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SymPy is a Python library for symbolic mathematics. It aims to become a
full-featured computer algebra system (CAS) while keeping the code as simple
as possible in order to be comprehensible and easily extensible.  SymPy is
written entirely in Python. It depends on mpmath, and other external libraries
may be optionally for things like plotting support.

See the webpage for more information and documentation:

    https://sympy.org

    N)      z2Python version 3.8 or above is required for SymPy.zSymPy now depends on mpmath as an external library. See https://docs.sympy.org/latest/install.html#mpmath for more information.)__version__)lazy_functiondevc                  C   s    dd l } | jddtdd ~ d S )Nr   defaultz.*zsympy.*)module)warningsfilterwarningsDeprecationWarning)r	    r   b/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/__init__.pyenable_warnings!   s   r   c                  C   s0   dd l } | dd}|dv rt|S td| )Nr   SYMPY_DEBUGFalse)Truer   z&unrecognized value for SYMPY_DEBUG: %s)osgetenvevalRuntimeError)r   	debug_strr   r   r   __sympy_debug)   s   r      )^sympifySympifyErrorcacheitBasicAtompreorder_traversalSExpr
AtomicExprUnevaluatedExprSymbolWildDummysymbolsvarNumberFloatRationalIntegerNumberSymbol
RealNumberigcdilcmseterrEInanoopizooAlgebraicNumbercompmod_inversePowinteger_nthrootinteger_logtrailingMulprodAddModRelEqNeLtLeGtGeEqualityGreaterThanLessThan
UnequalityStrictGreaterThanStrictLessThan	vectorizeLambdaWildFunction
DerivativediffFunctionClassFunctionSubsexpand	PoleError	count_ops
expand_mul
expand_logexpand_funcexpand_trigexpand_complexexpand_multinomialnfloatexpand_power_baseexpand_power_exparityPrecisionExhaustedNevalfTupleDict	gcd_termsfactor_terms	factor_ncevaluateCatalan
EulerGammaGoldenRatioTribonacciConstant	bottom_upusepostorder_traversaldefault_sort_keyordered
num_digits)to_cnfto_dnfto_nnfAndOrNotXorNandNorImplies
EquivalentITEPOSformSOPformsimplify_logicbool_maptruefalsesatisfiable)	AppliedPredicate	PredicateAssumptionsContextassumingQaskregister_handlerremove_handlerrefine)PolyPurePolypoly_from_exprparallel_poly_from_exprdegreetotal_degreedegree_listLCLMLTpdivprempquopexquodivremquoexquo
half_gcdexgcdexinvertsubresultants	resultantdiscriminant	cofactorsgcd_listgcdlcm_listlcm	terms_gcdtruncmoniccontent	primitivecompose	decomposesturmgff_listgffsqf_normsqf_partsqf_listsqffactor_listfactor	intervalsrefine_rootcount_roots	all_roots
real_rootsnrootsground_rootsnth_power_roots_polycancelreducedgroebneris_zero_dimensionalGroebnerBasispoly
symmetrizehornerinterpolaterational_interpolatevietetogetherBasePolynomialErrorExactQuotientFailedPolynomialDivisionFailedOperationNotSupportedHeuristicGCDFailedHomomorphismFailedIsomorphismFailedExtraneousFactorsEvaluationFailedRefinementFailedCoercionFailedNotInvertibleNotReversibleNotAlgebraicDomainErrorPolynomialErrorUnificationFailedGeneratorsErrorGeneratorsNeededComputationFailedUnivariatePolynomialErrorMultivariatePolynomialErrorPolificationFailedOptionError	FlagErrorminpolyminimal_polynomialprimitive_elementfield_isomorphismto_number_fieldisolate	round_twoprime_decompprime_valuationgalois_groupitermonomialsMonomiallexgrlexgrevlexilexigrlexigrevlexCRootOfrootofRootOfComplexRootOfRootSumrootsDomainFiniteFieldIntegerRingRationalField	RealFieldComplexFieldPythonFiniteFieldGMPYFiniteFieldPythonIntegerRingGMPYIntegerRingPythonRationalGMPYRationalFieldAlgebraicFieldPolynomialRingFractionFieldExpressionDomain	FF_pythonFF_gmpy	ZZ_pythonZZ_gmpy	QQ_pythonQQ_gmpyGFFFZZQQZZ_IQQ_IRRCCEXEXRAWconstruct_domainswinnerton_dyer_polycyclotomic_polysymmetric_polyrandom_polyinterpolating_polyjacobi_polychebyshevt_polychebyshevu_polyhermite_polyhermite_prob_polylegendre_polylaguerre_polyapart
apart_listassemble_partfrac_listOptionsringxringvringsringfieldxfieldvfieldsfield)OrderOlimitLimitgruntzseriesapproximantsresidueEmptySequenceSeqPer
SeqFormulasequenceSeqAddSeqMulfourier_seriesfpsdifference_delta	limit_seq)	factorial
factorial2rfffbinomialRisingFactorialFallingFactorialsubfactorial
carmichael	fibonaccilucasmotzkin
tribonacciharmonic	bernoullibelleulercatalangenocchiandre	partitiondivisor_sigmalegendre_symboljacobi_symbolkronecker_symbolmobiusprimenu
primeomegatotientreduced_totientprimepisqrtrootMinMaxId	real_rootRemcbrtreimsignAbs	conjugatearg
polar_liftperiodic_argumentunbranched_argumentprincipal_branch	transposeadjointpolarify
unpolarifysincostanseccsccotsincasinacosatanasecacscacotatan2	exp_polarexplnlogLambertWsinhcoshtanhcothsechcschasinhacoshatanhacothasechacschfloorceilingfrac	Piecewisepiecewise_foldpiecewise_exclusiveerferfcerfierf2erfinverfcinverf2invEiexpintE1liLiSiCiShiChifresnelsfresnelcgamma
lowergamma
uppergamma	polygammaloggammadigammatrigamma
multigammadirichlet_etazetalerchphipolylog	stieltjesEijk
LeviCivitaKroneckerDeltaSingularityFunction
DiracDelta	Heavisidebspline_basisbspline_basis_setinterpolating_splinebesseljbesselybesselibesselkhankel1hankel2jnynjn_zeroshn1hn2airyaiairybiairyaiprimeairybiprimemarcumqhypermeijergappellf1legendreassoc_legendrehermitehermite_prob
chebyshevt
chebyshevuchebyshevu_rootchebyshevt_rootlaguerreassoc_laguerre
gegenbauerjacobijacobi_normalizedYnmYnm_cZnm
elliptic_k
elliptic_f
elliptic_eelliptic_pibetamathieusmathieucmathieusprimemathieucprime
riemann_xibetaincbetainc_regularized)4	nextprime	prevprimeprime
primerange	randprimeSievesieve	primorialcycle_length	compositecompositepiisprimedivisorsproper_divisors	factorintmultiplicityperfect_powerpollard_pm1pollard_rhoprimefactorsdivisor_countproper_divisor_count	factorratmersenne_prime_exponent
is_perfectis_mersenne_primeis_abundantis_deficientis_amicableis_carmichael	abundancenpartitionsis_primitive_rootis_quad_residuen_ordersqrt_modquadratic_residuesprimitive_rootnthroot_modis_nthpow_residuesqrt_mod_iterdiscrete_logquadratic_congruencebinomial_coefficientsbinomial_coefficients_listmultinomial_coefficientscontinued_fraction_periodiccontinued_fraction_iteratorcontinued_fraction_reducecontinued_fraction_convergentscontinued_fractionegyptian_fraction)productProduct	summationSum)fftifftnttinttfwhtifwhtmobius_transforminverse_mobius_transformconvolutioncovering_productintersecting_product) simplify	hypersimphypersimilar
logcombineseparatevarsposify
besselsimpkroneckersimpsignsimp	nsimplifyFUfu
sqrtdenestcseepathEPathhyperexpandcollectrcollectradsimpcollect_constfractionnumerdenomtrigsimpexptrigsimppowsimp	powdenestcombsimp	gammasimpratsimpratsimpmodprime)SetIntervalUnionEmptySet	FiniteSet
ProductSetIntersectionDisjointUnionimageset
ComplementSymmetricDifferenceImageSetRangeComplexRegion	ComplexesRealsContainsConditionSetOrdinal
OmegaPowerord0PowerSetNaturals	Naturals0UniversalSetIntegers	Rationals))solvesolve_linear_systemsolve_linear_system_LUsolve_undetermined_coeffsnsolvesolve_linearchecksol	det_quick	inv_quickcheck_assumptionsfailing_assumptionsdiophantinersolversolve_polyrsolve_ratiorsolve_hypercheckodesolclassify_odedsolvehomogeneous_ordersolve_poly_systemsolve_triangulatedpde_separatepde_separate_addpde_separate_mulpdsolveclassify_pdecheckpdesol	ode_orderreduce_inequalitiesreduce_abs_inequalityreduce_abs_inequalitiessolve_poly_inequalitysolve_rational_inequalitiessolve_univariate_inequality
decompogensolvesetlinsolvelinear_eq_to_matrixnonlinsolvesubstitution)F
ShapeErrorNonSquareMatrixErrorGramSchmidt
casoratiandiageyehessianjordan_cell
list2numpymatrix2numpymatrix_multiply_elementwiseones
randMatrix	rot_axis1	rot_axis2	rot_axis3symarray	wronskianzerosMutableDenseMatrixDeferredVector
MatrixBaseMatrixMutableMatrixMutableSparseMatrixbandedImmutableDenseMatrixImmutableSparseMatrixImmutableMatrixSparseMatrixMatrixSliceBlockDiagMatrixBlockMatrixFunctionMatrixIdentityInverseMatAddMatMulMatPow
MatrixExprMatrixSymbolTrace	Transpose
ZeroMatrix	OneMatrixblockcutblock_collapsematrix_symbolsAdjointhadamard_productHadamardProductHadamardPowerDeterminantdetdiagonalize_vector
DiagMatrixDiagonalMatrix
DiagonalOftrace
DotProductkronecker_productKroneckerProductPermutationMatrixMatrixPermute	Permanentperrot_ccw_axis1rot_ccw_axis2rot_ccw_axis3
rot_givens)PointPoint2DPoint3DLineRaySegmentLine2D	Segment2DRay2DLine3D	Segment3DRay3DPlaneEllipseCirclePolygonRegularPolygonTriangleraddegare_similarcentroidconvex_hullidiffintersectionclosest_pointsfarthest_pointsGeometryErrorCurveParabola)flattengrouptakesubsets
variationsnumbered_symbolscartescapture
dict_mergeprefixes	postfixessifttopological_sort	unflattenhas_dupshas_varietyreshape	rotations
filldedentlambdifythreaded	xthreadedpublicmemoize_propertytimed)	integrateIntegralline_integratemellin_transforminverse_mellin_transformMellinTransformInverseMellinTransformlaplace_transformlaplace_correspondencelaplace_initial_condsinverse_laplace_transformLaplaceTransformInverseLaplaceTransformfourier_transforminverse_fourier_transformFourierTransformInverseFourierTransformsine_transforminverse_sine_transformSineTransformInverseSineTransformcosine_transforminverse_cosine_transformCosineTransformInverseCosineTransformhankel_transforminverse_hankel_transformHankelTransformInverseHankelTransformsingularityintegrate)IndexedBaseIdxIndexedget_contraction_structureget_indicesshapeMutableDenseNDimArrayImmutableDenseNDimArrayMutableSparseNDimArrayImmutableSparseNDimArray	NDimArraytensorproducttensorcontractiontensordiagonalderive_by_arraypermutedimsArrayDenseNDimArraySparseNDimArray)
parse_expr)euler_equationssingularitiesis_increasingis_strictly_increasingis_decreasingis_strictly_decreasingis_monotonicfinite_diff_weightsapply_finite_diffdifferentiate_finiteperiodicitynot_empty_inAccumBounds	is_convexstationary_pointsminimummaximum)
Quaternion))pager_printprettypretty_printpprintpprint_use_unicodepprint_try_use_unicodelatexprint_latexmultiline_latexmathmlprint_mathmlpythonprint_pythonpycodeccodeprint_ccodesmtlib_code	glsl_code
print_glslcxxcodefcodeprint_fcodercodeprint_rcodejscodeprint_jscode
julia_codemathematica_codeoctave_code	rust_code	print_gtkpreviewsrepr
print_tree
StrPrintersstrsstrrepr	TableFormdotprint
maple_codeprint_maple_codezsympy.testing.runtests_pytesttestzsympy.testing.runtestsdoctest)plottextplotplot_backendsplot_implicitplot_parametric)init_sessioninit_printinginteractive_traversal(  r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rn  rm  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  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  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  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$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rl  rk  rm  rn  ro  rp  rq  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  rr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r/  r0  r-  r.  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  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  )algebrasassumptionscalculusconcretediscreteexternal	functionsgeometryinteractivemultipledispatchntheoryparsingplottingpolysprintingrelease
strategiestensor	utilities(  __doc__sysversion_infoImportErrormpmathsympy.releaser   sympy.core.cacher   r   r   r   corer   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   logicrw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r  r   r   r   r   r   r   r   r   r   r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  rC  r>  r?  r@  rA  rB  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  r  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  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  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  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$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r  r5  r6  r7  r8  r  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  setsrd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  solversr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  matricesr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  	integralsr%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  r  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  r  rV  r  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  r  rh  r  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  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  _create_evalf_table__all__extendr   r   r   r   <module>   s    
	 T,   "      *b T  > T 	2"

  