
    \h.                        S SK Jr  S SK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Jr  S	 V s/ s H  n \
" U 5      PM     sn u  rrrrrrrrS
 rS rS rS rS r S r!S r"S r#S r$S r%S r&S r'S r(S r)gs  sn f )    )Mul)IIntegerRational)Symbol)rootsqrt)cos)Integral)
sqrtdenest)_subsets_sqrt_numeric_denest)               
         c                  z   [        SS[        -  -   5      [        [        -   [        SS[        -  -   5      [        SS[        -  -   5      [        SS[        SS[        -  -   5      -  -   5      [        SS[        -  -   S[        -  -   5      [        [        5      [        [        5      [        S[        -   5      [        S[        -   5      [        S[        SS[        -  -   5      -   5      S[        -  SS[        -  -   [        SS5      -  -  S[        SS[        -  -   5      -  -  [        [        SS[        -  -   5      -  SSS[        -  -   [        SS5      -  -  -  -   [        SS[        -  -   5      S[        SS5      -  [        S-  S[        -  S-  -   -  S-  0n U  H  n[        U5      X   :X  a  M   U5       e   g )Nr   r   g      @   r      r   )r	   r6r2r3r7r   r   )dis     \/var/www/auris/envauris/lib/python3.13/site-packages/sympy/simplify/tests/test_sqrtdenest.pytest_sqrtdenestr!      sv   	a!b&j	27R!b&[4QV,R!DQV$$$%tC!B$J2,='>R$r(QVd1r6lQa!B$h 	
2q1R4x(1a.(	(!DQrTN*:	;	DQrTN	Aq1R4x(1a.88	9
:Q2X8Aq>)2a4!B$q&=9!;	=A !}$'a'$     c                     [        [        SS[        -  -
  S[        SS[        -  -
  5      -  -   5      5      [        [        SS[        -  -
  5      -   :X  d   e[        [        * [        S[        -  S[        S[        -  S-   5      -  -   S-   5      -   5      n [        U 5      [	        S[        -  S-   S5      :X  d   e[        S	[
        -   5      n[        [        S	U-   5      5      [        S	U-   5      :X  d   e[        S	[        S	S[        S
[        -   [        -   5      -  -   5      -   S-  R                  5       5      n [        U 5      S	[        S	S[        [        [        -   S
-   5      -  -   5      -   :X  d   e[        [        S[        -  S[        -  -   5      5      [        S5      [	        S
S5      -  [	        S
S5      S
-  -   :X  d   e[        [        S	[        -   [        S	[        -   5      -   S-  R                  5       5      5      S	[        -   [        S	[        -   5      -   :X  d   e[        [        S	[        -   [
        -   [        S	[        -   5      -   S-  R                  5       5      5      S	[        S	[        -   5      -   [        -   [
        -   :X  d   e[        S	[        S5      -   [        S
5      -   [        S	[        -   5      -   S-  R                  5       5      n [        U 5      [        S
5      [        S5      -   S	-   [        S	[        -   5      -   :X  d   e[        S[        -  S[        -  [        S[        -  S-   5      -  -   S-   5      n [        U 5      [        S[        -  S[        -  -
  S[        -  -   S-   5      :X  d   e[        S[        -  [        S5      -   S[        S[        -  S-   5      -  -   S-   5      n[        U5      U:X  d   e[        [        [        [        S5      -   5      5      [        [        [        S5      -   5      :X  d   e[        SS[        S5      -  -
  S[        SS[        -  -
  5      -  -   5      n[        U5      U:X  d   eg )N   r   7   r      r   r   r   r   r      r      )r   r	   r29r5r   r   r   expandr   r
   r10r   )erzs      r    test_sqrtdenest2r2      s   d2#:$rBsF{*;(;;<=
T"qu*  bS434C"#5!55:;;<Aa=DC"a0000QVAd1q5k"d1q5k111q4Ad1r6B;///0014<<>?Aa=AQ4R!+<)<%< =====d1R4!B$;'(QQ
T!QZ]*+ + + dQVd1r6l2Q6>>@AB	Ba"f   dQVb[4B<7!;CCEFG	DRL2"# # # 	q3q6zCF"T!b&\1A5==?@Aa=CFSVOa/$q2v,>>>>RVad43,,,r12Aa=DC!B$2!5!:;;;; 	RVc!f_qc#gl!333b89Aa=Ad2R=)*d2R=.AAAAR!DH*_qb2c6k!2223Aa=Ar"   c            	         [        [        S[        S5      -  S[        -  -
  S[        S5      -  -   S-   5      5      [        * [        -   S[
        -  -   :X  d   e[        [        S[
        -  S[        -  -
  S[        S5      -  -   S	-   5      5      S
[        -   S[
        -  -   :X  d   e[        [        S[        -  S-  S[        S5      -  S-  -   S[        S5      -  S-  -   S-   5      5      [        S5      [        S-   [        S5      -   -  S-  :X  d   e[        [        S[        -  S[        -  -   S[        -  -   S-   5      5      S[        -  S-   S[        -  -   :X  d   e[        S[        -  S[        S5      -  -
  S[        S5      -  -
  S-
  5      n [        U 5      [        S5      S[        -  S[        -  -   S[        S5      -  -   -  :X  d   e[        S[        S5      -  S[        -  -
  S[        S5      -  -   S-   5      n [        U 5      U :X  d   e[        [        S[        -  S[        -  -
  S -   5      5      [        * S!-   [        -   [        -   :X  d   e[        [        S"[        -  S[        -  -   S -
  5      5      [        S5      [        * S!-   [        -   [        -   -  :X  d   e[        [        S"[        -  S-  S[        -  S-  -   [        S#S5      -   5      5      [        * S-  [        -   [        -   S-   :X  d   e[        [        [        S[        -  S$-   5      [        S[
        -  S"-   5      -   5      5      [        S![        -   [        -   [
        -   5      :X  d   e[        [        S[        -  S"[        -  -   S%[        -  -   S&-   5      5      S![        -   [        -   [        -   :X  d   eS![        -   [        -   [        -   [
        -   n[        [        US-  R                  5       5      5      U:X  d   e[        US-  R                  5       S!-   5      n [        U 5      U :X  d   e[        S[        -  S[        -  -   S[        -  -   S%-   S'[        -  -   S([        -  -   5      n [        U 5      U :X  d   eg ))Nr)   r   r      !   i#   R   ir   r&      r   i  i  i`  iM  	      8   ib   s   iY  i;  r      "      r         r         r      )r   r	   r   r   r   r   r,   r15r.   r   r-   )r1   ws     r    test_sqrtdenest_recrK   @   s   d2d2h;2-$r(
:R?@A	b1R4  d3r6BrE>Ad2hJ6;<=
R!B$  d1R47QtBxZ]2QtBxZ]BQFGHR"q&48#$R'( ( (d3r6DG+d2g5=>?	"r	BrE  T"Wr$s)|#bcl2T9:Aa=DHadQsUlQtBxZ&?@@@@RR[1R4!DH*,r12Aa=Ad2b51R4<",-.3$(R-"2DDDDd1R4!B$;+,-R3$(R-"$%& & &d1R46BrE!G+hsA.>>?@	Qb1  d4"q>D2N:;<QVb[2  d1S51R4<"R%/"456!b&2+:KKKK	Bb2AdAqD==?+,111ad]]_q !Aa=AQsUQrT\AbD 2%3.B67Aa=Ar"   c                  n    [        SS[        S5      -  -   S[        -  -   5      n [        U 5      U :X  d   eg )Ni    r   @   )r	   rI   r   )r1   s    r    test_issue_6241rO   _   s4    dRQZ"S&()Aa=Ar"   c                  ~   [        SS[        -  -
  S[        -  [        S[        -  S-   5      -  -   5      n [        U 5      S[        -   [        -   :X  d   e[        U SS9S[        S5      -   [        S5      -   :X  d   e[        [        [        S-   5      S-   5      n [        U 5      U :X  d   e[        [        S[        -  S	[        -  [        S[        -  S-   5      -  -   S
-   5      5      [        S[        -  S	[        -  -
  S[        -  -   S
-   5      :X  d   e[        [        SS[        -  -   SS[        -  -   [        -  -   5      5      [        S-   S	[        -  -   S[        -  -   :X  d   e[        S[        S[
        -  S-   5      [        S[        -  S[        S[        -  S-   5      -  -   S-   5      -  -   5      n [        S[        -  S-   5      n[        U 5      [        [        U-  [        U-  -   [        -   [        -   S-   5      :X  d   e[        S[
        -  S-  S[        -  S-  -   S[        S5      -  S-  -   S-   5      n[        SS[        -  -
  S[        SS[        -  -
  5      -  -   5      n[        X#-  5      [        S[
        -   [        -   -  [        S[        S[        -  S-   5      [        -   SS9-  :X  d   eg )N   r   r'   r&   r?   r   )max_iterr   r      rD   p   F   .   rA   r   r   r(   r%   r$   r   *   F)evaluate)r	   r.   r   r   r,   r   r+   r   rI   r   r   )r1   r0   nr   s       r    test_sqrtdenest3rZ   d   s~   R!C%Z!B$tBsFRK0001Aa=BGcM)))a!$T!WtBx(????T"q&\AAa=Ad2c6AbDbfrk):$::R?@ARVad]QrT!B&'( ( (dC"R%KBBJ?:;<a!B$2  QadQhRVaSWr\0B.B%BR%G HHHIARVb[Aa=DA1s!2S!81!<====QrT!Vad1f_qbz!|+a/0AR!C%Z!Dbf---.Aac?b!b&2+.ARVb[8IB8N=B1D E E E Er"   c                  H   [        S[        [        S[        -
  5      -  -
  [        S5      S[        -   -  -
  5      n [        U 5      n[        [        * S-   5      n[        * U-  [
        U-  -
  U-   [        U-  -   [        -
  [        -
  [        -   [        S5      -   S-  R                  5       n[        U 5      U:X  d   e[        S[        -  [        [        S-   5      -  S[        -  -   S[        [        S-   5      -  -   S-   5      n [        U 5      [        [        [        S-   5      -   S-   :X  d   eS[        -   [
        -   S[
        -   [        S[        -   S[
        -  -   5      -  -   n[        US-  R                  5       5      n [        U 5      UR                  5       :X  d   eg )NrD   r   r   r   rH   r   r   )	r	   r   r,   r   rI   r   r   r.   r-   )r1   z1crJ   s       r    test_sqrtdenest4r^   x   sV   QDRL 47AF#334A	ABbS1WA46BqD=1r!t#b(2-3d2h>
A	I	I	KBa=BQrT$rAv,2%$rAv,6:;Aa=Bb1f-1111	Bq2vtAFQrTM222Aad]]_Aa=AHHJ&&&r"   c                     [        S5      n [        S[        [        SU -   5      S-   5      -   S-  R                  5       5      n[        U5      [        S[        [        SU -   5      S-   5      -   S-  5      :X  d   e[        S[        [        S[	        S5      -   5      S-   5      -   S-  R                  5       5      n[        U5      S[        [        S[	        S5      -   5      S-   5      -   :X  d   eS[	        S5      -   S-  S-   R                  5       n[        U5      U:X  d   e[        S[        [        S[	        SU -  5      -   5      S-   5      -   S-  S-   R                  5       5      n[        U5      U:X  d   e[	        S5      nUS-  n[        [        S[        S[
        -   5      -  U-  U-   S-   [
        U-  -   5      5      S[        S[
        -   5      U-  -
  :X  d   e[        S[
        -   5      n[        SU-  [        SS[
        -  -   5      -  S[
        -  U-  [        SS[
        -  -   5      -  -   S	[
        -  -   S
-   5      n[        U5      U:X  d   eg )Nxr   r   r   r   r?   rS   rF   rN   rT   )r   r	   r-   r   r
   r   )r`   r1   r]   c2ras        r    test_sqrt_symbolic_denestrc      s   sAq4QUa((1,4467Aa=D!d4A;?&;";a!?@@@@q4QQZ(1,--199;<Aa=AT!c!f*%5%9 :::::
c!f*q1	$$&Aa=Aq4QQqS\*Q.//!3a7??ABAa=AAA	
ABd1T!b&\>!+b014r"u<=>
T!b&\!^  	a"fBRU4AbD>!BrE"HT!ad(^$;;beCcIJAa=Ar"   c                     SSK Jn Jn  [        SS[        -  S-   -  S-   5      n[
        [        -   [        S-   -  n[        U5      U:X  d   e[        SU-   5      SU-   :X  d   e[        [        US-   U SS45      5      [        SU-   U SS45      :X  d   e[        U [        U5      -   5      U [        U5      -   :X  d   e[
        [        -   [        S-   -  n[        U5      U:X  d   e[        SU-   5      SU-   :X  d   e[        [        US-   U SS45      5      [        SU-   U SS45      :X  d   e[        U [        U5      -   5      U [        U5      -   :X  d   eg )Nr   )r`   yr   r   r   r   )		sympy.abcr`   re   r	   r   r   r   r   r   )r`   re   r1   anss       r    test_issue_5857rh      s\   Q"q\AA7R!V
Ca=Ca!eC'''hq1uq!Qi01S1a)$% % %a$q'k"a$q'k1117R!V
Ca=Ca!eC'''hq1uq!Qi01S1a)$% % %a$q'k"a$q'k111r"   c                      [        S5      S//:X  d   e[        S5      / SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ S	Q/ S
Q/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/ SQ/:X  d   eg )Nr   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   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )r   r   r   r   )subsets r"   r    test_subsetsrl      sX    1:1#1:lL,lL,lL,N N N Nr"   c                      [        [        S[        S[        S5      -   5      -   5      5      [        S[        S[        S5      -   5      -   5      :X  d   eg )Nr   )r   r	   rk   r"   r    test_issue_5653rn      sP    Qa$q'k""#%(,Qa$q'k1B-B(CD D Dr"   c            	         [        S[        S5      [        SS[        -  -   5      -  -
  S[        -  -   S-  5      [        :X  d   eS[        S5      [        S[        -   5      -  -
  S[        -  -   n [        U 5      U :X  d   eg )Nr   r   r   )r   r	   r   r/   s    r    test_issue_12420rq      ss    q474AaC=001Q369:a???	DGDQK!A#%Aa=Ar"   c                      [        [        S[        -   5      [        SS[        -  -   5      -   [        SS[        -  -   5      -
  5      S:X  d   eg )Nr   r   r   r   r   )r   r	   r   rk   r"   r    test_sqrt_ratcombrs      s?    d1r6lT!ad(^3d2"9oEF!KKKr"   c                      [        SS[        S5      -  [        -  -   5      * n [        U 5      S[        S5      [        -  -
  :X  d   eg )Nr'   r   r   r?   )r	   r   r   rp   s    r    test_issue_18041ru      s>    	b1T!W9Q;	Aa=BaN***r"   c                  ~   [        S5      n [        S5      n[        S5      nX -  X-  U-  -
  n[        XX#5      [        S5      [        -  S-  S[        S5      -  [        -  S-  -   :X  d   e[	        [        S[        S5      -
  5      5      [        S5      [        -  S-  S[        S5      -  [        -  S-  -   :X  d   eg )NrB   r?   ?   r)   r   r   )r   r   r	   r   r   )abr0   d2s       r    test_issue_19914r{      s    AAA	
qs1uBa,R
1qay{1}$% % %d2d2h;'(DHQJqL1T!W9Q;q=,HHHHr"   N)*sympy.core.mulr   sympy.core.numbersr   r   r   sympy.core.symbolr   (sympy.functions.elementary.miscellaneousr   r	   (sympy.functions.elementary.trigonometricr
   sympy.integrals.integralsr   sympy.simplify.sqrtdenestr   r   rj   r   r   r   r,   r   r   r.   rI   r+   r!   r2   rK   rO   rZ   r^   rc   rh   rl   rn   rq   rs   ru   r{   )r`   s   0r    <module>r      s     5 5 $ A 8 . 0/72 %3 72T!W 72 %3 !BBCc( F>
E(' &2"ND
L+Is%3s   B