
    \h                         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Jr  S SKJr  S SKJr  S SKJr  S rS	 rS
 rS rg)    )Eq)S)xyzst)	FiniteSetEmptySet)Point)ImplicitRegion)raisesc                  n   [        [        [        4[        S-  S-  [        S-  S-  -   S-
  5      n U R                  [        S-  S-  [        S-  S-  -   S-
  :X  d   eU R                  [        [        4:X  d   eU R
                  S:X  d   e[        [        [        [        4[        [        S-  [        S-  -   [        [        -  -
  S5      5      nUR                  [        S-  [        S-  -   [        [        -  -
  S-
  :X  d   eUR                  [        [        [        4:X  d   eUR
                  S:X  d   eg )N               )r   r   r   equation	variablesdegreer   r   )ellipsers     ^/var/www/auris/envauris/lib/python3.13/site-packages/sympy/vector/tests/test_implicitregion.pytest_ImplicitRegionr   
   s   aVad1fq!tBw&6&:<Gq!tAv1R/!3333A&&&>>Q1ay"QTAqD[1Q3%6":;A::A1qs*Q....;;1a)###88q==    c                  0  ^ [        [        4[        S-  S-
  5      n U R                  5       S:X  d   e[        [        [        4[        S-  [        S-  -   S-
  5      nUR                  5       S:X  d   e[        [        [        4[        [	        S5      S-  -
  S-  [        S-  -   [	        S5      S-  S-  -
  5      nUR                  5       [	        S5      S-  [	        S5      * S-  4:X  d   e[        [        [        4[        S-
  S-  S[        S-
  -  -
  5      nUR                  5       S:X  d   e[        [        [        4[        S-  S[        -  [        -  -
  S	[        S-  -  -
  S[        -  -   S
[        -  -   S-
  5      nUR                  5       [	        S5      S-  [	        S5      S-  4:X  d   e[        [        [        4[        S-  S[        -  [        -  -
  S	[        S-  -  -   S[        -  -
  S[        -  -
  S-   5      m[        [        U4S j5        g )Nr   r   )r   )r      r   )r    r             	   g      ?c                  $   > T R                  5       $ N)regular_point)r3s   r   <lambda>$test_regular_point.<locals>.<lambda>!   s    r//1r   )r   r   r'   r   r   r   
ValueError)r1c1c2c3r2r(   s        @r   test_regular_pointr1      s   	adRi	(B&&&	A1q!ta	0B(((	AQqT!Va!Q$ 6!A$q&1 D	EB!A$q&1Q4%'!2222	AQ
b!a%j 8	9B'''	A1qs1uqAv 5! ;ac AA E	FB!A$q&!A$q&!1111	A1qs1uqAv 5! ;ac AC G	HB
:12r   c                     [        [        [        [        4[	        [        [        -   [        -   S5      5      n U R                  5       [        :X  d   e[        [        [        [        4[        [        -  [        -  [        S-  -   [        S-  [        S-  -  -
  5      nUR                  5       [        SS[        4[        SS45      :X  d   eUR                  S5      S:X  d   eUR                  S5      S:X  d   e[        [        [        [        4[        S-  [        S-  -
  [        S-  -
  5      nUR                  5       [        S5      :X  d   eUR                  S5      S:X  d   e[        [        [        4[        S-  [        S-  -   S[        -  -
  5      nUR                  5       [        :X  d   eUR                  [        SS5      5      S:X  d   eg )Nr   r   r   )r   r   r   r!   )r   r   r   r   )
r   r   r   r   r   singular_pointsr   r
   multiplicityr   )r,   r0   r(   r4s       r   $test_singular_points_and_multiplictyr6   $   sx   	Aq	2a!eai#3	4B8+++	Aq	1Q3q51a4<Aad#:	;B9aAYAq	#BBBB??9%***??9%***	Aq	1a4!Q$;A#5	6B9Y#7777??9%***	A1q!tac 1	2B8+++??5A;'1,,,r   c            	      D  ^^ [        [        4[        S-
  5      n U R                  5       [        S-
  4:X  d   e[        [        [        4[	        [        S[        -  S-   5      5      nUR                  5       [        S[        -  S-   4:X  d   e[        [        [        4[        S-
  S-  [        S-   S-  -   S-
  5      nUR                  [
        S9S[
        -  [
        S-  S-   -  S-   S[
        S-  -  [
        S-  S-   -  S-
  4:X  d   e[        [        [        4[        [        R                  -
  S-  [        S-  -   [        S5      S-  S-  -
  5      nUR                  [
        S9[
        [
        S-  S-   -  [        S5      S-  -   [
        S-  [
        S-  S-   -  [        S5      S-  -
  4:X  d   e[        [        [        4[	        [        S-  [        S-  -   S[        -  5      5      nUR                  [
        4S9S[
        -  [
        S-  S-   -  S-   S[
        S-  -  [
        S-  S-   -  S-
  4:X  d   e[        [        [        4[        S-
  S-  S[        S-   -  -
  5      nUR                  [
        5      SS[
        S-  -  -   SS[
        -  -   4:X  d   e[        [        [        4[        [        -  S-
  5      nUR                  [
        5      S	[
        S-   [
        -  -   [
        4:X  d   e[        [        [        4[        S-  [        S-  -   [        S-  -
  5      nUR                  [
        S9[
        S-  S-
  [
        [
        S-  S-
  -  4:X  d   e[        [        [        4[        S-  [        S-  -
  5      nUR                  [
        5      [
        S-  [
        S-  4:X  d   e[        [        [        4[        S-  [        S-  -   [        S-  -
  5      n	U	R                  [
        5      [
        S-  S-
  [
        [
        S-  S-
  -  4:X  d   e[        [        [        [        4[	        [        S-  [        S-  -   [        S-  -   S[        -  5      5      n
U
R                  [        [
        4S9S[        S-  [
        S-  -   S-   -  S[
        -  [        S-  [
        S-  -   S-   -  S[        -  [        S-  [
        S-  -   S-   -  4:X  d   e[        [        [        4[	        [        S-  S[        -  [        -  -   S[        S-  -  -   [        -   [        -
  S
-   S5      5      nUR                  [
        5      [        S5      S-  SS[
        S-  -  S[
        -  -   S-   -  -   S[
        -  S[
        S-  -  S[
        -  -   S-   -  [        S5      S-  -
  4:X  d   e[        [        [        4[        S-  [        S-  -
  [        -   5      m[        [        U4S j5        [        [        [        4[        S-  [        S-  -
  [        S-  -
  S-   5      m[        [        U4S j5        g )Nr   r!   r   )
parametersr   r    r   i
   r         c                  $   > T R                  5       $ r&   rational_parametrization)r,   s   r   r)   /test_rational_parametrization.<locals>.<lambda>X       (C(C(Er   c                  $   > T R                  5       $ r&   r>   )r0   s   r   r)   r@   Z   rA   r   )r   r   r?   r   r   r	   r   Halfr   r   r   NotImplementedError)plinecircle1circle2circle3parabolarect_hyperbolacubic_curvecuspidalIsphereconicr,   r0   s               @@r   test_rational_parametrizationrQ   3   s   tQU#A%%'AE83331a&"Q!a.1D((*q!A#'l:::aVacAX1q%81%<=G++q+9ac1a4!8nq>PRSTUWXTXRXZ[]^Z^abZbRcfgRg=hhhhaVa!&&j1_q!t%;qtAvk%IJG++q+9aAlQqTRSV>SUVXYUY[\^_[_bc[cUdghijgklmgmUm=nnnnaVR1q!tQqS%9:G++t+<1adQhRSASUVWXZ[W[U[]^`a]ade]eUfijUj@kkkkq!fq1uqj1a!e9&<=H,,Q/B1a4KQqS3IIII#QFAaC!G4N2215"Aqy.!9LLLL !QA1q!t);<K//A/?AqD1HaQRTUQUXYQYlC[[[[q!fq!tad{4H,,Q/AqD!Q$<???1vq!tad{QT12A%%a(QTAXq!Q$(|,DDDDQ1Ir!Q$A+1*<ac'BCF**q!f*=!QTAqD[ST_BUWXYZWZ\]_`\`cdfgcg\gjk\kWlnopqnqstvwswz{}~z~s~  BC  tC  oD  BE  E  E  EAq62adQqSUlQq!tV&;a&?!&Cb&H!#LME))!,	"a!Qq!tVac\A%&&!Qq!tVac\A-=(>2q(H1J J J J 
A1q!ta	0B
 EF	A1q!tad 2Q 6	7B
 EFr   N)sympy.core.relationalr   sympy.core.singletonr   	sympy.abcr   r   r   r   r	   
sympy.setsr
   r   sympy.geometryr   sympy.vectorr   sympy.testing.pytestr   r   r1   r6   rQ    r   r   <module>rZ      s2    $ " # # *   ' '3-'Gr   