ  w  o
p R Fw  o	\        S	V S
^4      p\        V	V
3R	 lV ^R
7      pVP                  V4      '       g   Q h\        S	V S
^4      p\        V	V
3R lV ^R
7      pVP                  V4      '       d   Kw  Q h	  K…  	  \        ^,          o
\        p ^ .^,          p\        ^V S
^4      \        ^V S
^4      ,          V^&   R F&  o	\        S	V S
^4      \        S	V S
4      ,          VS	&   K(  	  V^,          V^,          ,           V^,          ,           V^,          ,
          pVP                  ^ 4      '       g   Q h^\         n        R# )r[   z$1.5555195883277196036090928995803201z%0.02439761276895463494054149673076275z%0.19825296689470982332701283509685662z%0.46038135182282106983251742935250009z%0.36492498415476212680896699407390026z%0.57743812698666990209897034525640369z&-0.38936892528126996010818803742007352z%0.66549886179739128256269617407313625c                 ó   <€ \        SV S4      # rF   rG   ©ÚzzrI   r>   s   &€€r   r   Útest_djtheta.<locals>.<lambda>m  ó   ø€ ¤¨¨2¨qÔ!1r   )rI   c                 ó   <€ \        SV S4      # rF   rG   rw   s   &€€r   r   ry   p  rz   r   N)é   é   r]   é   )r}   r]   r~   )r'   r(   rM   r_   r<   rH   r   rL   rS   r   Údiffr;   )rJ   r
   rU   r@   r   r   rd   ra   rm   rI   r>   s            @@r   Útest_djthetar€   C  s/  ù€ Ø„B„FäˆA�”�!•�€AÜˆA�”�!•�€Aä
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6Ü
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:õ;€Cä�A�q˜!˜QÓ€FÜ�&×ÒÐÐô Ð5Ó
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:õ;€Cä�A�q˜!˜QÓ€FÜ�&×ÒÐÐô Ð6Ó
7Ü
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:õ;€Cä�A�q˜!˜QÓ€FÜ�&×ÒÐÐä�2ŽYˆÜ”—’“Õ ¤1¤V§]¢]£_Õ#4Õ4°aÕ7ˆä�1�a˜˜AÓˆÜ�1�a˜‹OœF 1 a¨›OÕ+¬F°1°a¸«OÕ;ˆØ�t‰t�A�wŒwˆˆwñ ð „B„FÜ�Q•œ˜A��¤ Q¥¬¨1­¥¬c°!­eÐ 4Ü	ˆQ�”�A•œ˜!�•Ðœs 1�u¤q¨¥s�{¬C°­E´A°aµC­KÐ8ó:‰ˆˆ!ãˆAÜ�q˜!˜Q Ó"ˆAÜÕ1°1¸Ô:ˆBØ—4‘4˜—8’8ˆO�8Ü�q˜!˜Q Ó"ˆAÜÕ1°1¸Ô:ˆBØ—4‘4˜—8”8ˆO�8ó ñ:ô 	ˆA�€AÜ€AØ	
ˆˆA�€AÜ�!�Q˜˜1Óœf Q¨¨1¨aÓ0Õ0€A€a�DÛˆÜ�a˜˜A˜qÓ!¤&¨¨A¨q£/Õ1ˆˆ!‹ñ à��t�a˜•d�{˜Q˜q�TÕ! A a¥DÕ(€HØ�;‰;�q�>Š>Ðˆ>Ø„B†Fr   c                 óH  € ^d\         n        \        \        \        4      p V \        8X  g   Q h\	        ^
4       FU  p\        \        P                  ! 4       4      p\        V4      p\        \        V4      pVP                  ^ 4      '       d   KU  Q h	  ^\         n        \        ^
,          p\        R4      p\        \        R4      p\        WW4      p V P                  V4      '       g   Q h\        R4      p\        WU4      p V P                  V4      '       g   Q h^\         n        R# )z3
Test some special cases of the sn(z, q) function.
z0.09983341664682815230681420z0.09981686718599080096451168Néœÿÿÿ)r'   r(   Újsnr;   rL   rR   rS   r<   r   rM   rg   )rU   r@   rX   r>   rm   Úargr
   rA   s           r   Útest_jsnr…   ~  sÝ   € ð „B„Fô ””t‹_€FØ”TŒ>Ðˆ>ô �2ŽYˆÜ”f—m’m“oÓ&ˆÜ�‹Lˆä”t˜Q“<ˆØ�{‰{˜1�~Œ~Ðˆ~ñ ð" „B„FÜ
ˆb�&€Cä
Ð,Ó
-€CÜŒc�4Ó€AÜ�‹[€FØ�9‰9�S�>Š>Ðˆ>ô Ð,Ó
-€CÜ�‹]€FØ�9‰9�S�>Š>Ðˆ>Ø„B†Fr   c                 óê  € ^d\         n        \        \        P                  ! 4       4      p \	        V 4      p\        \        V4      pVP                  \        4      '       g   Q h^\         n        \        ^
,          p\        \        R4      p\	        R4      p\        W44      pVP                  V4      '       g   Q h\	        R4      p\        W34      pVP                  V4      '       g   Q h^\         n        R# )z3
Test some special cases of the cn(z, q) function.
z0.9950041652780257660955620z0.9950058256237368748520459Nr‚   )
r'   r(   rR   rS   r<   Újcnr;   r   rM   rg   )rX   r>   r   r„   rA   r
   rU   s          r   Útest_jcnrˆ   «  s¶   € ð „B„Fô ”&—-’-“/Ó"€GÜˆG‹€AÜ	ŒT�1‹€BØ�5‰5”�:Š:Ðˆ:ð „B„FÜ
ˆb�&€CÜŒc�4Ó€Aä
Ð+Ó
,€CÜ�‹[€FØ�9‰9�S�>Š>Ðˆ>ô Ð+Ó
,€CÜ�‹]€FØ�9‰9�S�>Š>Ðˆ>Ø„B†Fr   c                 ól  € ^d\         n        \        \        P                  ! 4       4      p \	        V 4      p\        \        V4      pVP                  \        4      '       g   Q h^\         n        \	        R4      p\        ^
,          p\        WD4      pVP                  V4      '       g   Q h^\         n        R# )z3
Test some special cases of the dn(z, q) function.
z0.9995017055025556219713297N)	r'   r(   rR   rS   r<   Újdnr;   r   rM   )ÚmstringrA   r   r
   r„   rU   s         r   Útest_jdnrŒ   Ð  s€   € ð „B„Fô ”&—-’-“/Ó"€GÜˆG‹€Aä	ŒT�1‹€BØ�5‰5”�:Š:Ðˆ:à„B„Fä
Ð+Ó
,€CÜ
ˆb�&€CÜ�‹]€FØ�9‰9�S�>Š>Ðˆ>Ø„B†Fr   c                 ó<  € ^d\         n        ^p \        V 4       F­  p\        \        P                  ! 4       4      p\        V4      p\        ^d\        P                  ! 4       ,          4      p\        V4      p\        WS4      ^,          p\        WS4      ^,          p\        V,
          V,
          pVP                  ^ 4      '       d   K­  Q h	  \        V 4       FË  p\        \        P                  ! 4       4      p	\        X4      p
V
P                  4       p\        ^
\        P                  ! 4       ,          4      p\        V4      pV^,          \        WZ4      ^,          ,          p\        WZ4      ^,          p\        V,
          V,
          pVP                  ^ 4      '       d   KË  Q h	  \        V 4       EF]  p\        \        P                  ! 4       4      p	\        V	4      p
V
P                  4       p\        \        P                  ! 4       4      p\        V4      pV^,          \        WZ4      ^,          ,          p^V^,          ,
          p\        WZ4      ^,          pWÆ,
          V,
          pVP                  ^ 4      '       g   Q h\        V^,          4      p\        WÚ4      pVP                  \        4      '       g   Q h\        WÚ4      pVP                  ^ 4      '       g   Q hT
p\        V\        4      pVP                  \        4      '       d   EK^  Q h	  ^\         n        R# )zl
Tests the some of the jacobi elliptic function identities found
on Mathworld. Haven't found in Abramowitz.
N)r'   r(   rL   rR   rS   r<   rƒ   r‡   rM   r   r=   rŠ   Úellipkr;   )ÚNr@   rX   r>   ri   rJ   rj   rk   rm   r‹   rA   r   rl   ÚKrd   rT   s                   r   Útest_sn_cn_dn_identitiesr‘   ç  s8  € ð
 „B„FØ	€AÜ�1ŽXˆÜ”f—m’m“oÓ&ˆÜ�‹LˆÜ�cœ&Ÿ-š-›/Õ)Ó*ˆÜ�‹Lˆô �A“	˜1•ˆÜ�A“	˜1•ˆÜ˜•; Õ&ˆØ�{‰{˜1�~Œ~Ðˆ~ñ ô �1ŽXˆÜ”f—m’m“oÓ&ˆÜ�‹LˆØ�F‰F‹HˆÜ�bœŸš›Õ(Ó)ˆÜ�‹LˆØ�1•”s˜1“y !•|Õ#ˆÜ�A“	˜1•ˆÜ˜•; Õ&ˆØ�{‰{˜1�~Œ~Ðˆ~ñ ô �1�XˆÜ”f—m’m“oÓ&ˆÜ�‹LˆØ�F‰F‹HˆÜ”f—m’m“oÓ&ˆÜ�‹Lˆð �1•”s˜1“y !•|Õ#ˆØ�A�q•D•ˆÜ�A“	˜1•ˆØ•= 5Õ(ˆØ�{‰{˜1�~Š~Ðˆ~ä�1�a•4‹Lˆô �‹IˆØ�t‰t”C�yŠyÐˆyô �q“9ˆØ�{‰{˜1�~Š~Ðˆ~ð ˆÜ�A”t“ˆØ�x‰xœ�}�}Ðˆ}ñ= ð@ „B†Fr   c                  óZ  € ^\         n        \        R4      \        R4      \        ,          ,           p \        ^4      ^,          \        ^,          ,           p\        ^4      ^,          \        ^,          ,           p\	        W4      p\        W04      '       g   Q h\        R4      \        R4      \        ,          ,
          p \        W4      p\        W04      '       g   Q h\        R4      \        R4      \        ,          ,
          p \        W4      p\        W04      '       g   Q h^\         n        R# )r[   z!0.2495674401066275492326652143537z"0.12017344422863833381301051702823z!0.9762691700944007312693721148331z!0.0307203994181623243583169154824z%0.99639490163039577560547478589753039z%0.01346296520008176393432491077244994N)r'   r(   r<   r_   rƒ   r   r‡   rŠ   )r
   ÚurA   rd   s       r   Útest_sn_cn_dn_complexr”   +  sß   € Ø„B„Fä
Ð1Ó
2Ü
Ð2Ó
3´aÕ
7õ8€CäˆA‹ˆq�”1�Q•3�€AÜˆA‹ˆq�”1�Q•3�€AÜˆA‹	€AÜ�!�>Š>Ðˆ>ô Ð1Ó
2Ü
Ð1Ó
2´1Õ
4õ5€CäˆA‹	€Aô �!�>Š>Ðˆ>ô Ð5Ó
6Ü
Ð5Ó
6´qÕ
8õ9€CäˆA‹	€AÜ�!�>Š>Ðˆ>Ø„B†Fr   c                  óÒ  € ^\         n        \        ^ ^^4      P                  R4      '       g   Q h\        ^^^4      P                  R4      '       g   Q h\        \        \        ) ^4      P                  R4      '       g   Q h\        ^ \        \        ) 4      P                  R34      '       g   Q h\        ^ \        ^,
          \        4      P                  R44      '       g   Q h\        R5\        ,
          \        ) R6\        ,           4      P                  R74      '       g   Q h\        ^ ^ ^ 4      ^ 8X  g   Q h\        ^ ^ ^4      P                  ^4      '       g   Q h\        ^ ^^ 4      P                  ^4      '       g   Q h\        ^^ ^ 4      P                  ^4      '       g   Q h\        ^^^ 4      P                  R4      '       g   Q h\        ^^ ^4      P                  R4      '       g   Q h\        ^ ^^4      P                  R4      '       g   Q h^RR8r!p \        WV4      P                  R94      '       g   Q h\        WV4      P                  R94      '       g   Q h\        WV4      P                  R94      '       g   Q h\        WV 4      P                  R94      '       g   Q h\        W V4      P                  R94      '       g   Q h\        W!V 4      P                  R94      '       g   Q hR: EFk  pV\         n        \        ^^^ 4      P                  R4      '       g   Q h\        R^^ 4      P                  R4      '       g   Q h\        \        \        ) ^ 4      P                  R4      '       g   Q h\        \        ^,
          \        ^ 4      P                  \        R	R
4      4      '       g   Q h\        ^^^4      P                  R4      '       g   Q h\        \        \        ) ^4      P                  R4      '       g   Q h\        \        ^,
          \        ^\        ,
          4      P                  \        RR4      4      '       g   Q h\        ^ R4      P                  \        54      '       g   Q h\        R^4      P                  \        54      '       g   Q h\        ^ \        4      P                  \        RR4      4      '       g   Q h\        \        ) \        4      P                  \        RR4      4      '       g   Q h\        RR54      P                  \        ^,          4      '       g   Q h\        \        R64      P                  \        RR4      4      '       g   Q h\        ^ ^^^4      P                  R4      '       g   Q h\        ^^^^4      P                  R4      '       g   Q h\        ^^^R6\        ,           4      P                  \        RR4      4      '       g   Q h\        \        \        ) ^ ^4      P                  R4      '       g   Q h\        R6\        ,           R6\        ,
          ^^4      P                  R4      '       g   Q h\        \        \        ) ^ ^\        ,
          4      P                  \        RR4      4      '       g   Q h\        R6\        ,           R6\        ,
          ^R;\        ,           4      P                  \        RR 4      4      '       g   Q h\        R6\        ,           R5\        ,
          \        ) R6\        ,           4      P                  \        R!R"4      4      '       g   Q h\        ^ ^^4      P                  \        54      '       g   Q h\        ^^^4      P                  R#4      '       g   Q h\        ^ \        \        ) 4      P                  R$4      '       g   Q h\        \        ^,
          \        ^ 4      P                  \        R%R&4      4      '       g   Q h\        \        ) \        ^,
          \        4      P                  \        R'R(4      4      '       g   Q h\        ^ \        R)4      ^4      P                  R*4      '       d   EKl  Q h	  ^\         n        \        R<R=R>R?4      P                  R@R+R,7      '       g   Q h\        R-RA^ RB4      P                  RCR+R,7      '       g   Q h\        R.RDR/RE4      P                  RFR+R,7      '       g   Q h\        R.RGR/RE4      P                  RHR0R,7      '       g   Q h\        R.RIR/RE4      P                  RJR+R,7      '       g   Q h\        R.RKR/RE4      P                  RLR+R,7      '       g   Q h\        R.RMR/RE4      P                  RN4      '       g   Q h\        R.ROR/RE4      P                  RP4      '       g   Q h\        RQRRRS4      P                  RT4      '       g   Q h\        RURV4      P                  RW4      '       g   Q h\        RXRY4      P                  RZ4      '       g   Q h\        R1R[4      P                  R\4      '       g   Q h\        RVRU4      P                  R]4      '       g   Q h\        RVR14      P                  R^4      '       g   Q hR2# )_r   g2e¤_Áü?gçÃ×i+"Å?g€P$Må?g»{ I|`ó?y              ð?zo1.3110287771460599052324197949455597068413774757158115814084108519003952935352071251151477664807145467230678763r&   zn1.854074677301371918433850347195260046217598823521766905585928045056021776838119978357271861650371897277771871zp0.79612586584233913293056938229563057846592264089185680214929401744498956943287031832657642790719940442165621412zp-1.2138566698364959864300942567386038975419875860741507618279563735753073152507112254567291141460317931258599889zp0.58408284167715170669284916892566789240351359699303216166309375305508295130412919665541330837704050454472379308zo1.0441445654064360931078658361850779139591660747973017593275012615517220315993723776182276555339288363064476126zp0.93912050218619371196624617169781141161485651998254431830645241993282941057500174238125105410055253623847335313zq-0.53296252018635269264859303449447908970360344322834582313172115220559316331271520508208025270300138589669326136r   g      @zo1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zp-1.1107207345395915617539702475151734246536554223439225557713489017391086982748684776438317336911913093408525532zo1.2260849569072198222319655083097718755633725139745941606203839524036426936825652935738621522906572884239069297zq-0.34471136988767679699935618332997956653521218571295874986708834375026550946053920574015526038040124556716711353zp0.77778596920447389875196055840799837589537035343923012237628610795937014001905822029050288316217145443865649819zo0.1983248499342877364755170948292130095921681309577950696116251029742793455964385947473103628983664877025779304zp0.77688623778582332014190282640545501102298064276022952731669118325952563819813258230708177398475643634103990878zp0.14297579667156753833233879421985774801466647854232626336218889885463800128817976132826443904216546421431528308zp0.13613945827770535203521374457913768360237593025944342652613569368333226052158214183059386307242563164036672709zq-0.38207561624427164249600936454845112611060375760094156571007648297226090050927156176977091273224510621553615189zo1.6490011662710884518243257224860232300246792717163891216346170272567376981346412066066050103935109581019055806zp0.94148358841220238083044612133767270187474673547917988681610772381758628963408843935027667916713866133196845063zo1.8260115229009316249372594065790946657011067182850435297162034335356430755397401849070610280860044610878657501zo1.2290661908643471500163617732957042849283739403009556715926326841959667290840290081010472716420690899886276961zq-0.61127970812028172123588152373622636829986597243716610650831553882054127570542477508023027578037045504958619422zp-1.0684038390006807880182112972232562745485871763154040245065581157751693730095703406209466903752930797510491155zo1.8249027393703805304622013339009022294368078659619988943515764258335975852685224202567854526307030593012768954zp-1.2218475784827035854568450371590419833166777535029296025352291308244564398645467465067845461070602841312456831zo1.7255030280692277601061148835701141842692457170470456590515892070736643637303053506944907685301315299153040991zp0.42360654239698954330324956174109581824072295516347109253028968632986700241706737986160014699730561497106114281zp0.44660591677018372656731970402124510811555212083508861036067729944477855594654762496407405328607219895053798354zp0.70768352357515390073102719507612395221369717586839400605901402910893345301718731499237159587077682267374159282zp0.36023392184473309033675652092928695596803358846377334894215349632203382573844427952830064383286995172598964266zp0.40348623401722113740956336997761033878615232917480045914551915169013722542827052849476969199578321834819903921z0.0796zo1.028475809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