
    \h                     r    S r SSKJr  SSKJr  SSKJr  SSKJ	r	J
r
JrJrJr  SSKJr  S rS rS	 rS
 rS rg)z>Tests for efficient functions for generating Appell sequences.    )Rational)Poly)raises)bernoulli_polybernoulli_c_poly
euler_polygenocchi_poly
andre_poly)xc                     [        [        S 5        [        S[        SS9[	        [        [        SS5      -
  5      :X  d   e[        S[        5      S:X  d   e[        S[        5      [        [        SS5      -
  :X  d   e[        S[        5      [        S-  [        -
  [        SS5      -   :X  d   e[        S[        5      [        S-  [        SS5      [        S-  -  -
  [        SS5      [        -  -   :X  d   e[        S	[        5      [        S	-  S[        S-  -  -
  [        S-  -   [        SS
5      -
  :X  d   e[        S[        5      [        S-  [        SS5      [        S	-  -  -
  [        SS5      [        S-  -  -   [        SS5      [        -  -
  :X  d   e[        S[        5      [        S-  S[        S-  -  -
  [        SS5      [        S	-  -  -   [        SS5      [        S-  -  -
  [        SS5      -   :X  d   e[        S5      R                  [        [        SS5      -
  5      (       d   e[        SSS9[	        [        [        SS5      -
  5      :X  d   eg )Nc                  "    [        S[        5      $ N)r   r        Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/polys/tests/test_appellseqs.py<lambda>%test_bernoulli_poly.<locals>.<lambda>
   s    ~b!4r      Tpolys   r                  *   )r   
ValueErrorr   r   r   Qdummy_eqr   r   r   test_bernoulli_polyr"   	   s   
:45!Qd+tA!AJ/????!Q1$$$!Q1q1v:---!Q1a4!8a!f#4444!Q1a4!Aa&A+#5!Aq#@@@@!Q1a4!AqD&=1a4#7!Ab'#AAAA!Q1a4!Aa&A+#5!Aq!t#Ca!fQh#NNNN!Q1a4!AqD&=1Qq6!Q$;#>1Q1#LqQRSUw#VVVV!%%a!Aa&j1111!4(DQqV,<<<<r   c                  X   [        [        S 5        [        S[        SS9[	        [        SS9:X  d   e[        S[        5      S:X  d   e[        S[        5      [        :X  d   e[        S[        5      [        S-  [        SS	5      -
  :X  d   e[        S	[        5      [        S	-  [        -
  :X  d   e[        S
[        5      [        S
-  S[        S-  -  -
  [        SS5      -   :X  d   e[        S[        5      [        S-  [        SS	5      [        S	-  -  -
  [        SS	5      [        -  -   :X  d   e[        S[        5      [        S-  S[        S
-  -  -
  S[        S-  -  -   [        SS5      -
  :X  d   e[        S5      R                  [        5      (       d   e[        SSS9[	        [        SS9:X  d   eS[        S[        S-   S-  5      R                  5       -  [        S[        5      :X  d   eS[        S[        S-   S-  5      R                  5       -  [        S[        5      :X  d   eg )Nc                  "    [        S[        5      $ r   )r   r   r   r   r   r   'test_bernoulli_c_poly.<locals>.<lambda>   s    /A6r   r   Tr   QQ)domainr   r   r   r         r   
   r               i   	   )	r   r   r   r   r   r    r!   r   expandr   r   r   test_bernoulli_c_polyr1      s   
:67Aq-a1EEEEAq!Q&&&Aq!Q&&&Aq!QTAaF]222Aq!QTAX---Aq!QTAadF]QqW%<<<<Aq!QTAbGAqDL%81Qq6!8%CCCCAq!QTAadF]Qq!tV%;a2h%FFFFA''****AT*d1T.BBBB.QqS!G,33559I!Q9OOOO.QqS!G,33559I!Q9OOOOr   c                  &   [        [        S 5        [        S[        SS9[	        S[        -  S-   5      :X  d   e[        S[        5      S:X  d   e[        S[        5      S:X  d   e[        S[        5      SS[        -  -
  :X  d   e[        S	[        5      S	[        -  S	[        S-  -  -
  :X  d   e[        S
[        5      SS[        S-  -  -   S
[        S	-  -  -
  :X  d   e[        S[        5      S[        -  S[        S	-  -  -   S[        S
-  -  -
  :X  d   e[        S[        5      S	S[        S-  -  -
  S[        S
-  -  -   S[        S-  -  -
  :X  d   e[        S5      R                  S[        -  S-   5      (       d   e[        SSS9[	        S[        -  S-   5      :X  d   eS[        S[        5      [        S[        5      -
  -  [        S[        5      :X  d   eS[        S[        5      [        S[        5      -
  -  [        S[        5      :X  d   eg )Nc                  "    [        S[        5      $ r   )r	   r   r   r   r   r   $test_genocchi_poly.<locals>.<lambda>+   s    }R3r   r   Tr   r   r   r   r   r   r   r   r*   r)   r.   r/   )r   r   r	   r   r   r!   r   r   r   r   r   test_genocchi_polyr7   *   s   
:34AT*d2a4!8n<<<A!###A"$$$A!ac')))A!A#!Q$,...A"qAv+!Q$"6666A"Q$AqD.1QT6"9999A!bAg+1a4"7!AqD&"@@@@$$RTAX....$'41q>999q!$'71'==>-PQSTBUUUUq!$'71'==>-PQSTBUUUUr   c                     [        [        S 5        [        S[        SS9[	        [        [        SS5      -
  5      :X  d   e[        S[        5      S:X  d   e[        S[        5      [        [        SS5      -
  :X  d   e[        S[        5      [        S-  [        -
  :X  d   e[        S[        5      [        S-  [        SS5      [        S-  -  -
  [        SS5      -   :X  d   e[        S[        5      [        S-  S[        S-  -  -
  [        -   :X  d   e[        S	[        5      [        S	-  [        S	S5      [        S-  -  -
  [        S	S5      [        S-  -  -   [        SS5      -
  :X  d   e[        S
[        5      [        S
-  S[        S	-  -  -
  S	[        S-  -  -   S[        -  -
  :X  d   e[        S5      R                  [        [        SS5      -
  5      (       d   e[        SSS9[	        [        [        SS5      -
  5      :X  d   e[        S[        5      [        S[        5      S-  :X  d   e[        S[        5      [        S[        5      S-  :X  d   eg )Nc                  "    [        S[        5      $ r   )r   r   r   r   r   r   !test_euler_poly.<locals>.<lambda>=       z"a0r   r   Tr   r   r   r   r   r   r   r/   r.   ir*   i)r   r   r   r   r   r    r!   r	   r   r   r   test_euler_polyr<   <   s   
:01a$'4AaF
+;;;;aq   aq1Qq6z)))aq!tax'''aq!ta!fQTk1AaF::::aq!ta1f}q0000aq!ta!fQTk1AaF1a4K?!Aa&HHHHaq!ta1f}qAv5!;;;;a=!!!a!f*----at$Q1QZ(8888A*Q"2R"7777Q:a#3c#9999r   c                     [        [        S 5        [        S[        SS9[	        [        5      :X  d   e[        S[        5      S:X  d   e[        S[        5      [        :X  d   e[        S[        5      [        S-  S-
  :X  d   e[        S[        5      [        S-  S[        -  -
  :X  d   e[        S[        5      [        S-  S	[        S-  -  -
  S
-   :X  d   e[        S
[        5      [        S
-  S[        S-  -  -
  S[        -  -   :X  d   e[        S	[        5      [        S	-  S[        S-  -  -
  S[        S-  -  -   S-
  :X  d   e[        S5      R                  [        5      (       d   e[        SSS9[	        [        5      :X  d   eg )Nc                  "    [        S[        5      $ r   )r
   r   r   r   r   r   !test_andre_poly.<locals>.<lambda>O   r;   r   r   Tr   r   r   r   r   r   r   r*      r)   K   =   )r   r   r
   r   r   r!   r   r   r   test_andre_polyrC   N   sS   
:01a$'47222aq   aq   aq!tax'''aq!tacz)))aq!ta1f}q0000aq!tbAg~14444aq!tbAg~1a47"<<<<a=!!!$$$$at$Q///r   N)__doc__sympy.core.numbersr   r    sympy.polys.polytoolsr   sympy.testing.pytestr   sympy.polys.appellseqsr   r   r   r	   r
   	sympy.abcr   r"   r1   r7   r<   rC   r   r   r   <module>rJ      s9    D , & '+ + =P$V$:$0r   