U -e9@sdZddlmZddlmZddlmZddZddZd d Z d d Z d dZ ddZ ddZ ddZddZddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Zd3S)4zC The module contains implemented functions for interval arithmetic.reduce)interval) import_modulecCszt|ttfrtt|St|trr|jdkrZ|jdkrZtdtt|jt|j|jdStt|jt|jSnt dS)Nris_valid) isinstanceintfloatrabsstartendmaxrNotImplementedErrorxri/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/plotting/intervalmath/lib_interval.pyAbss  "rcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z(evaluates the exponential of an intervalnumpyrN) rrr r rexpr r rrrnprrrrs   rcCstd}t|ttfrB|dkr2t|j |jddSt||Snt|tr|jsht|j |j|jdS|jdkrt|j |jddS|j dkrt|j |jddSt||j ||jSt dS)z.evaluates the natural logarithm of an intervalrrFrN) rrr r rinflogrr r rrrrrr"s   rcCstd}t|ttfrB|dkr2t|j |jddSt||Snt|tr|jsht|j |j|jdS|jdkrt|j |jddS|j dkrt|j |jddSt||j ||jSt dS)z5evaluates the logarithm to the base 10 of an intervalrrFrN) rrr r rrlog10rr r rrrrrr8s   rcCs^td}t|ttfr$t||St|trV||j}||j}t|||jdSt dS)z(evaluates the tan inverse of an intervalrrN) rrr r rZarctanr r rrrrr r rrratanMs   rcCs(td}t|ttfr$t||St|tr |jsFtdd|jdSt|j|j d\}}t|j |j d\}}t ||j||j }t ||j||j }||dkrtdd|jdS||krt|||jdS|dd|ddkrd}|dd|ddkrd}t||Snt dS) z!evaluates the sine of an intervalrr@N)rrr r rsinrdivmodr pir minrrrrna__nbr r rrrr#[s(   r#cCs:td}t|ttfr$t||St|tr2||jrH||jsXtdd|j dSt |j|j d\}}t |j|j d\}}t | |j| |j}t| |j| |j}||dkrtdd|j dS||krt|||j dS|d|dkrd}|dd|ddkr d}t|||j dSntdS) z Evaluates the cos of an intervalrrrrr r!N)rrr r rr#isfiniter r rr$r%r&cosrrr'rrrr-xs(  r-cCst|t|S)z Evaluates the tan of an interval)r#r-rrrrtansr.cCstd}t|ttfrB|dkr,t||St|j |jddSnlt|tr|jdkrjt|j |jddS|jdkrt|j |jddSt||j||j|j dSnt dS)z(Evaluates the square root of an intervalrrFrN) rrr r rsqrtrr r rrrrrrr/s   r/cGstd}tdd|DstSdd|D}t|dkrrtdd|Dr^t|j |jdd St|j |jd d Sd d|D}d d|D}tt|t|Sd S) z,Evaluates the minimum of a list of intervalsrcss|]}t|tttfVqdSNrr r r.0argrrr szimin..cSs$g|]}t|ttfs|jr|qSrrr r rr3arrr szimin..rcss|]}|jdkVqdSFNrr7rrrr5sFrNcSs$g|]}t|ttfr|n|jqSrrr r r r7rrrr9scSs$g|]}t|ttfr|n|jqSrrr r r r7rrrr9s)rallrlenrrr&argsrnew_argsZ start_array end_arrayrrrimins rCcGstd}tdd|DstSdd|D}t|dkrrtdd|Dr^t|j |jdd St|j |jd d Sd d|D}d d|D}tt|t|Sd S) z,Evaluates the maximum of a list of intervalsrcss|]}t|tttfVqdSr0r1r2rrrr5szimax..cSs$g|]}t|ttfs|jr|qSrr6r7rrrr9szimax..rcss|]}|jdkVqdSr:rr7rrrr5sFrNcSs$g|]}t|ttfr|n|jqSrr;r7rrrr9scSs$g|]}t|ttfr|n|jqSrr<r7rrrr9s)rr=rr>rrrr?rrrimaxs rDcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z,Evaluates the hyperbolic sine of an intervalrrN) rrr r rsinhr r rrrrrrrEs   rEcCstd}t|ttfr,t||||St|tr|jdkrt|jdkrtt||j||j}td||j dS||j}||j}t|||j dSnt dS)z+Evaluates the hyperbolic cos of an intervalrrrrN) rrr r rcoshr r rrr)rrr r rrrrFs   rFcCs^td}t|ttfr,t||||St|trVt||j||j|jdSt dS)z+Evaluates the hyperbolic tan of an intervalrrN) rrr r rtanhr r rrrrrrrGs   rGcCstd}t|ttfrNt|dkr6t|j |jddSt||||Snt|tr|jdksv|j dksv|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSdS)z)Evaluates the inverse sine of an intervalrrFrrN) rrr r r rrZarcsinrr r rrrrasins    rHcCstd}t|ttfrNt|dkr6t|j |jddSt||||Snt|tr|jdksv|j dksv|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSdS)z(Evaluates the inverse cos of an intervalrrFrrN) rrr r r rrZarccosrr r rrrracoss    rIcCstd}t|ttfr$t||St|tr|jdkrLt|j |jddS||j}||j }||kr|t|||jdSt||ddSnt SdS)z$Evaluates the ceiling of an intervalrFrN) rrr r rceilrrr r rrrrrrJ4s    rJcCstd}t|ttfr$t||St|tr|jdkrLt|j |jddS||j}||j }||kr|t|||jdSt||ddSnt SdS)z"Evaluates the floor of an intervalrFrN) rrr r rfloorrrr r rrrrrrKIs    rKcCstd}t|ttfrB|dkr2t|j |jddSt||Sntt|tr|jdkrjt|j |jddS|jdkrt|j |jddS||j}||j}t|||j dSnt SdS)z6Evaluates the inverse hyperbolic cosine of an intervalrrFrN) rrr r rrZarccoshr r rrrrrracosh^s     rLcCs^td}t|ttfr$t||St|trV||j}||j}t|||jdSt SdS)z4Evaluates the inverse hyperbolic sine of an intervalrrN) rrr r rZarcsinhr r rrrrrrasinhws   rMcCstd}t|ttfrFt|dkr6t|j |jddSt||Snt|tr|jdksn|j dksn|j dkrt|j |jddS|j dks|j dkrt|j |jddS||j }||j }t|||jdSnt SdS)z7Evaluates the inverse hyperbolic tangent of an intervalrrFrrN) rrr r r rrZarctanhrr r rrrrratanhs    rNcGsdd}t||S)zZDefines the three valued ``And`` behaviour for a 2-tuple of three valued logic valuescSs|ddks|ddkrd}n"|ddks6|ddkr.reduce_andr)r@rRrrrAndsrScGsdd}t||S)zYDefines the three valued ``Or`` behaviour for a 2-tuple of three valued logic valuescSs|ddks|ddkrd}n"|ddks6|ddkr.reduce_orr)r@rTrrrOrsrUN)__doc__ functoolsrZsympy.plotting.intervalmathrZsympy.externalrrrrrrr#r-r.r/rCrDrErFrGrHrIrJrKrLrMrNrSrUrrrrs4