g9dZddlmZddlmZddlmZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdS)zC The module contains implemented functions for interval arithmetic.reduce)interval) import_modulec t|ttfrtt |St|tr|jdkrT|jdkrItdtt |jt |j|jStt |jt |jSt)Nris_valid) isinstanceintfloatrabsstartendmaxr NotImplementedErrorxs d/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/plotting/intervalmath/lib_interval.pyAbsrs!c5\"""A Ax " 7Q;;15199As3qw<<QU<zimin..3GG3z#UH566GGGGGGrcXg|]'}t|ttfs|j%|(Sr r r r r@as r zimin..C###!z!c5\'B'B#z#A###rrc3(K|] }|jduVdSFNrrGs rrBzimin..)5511:&555555rFrNcXg|]'}t|ttfr|n|j(SrEr r r rrGs rrIzimin..A***'q3,77DqqQW***rcXg|]'}t|ttfr|n|j(SrEr r r rrGs rrIzimin..A(((%Qe 55@QQ15(((r)rallrlenrrr.argsrnew_args start_array end_arrays riminr[s w  B GG$GGG G G:""##t### x==A  5555555 @%@@@@$????** (*** ((&((( K((#i..999rctd}td|DstSd|D}t|dkrStd|Drt |j |jdSt |j |jdSd |D}d |D}t t |t |S) z,Evaluates the maximum of a list of intervalsrc3ZK|]&}t|tttfV'dSr=r>r?s rrBzimax..rCrcXg|]'}t|ttfs|j%|(SrErFrGs rrIzimax..rJrrc3(K|] }|jduVdSrLrrGs rrBzimax..rMrFrNcXg|]'}t|ttfr|n|j(SrErOrGs rrIzimax..rPrcXg|]'}t|ttfr|n|j(SrErRrGs rrIzimax..rSr)rrTrrUrrrrVs rimaxrbs w  B GG$GGG G G:""##t### x==A  5555555 @%@@@@$????** (*** ((&((( K((#i..999rctd}t|ttfr6t ||||St|trGt ||j||j|jSt)z,Evaluates the hyperbolic sine of an intervalrr) rr r r rsinhrrr rrs rrdrd w  B!c5\""" BGGAJJ/// Ax "(("''!%..1:NNNN!!rcltd}t|ttfr6t ||||St|tr|jdkrb|jdkrWt||j||j}t d||j S||j}||j}t |||j St)z+Evaluates the hyperbolic cos of an intervalrrr'r) rr r r rcoshrrrr r)rrrrs rrgrgs w  B!c5\"" " BGGAJJ/// Ax " 7Q;;15199bggag&&77CAsQZ888 8GGAG$$E''!%..CE3<<< <!!rctd}t|ttfr6t ||||St|trGt ||j||j|jSt)z+Evaluates the hyperbolic tan of an intervalrr) rr r r rtanhrrr rrs rririrerctd}t|ttfrft |dkrt |j |jdSt ||||St|t r|jdus|j dks |j dkrt |j |jdS|j dks |j dkrt |j |jdS||j }||j }t |||jSdS)z)Evaluates the inverse sine of an intervalrr'Frr&N) rr r r r rrarcsinr rrr#s rasinrls8 w  B!c5\""= q66A::RVGRVe<<< <BIIaLL"))A,,77 7 Ax = :  !'A++RVGRVe<<< < Wr\\QUQYYRVGRVd;;; ;IIag&&E))AE""CE3<<< < = =rctd}t|ttfrft |dkrt |j |jdSt ||||St|t r|jdus|j dks |j dkrt |j |jdS|j dks |j dkrt |j |jdS||j }||j }t |||jSdS)z(Evaluates the inverse cos of an intervalrr'Frr&N) rr r r r rrarccosr rrr#s racosros8 w  B!c5\""= q66A::RVGRVe<<< <BIIaLL"))A,,77 7 Ax = :  !'A++RVGRVe<<< < Wr\\QUQYYRVGRVd;;; ;IIag&&E))AE""CE3<<< < = =rctd}t|ttfr"t ||St|tr|jdurt |j |jdS||j}||j }||krt |||jSt ||dStS)z$Evaluates the ceiling of an intervalrFrN) rr r r rceilr rrrrr#s rrqrq4s w  B!c5\""# ### Ax # :  RVGRVe<<< <GGAG$$E''!%..C||sQZ@@@@ sT::::""rctd}t|ttfr"t ||St|tr|jdurt |j |jdS||j}||j }||krt |||jSt ||dStS)z"Evaluates the floor of an intervalrFrN) rr r r rfloorr rrrrr#s rrsrsIs w  B!c5\""# $$$ Ax # :  RVGRVe<<< <HHQW%%E((15//C||sQZ@@@@ sT::::""rcPtd}t|ttfrE|dkrt |j |jdSt ||St|tr|jdkrt |j |jdS|jdkrt |j |jdS||j}||j}t |||j StS)z6Evaluates the inverse hyperbolic cosine of an intervalrr'FrN) rr r r rrarccoshrrr rr#s racoshrv^s w  B!c5\""# q55RVGRVe<<< <BJJqMM** * Ax # 5199RVGRVe<<< < Wq[[RVGRVd;;; ;JJqw''E**QU##CE3<<< <""rcjtd}t|ttfr"t ||St|trK||j}||j}t |||jStS)z4Evaluates the inverse hyperbolic sine of an intervalrr) rr r r rarcsinhrrr rr#s rasinhryws w  B!c5\""# 1 &&& Ax # 17##jjsQZ8888""rctd}t|ttfrRt |dkrt |j |jdSt ||St|t r|jdus|j dks |j dkrt |j |jdS|j dks |j dkrt |j |jdS||j }||j }t |||jStS)z7Evaluates the inverse hyperbolic tangent of an intervalrr'Frr&N) rr r r r rrarctanhr rrrr#s ratanhr|s( w  B!c5\""# q66Q;;RVGRVe<<< <BJJqMM** * Ax # :  !'Q,,!%2++RVGRVe<<< < W]]aeqjjRVGRVd;;; ;JJqw''E**QU##CE3<<< <""rc(d}t||S)zZDefines the three valued ``And`` behaviour for a 2-tuple of three valued logic valuesc|ddus |ddurd}n|d|dd}nd}|ddus |ddurd}n|d|dd}nd}||fS)NrFTr'rE cmp_intervala cmp_intervalbfirstseconds r reduce_andzAnd..reduce_ands  u $ $ a(8E(A(AEE 1  %q)9)AEEE  u $ $ a(8E(A(AFF 1  %q)9)AFFFvrr)rWrs rAndrs#    *d # ##rc(d}t||S)zYDefines the three valued ``Or`` behaviour for a 2-tuple of three valued logic valuesc|ddus |ddurd}n|d|dd}nd}|ddus |ddurd}n|d|dd}nd}||fS)NrTFr'rErs r reduce_orzOr..reduce_ors  t # #}Q'74'?'?EE 1  %q)9)AEEE  t # #}Q'74'?'?FF 1  %q)9)AFFFvrr)rWrs rOrrs# )T " ""rN)__doc__ functoolsrsympy.plotting.intervalmathrsympy.externalrrrrr r$r+r6r8r:r[rbrdrgrirlrorqrsrvryr|rrrErrrsII000000(((((( " " """"""","""* " " """":"""< """,:::*:::.""""""("""===,===,###*###*###2 # # ####4$$$(#####r