U
    ZÊ¹j+W  ã                   @   s¼  d dl mZ d dlmZmZmZmZmZmZm	Z	m
Z
 d dlmZmZmZmZmZmZ d dlmZ d dlmZmZ d dlmZ d dlmZmZ d dlmZmZmZ d d	l m!Z! d d
l"m#Z#m$Z$m%Z% d dl&m'Z'm(Z( d dl)m*Z* d dl+m,Z, d dl-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5 edƒZ6eddd�Z7eddd�Z8eddd�\Z9Z:dd„ Z;dd„ Z<dd„ Z=d d!„ Z>d"d#„ Z?d$d%„ Z@e4d&d'„ ƒZAd(d)„ ZBd*d+„ ZCd,d-„ ZDd.d/„ ZEd0d1„ ZFd2d3„ ZGd4S )5é    )ÚAccumBounds)ÚEÚFloatÚIÚRationalÚnanÚooÚpiÚzoo)ÚEqÚGeÚGtÚLeÚLtÚNe)ÚS)ÚSymbolÚsymbols)Ú	factorial)ÚexpÚlog)ÚceilingÚfloorÚfrac)Úsqrt)ÚsinÚcosÚtan)ÚRootOfÚCRootOf)ÚIntegers)ÚInterval)ÚImageSet)ÚLambda)Ú	unchanged)ÚXFAILÚraisesÚxÚiT)Z	imaginaryÚy©Úrealzk,n)Úintegerc                  C   sø  t tƒtkst‚t tƒtks t‚t t ƒt ks4t‚t tƒtksDt‚t dƒdksTt‚t dƒdksdt‚t dƒdkstt‚t tƒdks„t‚t t ƒdks–t‚t dt ƒdksªt‚t dt ƒdks¾t‚t tƒd	ksÎt‚t t ƒd
ksàt‚t tjƒdksòt‚t t	ddƒƒdk�s
t‚t t	dd	ƒƒdk�s"t‚t t	dd	ƒƒdk�s:t‚t t	dd	ƒ ƒdk�sTt‚t t
dƒƒdk�sjt‚t t
dƒ ƒdk�s‚t‚t t
dƒƒdk�s˜t‚t t
dƒ ƒdk�s°t‚t tƒtk�sÂt‚t t ƒt k�sØt‚t tƒ} | jt k�rü| jd tk�s t‚t tt ƒtt k�st‚t t t ƒt t k�s8t‚t ttt d ƒt ƒttt d ƒt k�sjt‚t dt ƒdt k�s„t‚t dt ƒdt k�sžt‚t td ƒdk�s´t‚t t d ƒt k�sÎt‚t td ƒdk�sät‚t td ƒdk�sút‚t tt ƒdk�st‚t tt ƒd	t k�s*t‚t t tƒƒd	k�s@t‚t t tƒƒt tƒk�sZt‚t t tƒƒt tƒk�stt‚tt tƒ�s„t‚tt dt ƒ�s˜t‚tt tt ƒ�s¬t‚t tƒtk�s¾t‚t dt ƒdt k�sØt‚t tt ƒtt k�sòt‚tt td ƒ�st‚tt tt ƒ�st‚t td	 ƒt tƒd	 k�s8t‚t tt ƒt tƒt k�sVt‚t td	 ƒt tƒd	 k�stt‚t tt ƒt tƒt k�s’t‚t d	tt  t ƒdt tƒt  k�s¼t‚t tt ƒtt k�sÖt‚tt tt ƒ�sêt‚t tt ƒtt k�st‚t t	ddƒtt  ƒdd	t  k�s,t‚t tdƒƒdk�sBt‚t tdƒƒdk�sXt‚t tdƒƒdk�snt‚t tdƒtdƒ ƒdk�sŒt‚tt tdƒtdƒ ƒjdd�ƒd	k�s¶t‚t tdƒtdƒ ƒdk�sÔt‚t tƒtk dk�sêt‚t tƒtkdk�s t‚t tƒtkdk�st‚t tƒtkdk�s,t‚t tƒtkj�s@t‚t tƒtkj�sTt‚t tƒtkj�sht‚t tƒtkj�s|t‚t tƒtkdk�s’t‚t tƒtk dk�s¨t‚t tƒt kdk�sÀt‚t tƒt kdk�sØt‚t tƒ t¡tttƒ k�søt‚t tƒ t¡tt ƒ k�st‚t tƒ t¡ tt ¡t t ƒk�s@t‚t tƒ t¡ tt¡t tƒk�sdt‚t tƒ t¡ tt¡tt ƒ k�sŒt‚t tƒ t¡ tt ¡ttƒ k�s´t‚tt tƒtttƒ ƒ�sÐt‚tt tƒtt ƒ ƒ�sìt‚t ddd�}t ddd �}t d!dd"�}t d#dd$�}t |ƒdk dk�s2t‚t |ƒdkdk�sHt‚t |ƒdkdk�s^t‚t |ƒdkdk�stt‚t |ƒdkdk�sŠt‚t |ƒdk|dkk�s¤t‚t |ƒdk |dk k�s¾t‚t |ƒdk dk�sÔt‚t |ƒdkdk�sêt‚t |ƒdk dk�	s t‚t |ƒdk|dk k�	st‚t |ƒdk|dkk�	s4t‚t |ƒdkdk�	sJt‚t |ƒd	k|d	kk�	sdt‚t |ƒdkdk�	szt‚t |ƒdkdk�	s�t‚t |ƒj!dk�	s¤t‚t |ƒj"dk�	s¸t‚t |ƒj!dk�	sÌt‚t |ƒj"dk�	sàt‚t |ƒj!dk�	sôt‚t |ƒj"dk�
st‚t |ƒj!d k�
st‚t |ƒj"d k�
s0t‚t ddd%�dkdk�
sJt‚t ddd%�dkdk�
sdt‚t ddd%�dkdk�
s~t‚t ddd%�dk dk�
s˜t‚t ddd%�dkdk�
s²t‚t ddd%�dkdk�
sÌt‚t ddd%�dkdk�
sæt‚t ddd%�dk dk�s t‚t ddd%�dkdk�st‚t ddd%�dkdk�s4t‚t ddd%�dkdk�sNt‚t ddd%�dk dk�sht‚t tƒd&kt#t tƒd&dd%�k�sŒt‚t tƒd'kt$t tƒd'dd%�k�s°t‚t tƒd(k t%t tƒd(dd%�k�sÔt‚t tƒd)kt&t tƒd)dd%�k�søt‚t tƒd&ktdk k�st‚t tƒd'ktdkk�s,t‚t tƒd(k td	k k�sFt‚t tƒd)ktdkk�s`t‚t tƒtkttd k k�s~t‚t tƒtkttkk�s˜t‚t tƒtk ttk k�s²t‚t tƒtkttd kk�sÐt‚t t'td	 d*t  dƒƒdk�sôt‚d S )+Nr   é   éÿÿÿÿé   éýÿÿÿé   éþÿÿÿiúÿÿÿé   éüÿÿÿé   éùÿÿÿç      1@é   éïÿÿÿçÃõ(\�Â@iøÿÿÿé   é   é   é   é
   é   T©Zchopé2   l    'öª~$DæA®7YáD3':ÿ^îXf FÚneg©ÚnegativeÚnn©ÚnonnegativeÚpos©ÚpositiveÚnp©Únonpositive©Úevaluateç      @çš™™™™™	Àç333333@ç333333û¿é   )(r   r   ÚAssertionErrorr   r
   r   r	   r   ÚHalfr   r   r   r(   ÚfuncÚargsr   r)   r'   r$   ÚkÚnr   r   ÚintÚevalfr   Úis_RelationalÚrewriter   r   Úsubsr   r   Zis_negativeZis_nonnegativer   r   r   r   r   )ÚerC   rF   rI   rL   © rb   úm/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/functions/elementary/tests/test_integers.pyÚ
test_floor   s    2*(*ÿ
  ($(($$$$rd   c                     s°  t tƒtkst‚t tƒtks t‚t t ƒt ks4t‚t tƒtksDt‚t dƒdksTt‚t dƒdksdt‚t dƒdkstt‚t tƒdks„t‚t t ƒdks–t‚t dt ƒdksªt‚t dt ƒdks¾t‚t tƒd	ksÎt‚t t ƒd
ksàt‚t tjƒdksòt‚t t	ddƒƒdk�s
t‚t t	ddƒƒdk�s"t‚t t	ddƒ ƒdk�s<t‚t t
dƒƒdk�sRt‚t t
dƒ ƒdk�sjt‚t t
dƒƒdk�s€t‚t t
dƒ ƒdk�s˜t‚t tƒtk�sªt‚t t ƒt k�sÀt‚t tƒ} | jt k�rä| jd tk�sèt‚t tt ƒtt k�st‚t t t ƒt t k�s t‚t ttt d	 ƒt ƒttt d	 ƒt k�sRt‚t dt ƒdt k�slt‚t dt ƒdt k�s†t‚t td ƒtk�sœt‚t t d ƒdk�s´t‚t td ƒdk�sÊt‚t td ƒdk�sàt‚t tt ƒdk�söt‚t tt ƒtd	 k�st‚t t tƒƒd	k�s&t‚t t tƒƒt tƒk�s@t‚t t tƒƒt tƒk�sZt‚tt tƒ�sjt‚tt dt ƒ�s~t‚tt tt ƒ�s’t‚t tƒtk�s¤t‚t dt ƒdt k�s¾t‚t tt ƒtt k�sØt‚tt td ƒ�sìt‚tt tt ƒ�s t‚t td ƒt tƒd k�st‚t td ƒt tƒd k�s<t‚t tdt  ƒt tƒdt  k�sbt‚t tt ƒt tƒt k�s€t‚t td ƒt tƒd k�sžt‚t tt ƒt tƒt k�s¼t‚t dt tt  ƒdt tƒt  k�sæt‚t tt ƒtt k�s t‚tt tt ƒ�st‚t tt ƒtt k�s.t‚t t	ddƒtt  ƒddt  k�sVt‚t tdƒƒdk�slt‚t tdƒƒdk�s‚t‚t tdƒƒdk�s˜t‚t tdƒ tdƒ ƒdk�s¸t‚tt tdƒ tdƒ ƒjdd�ƒd
k�sät‚t tdƒtdƒ ƒdk�st‚t tƒtkdk�st‚t tƒtkdk�s.t‚t tƒtk dk�sDt‚t tƒtkdk�sZt‚t tƒtkj�snt‚t tƒtk j�s‚t‚t tƒtkj�s–t‚t tƒtk j�sªt‚t tƒt kdk�sÂt‚t tƒt kdk�sÚt‚t tƒtkdk�sðt‚t tƒtk dk�st‚t tƒ t¡tt ƒ k�s&t‚t tƒ t¡ttt ƒ k�sHt‚t tƒ t¡ tt ¡ttƒ k�spt‚t tƒ t¡ tt¡tt ƒ k�s˜t‚t tƒ t¡ tt¡t tƒk�s¼t‚t tƒ t¡ tt ¡t t ƒk�sät‚tt tƒttt ƒ ƒ�st‚tt tƒtt ƒ ƒ�st‚t ddd�}t ddd�}t ddd �}t d!dd"�}t |ƒdkdk�sdt‚t |ƒdk |dkk�s~t‚t |ƒdkdk�s”t‚t |ƒdk|dkk�s®t‚t |ƒd
k|d
kk�sÈt‚t |ƒdk|dkk�sât‚t |ƒdk dk�søt‚t |ƒdkdk�	st‚t |ƒdk dk�	s$t‚t |ƒdkdk�	s:t‚t |ƒdkdk�	sPt‚t |ƒdkdk�	sft‚t |ƒdkdk�	s|t‚t |ƒd#k|d#kk�	s–t‚t |ƒdkdk�	s¬t‚t |ƒdkdk�	sÂt‚t |ƒj!dk�	sÖt‚t |ƒj"dk�	sêt‚t |ƒj!d k�	sþt‚t |ƒj"d k�
st‚t |ƒj!dk�
s&t‚t |ƒj"dk�
s:t‚t |ƒj!dk�
sNt‚t |ƒj"dk�
sbt‚t ddd$�dkdk�
s|t‚t ddd$�dkdk�
s–t‚t ddd$�dkdk�
s°t‚t ddd$�dk dk�
sÊt‚t ddd$�dkdk�
sät‚t ddd$�dkdk�
sþt‚t ddd$�dkdk�st‚t ddd$�dk dk�s2t‚t ddd$�dkdk�sLt‚t ddd$�dkdk�sft‚t ddd$�dkdk�s€t‚t ddd$�dk dk�sšt‚t tƒd%kt#t tƒd%dd$�k�s¾t‚t tƒd&kt$t tƒd&dd$�k�sât‚t tƒd'k t%t tƒd'dd$�k�st‚t tƒd(kt&t tƒd(dd$�k�s*t‚t tƒd%ktd#kk�sDt‚t tƒd&ktd)kk�s^t‚t tƒd'k tdkk�sxt‚t tƒd(ktdkk�s’t‚t tƒtkttkk�s¬t‚t tƒtkttd kk�sÊt‚t tƒtk ttd kk�sèt‚t tƒtkttkk�st‚t t'td d*t  dƒƒdk�s&t‚t(t)ttt*td# td  d dƒ ƒt+ƒ}t*td# td  d dƒ‰ t(t)ttˆ  ƒt+ƒ}| ,t-d+dƒ¡‡ fd,d-„t.d.d/ƒD ƒk�s¬t‚d S )0Nr   r-   r.   r3   r2   r/   r=   éûÿÿÿr;   r0   r5   r7   r8   r9   r:   r@   r6   é   g      @r>   r?   TrA   rB   l   ¡'öª~$DæA®7YáD3':ÿ^îXf FrC   rD   rF   rG   rI   rJ   rL   rM   r1   rO   rQ   rR   rS   rT   r4   rU   iöÿÿÿc                    s   h | ]}|ˆ  ’qS rb   rb   )Ú.0r(   ©Úfrb   rc   Ú	<setcomp>”  s     ztest_ceiling.<locals>.<setcomp>i÷ÿÿÿé   )/r   r   rV   r   r
   r   r	   r   rW   r   r   r   r(   rX   rY   r   r)   r'   r$   rZ   r[   r   r   r\   r]   r   r^   r_   r   r   r`   r   r   Zis_positiveZis_nonpositiver   r   r   r   r   r"   r#   r   r    Z	intersectr!   Úrange)ra   rC   rF   rI   rL   Úsrb   rh   rc   Útest_ceilingÖ   s    2&*( ,ÿ
 "(($($$$$$*rn   c            	      C   s¬
  t ttƒtƒst‚ttƒtddƒks(t‚tt ƒtddƒks@t‚ttƒtksPt‚ttƒdks`t‚ttƒtkspt‚tt	ddƒƒt	ddƒksŒt‚tt	ddƒ ƒt	ddƒksªt‚tt	ddƒƒt	ddƒksÆt‚t
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t|   ƒd
tt| ƒ  k�s6t‚ttt|   ƒtt| ƒ k�sXt‚tttt  ƒdk�srt‚ttttt  ƒ�sŠt‚tttt  ƒttƒk�s¨t‚ttƒ t¡tttƒ k�sÈt‚ttƒ t¡ttt ƒ k�sêt‚ttƒ t¡ tt¡ttƒk�st‚ttƒ t¡ tt ¡tt ƒk�s6t‚ttƒ t¡ tt ¡tt ƒk�s^t‚ttƒ t¡ tt¡ttƒk�s‚t‚tttƒtttƒ ƒ�sžt‚tttƒttt ƒ ƒ�s¼t‚t
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st‚t|dd�j�
st‚t|dd�j�
s,t‚t|dd�j �
s@t‚t| ƒj�
sPt‚t| ƒj �
s`t‚t| ƒjd k�
stt‚t| ƒjd k�
sˆt‚ttƒj�
s˜t‚ttƒj �
s¨t‚d S )Nr   r-   r;   r3   r/   r4   ÚrTr*   g      à?Úp_i)r,   rK   )r,   rE   Únp_i)r,   rN   Únn_i)r,   rH   Úp_rrJ   Ún_rrD   Únp_r)r+   rN   Únn_r)r+   rH   FrO   )!Ú
isinstancer   r'   rV   r   r   r
   r   r[   r   r   r   rZ   r$   r_   r   r   r)   r`   r	   r   r   Úhasr   r   r   r   r   r   Úis_zeroÚ	is_finiteÚ
is_integerZis_real)	ro   rp   Zn_irq   rr   rs   rt   ru   rv   rb   rb   rc   Ú	test_frac—  sð    "&" "$(($$$& & r|   c                  C   sì   t dƒ\} }t| ƒ | |d¡t|ƒks*t‚t| ƒ | |d¡t|ƒksHt‚t| ƒ | td¡dksbt‚t| ƒ | td¡dks|t‚t| ƒ | dd¡dks–t‚t| ƒ | dd¡dks°t‚t|  ƒ | dd¡dksÌt‚t|  ƒ | dd¡dksèt‚d S )Nzx,yéd   r3   r;   r   r-   r.   )r   r   ZnseriesrV   r   r	   )r'   r)   rb   rb   rc   Útest_series*  s    r~   c                   C   s�  t td t td t  ƒjtdd�dks.t‚t td t td t  ƒjtdd�dks\t‚t ttƒd t ƒjtdd�dks‚t‚t ttƒd t ƒjtdd�dks¨t‚t ttƒt ƒjtdd�dksÊt‚t ttƒt ƒjtdd�dksìt‚t ttƒ t ƒjtdd�dk�st‚t ttƒ t ƒjtdd�dk�s8t‚t ttƒt d ƒjtdd�dk�s`t‚t ttƒt d ƒjtdd�dk�sˆt‚ttd t td t  ƒjtdd�dk�s¸t‚ttd t td t  ƒjtdd�dk�sèt‚tttƒd t ƒjtdd�dk�st‚tttƒd t ƒjtdd�dk�s8t‚tttƒt ƒjtdd�dk�s\t‚tttƒt ƒjtdd�dk�s€t‚tttƒ t ƒjtdd�dk�s¦t‚tttƒ t ƒjtdd�dk�sÌt‚tttƒt d ƒjtdd�dk�sôt‚tttƒt d ƒjtdd�dk�st‚t ttƒt ƒjtdddd�dk�sDt‚t ttƒt ƒjtdddd�dk�slt‚t td t td t  ƒjtdddd�dk�s t‚t td t td t  ƒjtdddd�dk�sÔt‚tttƒt ƒjtdddd�dk�süt‚tttƒt ƒjtdddd�dk�s$t‚ttd t td t  ƒjtdddd�dk�sXt‚ttd t td t  ƒjtdddd�dk�sŒt‚d S )	Nr3   r/   r-   ©Úcdirr2   r.   r   r}   )	r   r'   Úas_leading_termrV   r   r   r   r   Zseriesrb   rb   rb   rc   Útest_issue_143556  s8    ..&&""&&((00(($$&&((((44((4r‚   c                   C   s|  t tƒ t¡tkst‚t tƒjtdd�tks0t‚t tƒjtdd�dksJt‚t ttj ƒjtdd�tjkslt‚t ttj ƒjtdd�tjksŽt‚t dt d ƒjtdd�tjks²t‚t dt d ƒjtdd�dt ksØt‚t ttƒd ƒjtdd�tksút‚t ttƒd ƒjtdd�tjk�s t‚t ttd ƒd ƒjtdd�td k�sLt‚t ttd ƒd ƒjtdd�td k�sxt‚d S )Nr-   r   r.   r2   r1   r/   )r   r'   r�   rV   r   rW   ZOner   rb   rb   rb   rc   Útest_frac_leading_termX  s    ""$&"&,rƒ   c                   C   sœ   t dtt  tt  ƒdt tt ƒt  ks0t‚t dt tt  tt  ƒt dt t ƒt ksdt‚t dt tt  tt  ƒdt tt ƒt  ks˜t‚d S )Nr3   r1   )r   r	   r   r)   rV   r   rb   rb   rb   rc   Útest_issue_4149f  s    04r„   c                  C   s2   t dddd�} dd|    }tt|ƒtƒs.t‚d S )NrZ   T)rK   r,   r/   )r   rw   r   rV   )rZ   r   rb   rb   rc   Útest_issue_21651m  s    r…   c                   C   sd   t t tƒƒt tƒkst‚t ttƒƒttƒks0t‚tt tƒƒt tƒksHt‚tttƒƒttƒks`t‚d S )N©r   r'   rV   r   rb   rb   rb   rc   Útest_issue_11207s  s    r‡   c                   C   sÔ   t t ttd ƒt ƒ ƒt ttd ƒt ƒ ks4t‚tt ttd ƒt ƒ ƒt ttd ƒt ƒ ksht‚t tt ttddƒ t ƒ ƒƒt ttddƒ t ƒ ks¤t‚ttt tƒt ƒ ƒ tt tƒt ƒksÐt‚d S )Nr3   r5   r/   )r   r   r'   r)   rV   r   rb   rb   rb   rc   Útest_nested_floor_ceilingz  s    44<rˆ   c                   C   sp   t t t tƒƒd ƒt tƒd ks$t‚ttttƒƒd ƒttƒd ksHt‚ttt tƒƒd ƒt tƒd kslt‚d S )Nr3   r-   r†   rb   rb   rb   rc   Útest_issue_18689€  s    $$r‰   c                   C   s0   t tdƒƒtjkst‚ttdƒƒtjks,t‚d S )Nr   )r   Úfloatr   ZZerorV   r   rb   rb   rb   rc   Útest_issue_18421…  s    r‹   c                     s@  t ddd�‰ t ddd�} t ddd�}tt‡ fdd	„ƒ tt‡ fd
d	„ƒ tt|  ƒjtdd�dksft‚tt|  ƒjtdd�dks„t‚tt| ƒjtdd�dks¢t‚tt| ƒjtdd�dksÀt‚tt|  ƒjtdd�dksÞt‚tt|  ƒjtdd�dksüt‚tt| ƒjtdd�dk�st‚tt| ƒjtdd�dk�s<t‚d S )NÚaTr*   ÚbrJ   ÚcrD   c                      s   t tˆ  ƒjtdd�S ©Nr-   r   )r   r'   r�   rb   ©rŒ   rb   rc   Ú<lambda>�  ó    z"test_issue_25230.<locals>.<lambda>c                      s   t tˆ  ƒjtdd�S r�   )r   r'   r�   rb   r�   rb   rc   r‘   Ž  r’   r-   r   r   r.   )r   r&   ÚNotImplementedErrorr   r'   r�   rV   r   )r�   rŽ   rb   r�   rc   Útest_issue_25230‰  s     r”   N)HZ!sympy.calculus.accumulationboundsr   Zsympy.core.numbersr   r   r   r   r   r   r	   r
   Zsympy.core.relationalr   r   r   r   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.combinatorial.factorialsr   Z&sympy.functions.elementary.exponentialr   r   Z#sympy.functions.elementary.integersr   r   r   Z(sympy.functions.elementary.miscellaneousr   Z(sympy.functions.elementary.trigonometricr   r   r   Zsympy.polys.rootoftoolsr   r   Zsympyr    Zsympy.sets.setsr!   Zsympy.sets.fancysetsr"   Zsympy.core.functionr#   Zsympy.core.exprr$   Zsympy.testing.pytestr%   r&   r'   r(   r)   rZ   r[   rd   rn   r|   r~   r‚   rƒ   r„   r…   r‡   rˆ   r‰   r‹   r”   rb   rb   rb   rc   Ú<module>   sJ   (  = B "
