g&JUddlZddlmZmZddlmZddlmZm Z ddl m Z ddl m Z ddlmZdd lmZmZmZmZmZmZmZmZ m!Z"m#Z$m%Z&m'Z(m)Z*m+Z,m-Z.m/Z0m1Z2m3Z4m5Z6m7Z8m9Z:m;Zm?Z@mAZBgd ZCgd ZDd ZEd ZFdZGdZHejIJddKZLdZMdZNeLdvreGeLZMeMdZLndZLeLdvreHeLZNeNdZLndZLeLdvr e ddZLddeezdz zdz ZOee dfePd<eLdkreNJdZQeNZRdZSdZTeUeVeRWdfZXeRjWZYeRjZZ[eRjZeRjZeRjZeRj\ZeRj]ZeRj#Z#eRj^ZeRjZeRjZeRj!Z!eRj%Z%eRj'Z'eRj)Z)eRj+Z+dZ-eRj/Z/eRj1Z1eRj3Z3eRj5Z5eRj7Z7eRj9Z9eRj;Z;eRj=Z=eRj?Z?eRjAZAdSeLdkr^eMJeMZQdZRdZSdZTeUeQj_fZXeQj_ZYeQj`Z[eZeZeZeZdZdZ#d Zd!Zd"Ze"Z!e&Z%e(Z'd#Z)e,Z+d$Z-e0Z/e2Z1e4Z3e6Z5e8Z7e:Z9eZ=e@Z?eBZAdSeLdkrCdZQdZRdZSdZTeUfZXeUZYeZ[eZeZeZeZeZe$Z#eZeZe Ze"Z!e&Z%e(Z'e*Z)e,Z+e.Z-e0Z/e2Z1e4Z3e6Z5e8Z7e:Z9eZ=e@Z?eBZAdSJ)%N)c_longsizeof)reduce)TupleType)warn) import_module) PythonMPQ) bit_scan1 bit_scan0remove factorialsqrtsqrtremgcdlcmgcdext is_squareinvertlegendrejacobi kroneckeriroot is_fermat_prp is_euler_prp is_strong_prpis_fibonacci_prp is_lucas_prpis_selfridge_prpis_strong_lucas_prpis_strong_selfridge_prp is_bpsw_prpis_strong_bpsw_prp) GROUND_TYPESHAS_GMPY SYMPY_INTSMPQMPZr r rrrrrrrrrrrrrrrrrrr r!r"r#r$)z0.6z0.7z0.8z0.9cb|ddd\}}|d|}|tvS)N.)split_PYTHON_FLINT_VERSION_NEEDED) flint_versionmajorminor flint_vers O/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/external/gmpy.py_flint_version_okayr4bsA &&s++BQB/LE5""5""I 4 44z2.0.0c|dvrdS ddl}ddlm}n&#t$r|dkrtdYdSwxYwt |r|S|dkrdStd|dt d |S) Nautoflintr) __version__r9zjSYMPY_GROUND_TYPES was set to flint but python-flint is not installed. Falling back to other ground types.r8zUsing python-flint zp because SYMPY_GROUND_TYPES is set to flint but this version of SymPy is only tested with python-flint versions r+)r9r: ImportErrorrr4r.)sympy_ground_typesr9_flint_versions r3 _get_flintr>ms!222t 7777777   ( ( B C C Ctt  >** v % %t K>KK+GKKK L L L s 66cp|dvrdStdtdd}|dkr|td|S)Nr8gmpygmpy2rBversion)min_module_versionmodule_version_attrmodule_version_attr_call_argsr8zBgmpy2 library is not installed, switching to 'python' ground types)r _GMPY2_MIN_VERSIONr)r<rAs r3 _get_gmpy2rIsY!:::t 5G ) M M MDV##  QRRR Kr5SYMPY_GROUND_TYPESr8r7r9r@rApython)r9rArKzmSYMPY_GROUND_TYPES environment variable unrecognised. Should be 'auto', 'flint', 'gmpy', 'gmpy2' or 'python'..r'r,cn|tkrt||St||SN)LONG_MAXrAr python_iroot)xns r3rrs1 ==::a## #Aq!!!r5cZt|SrN)r9fmpzisqrtrQs r3rrszz!}}""$$$r5c~|dkrdSt|ddkS)NrFr r9rTrrVs r3rrs6 q555zz!}}$$&&q)Q..r5cZt|SrNrXrVs r3rr szz!}}$$&&&r5crttjj|tdS)Nr)rr9rTrargss r3rr "ejndEJJqMM:::r5crttjj|tdS)Nr )rr9rTrr[s r3rrr]r5c|dks|dzstdt||S)Nrr,z#y should be an odd positive integer) ValueErrorr9rTr)rQys r3rrs@ 66Q6BCC Czz!}}##A&&&r5c|tkr8t||}|||z|kfSt ||SrN)rOr9rTrootrP)rQrRras r3rrsJ == 1 ""1%%Aadai< Aq!!!r5)aosctypesrr functoolsrtypingrtTuplerwarningsrsympy.externalr pythonmpqr ntheoryr python_bit_scan1r python_bit_scan0r python_removerpython_factorialr python_sqrtrpython_sqrtremr python_gcdr python_lcmr python_gcdextrpython_is_squarer python_invertrpython_legendrer python_jacobirpython_kroneckerrrPrpython_is_fermat_prprpython_is_euler_prprpython_is_strong_prprpython_is_fibonacci_prprpython_is_lucas_prpr python_is_selfridge_prpr!python_is_strong_lucas_prpr"python_is_strong_selfridge_prpr#python_is_bpsw_prpr$python_is_strong_bpsw_prp__all__r.r4rHr>rIenvirongetlower_SYMPY_GROUND_TYPES_flint_gmpyrO__annotations__r9rAr&r%inttypempzr'r)mpqr(facrU isqrt_remrTfmpqrDr5r3rs !!!!!!!!(((((((((((((( :0 0 0 n <;;5552    jnn%96BBHHJJ   +++ Z+ , ,F %$333 J* + +E $&999D CDDD" !FF6NN"Q& '1 , 49 &      E DHLttDHHQKK(()J (C (CII [FI :DInG (C (C [F [F}H [FI"""&M$L&M,$L,2":"K0G##     E DHLuz"J *C *C I I F I%%%/// ''';;;;;;F FH''' !I""" )M&L(M.&L.4<$K2H$$ E DHLJ C C I I F I D IG C C F FH F I E(M&L(M.&L.4<$K2Lr5