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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

é    N)é   é	   z2Python version 3.9 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.)Ú__version__)Úlazy_functionÚdevc                  ó@   — dd l } | j                  ddt        d¬«       ~ y )Nr   Údefaultz.*zsympy.*)Úmodule)ÚwarningsÚfilterwarningsÚDeprecationWarning)r   s    úc/Volumes/fast/ai/experiments/voice-extract-mac/.venv/lib/python3.12/site-packages/sympy/__init__.pyÚenable_warningsr   "   s!   € ÛØ×Ñ 	¨TÔ5GÐPYÐÔZÙó    c                  óh   — dd l } | j                  dd«      }|dv rt        |«      S t        d|z  «      ‚)Nr   ÚSYMPY_DEBUGÚFalse)ÚTruer   z&unrecognized value for SYMPY_DEBUG: %s)ÚosÚgetenvÚevalÚRuntimeError)r   Ú	debug_strs     r   Ú__sympy_debugr   *   s@   € ãØ—	‘	˜-¨Ó1€IØÐ%Ñ%Ü�I‹ÐäÐCØ$ñ%ó &ð 	&r   é   )^ÚsympifyÚSympifyErrorÚcacheitÚBasicÚAtomÚpreorder_traversalÚSÚExprÚ
AtomicExprÚUnevaluatedExprÚSymbolÚWildÚDummyÚsymbolsÚvarÚNumberÚFloatÚRationalÚIntegerÚNumberSymbolÚ
RealNumberÚigcdÚilcmÚseterrÚEÚIÚnanÚooÚpiÚzooÚAlgebraicNumberÚcompÚmod_inverseÚPowÚinteger_nthrootÚinteger_logÚtrailingÚMulÚprodÚAddÚModÚRelÚEqÚNeÚLtÚLeÚGtÚGeÚEqualityÚGreaterThanÚLessThanÚ
UnequalityÚStrictGreaterThanÚStrictLessThanÚ	vectorizeÚLambdaÚWildFunctionÚ
DerivativeÚdiffÚFunctionClassÚFunctionÚSubsÚexpandÚ	PoleErrorÚ	count_opsÚ
expand_mulÚ
expand_logÚexpand_funcÚexpand_trigÚexpand_complexÚexpand_multinomialÚnfloatÚexpand_power_baseÚexpand_power_expÚarityÚPrecisionExhaustedÚNÚevalfÚTupleÚDictÚ	gcd_termsÚfactor_termsÚ	factor_ncÚevaluateÚCatalanÚ
EulerGammaÚGoldenRatioÚTribonacciConstantÚ	bottom_upÚuseÚpostorder_traversalÚdefault_sort_keyÚorderedÚ
num_digits)Úto_cnfÚto_dnfÚto_nnfÚAndÚOrÚNotÚXorÚNandÚNorÚImpliesÚ
EquivalentÚITEÚPOSformÚSOPformÚsimplify_logicÚbool_mapÚtrueÚfalseÚsatisfiable)	ÚAppliedPredicateÚ	PredicateÚAssumptionsContextÚassumingÚQÚaskÚregister_handlerÚremove_handlerÚrefine)«ÚPolyÚPurePolyÚpoly_from_exprÚparallel_poly_from_exprÚdegreeÚtotal_degreeÚdegree_listÚLCÚLMÚLTÚpdivÚpremÚpquoÚpexquoÚdivÚremÚquoÚexquoÚ
half_gcdexÚgcdexÚinvertÚsubresultantsÚ	resultantÚdiscriminantÚ	cofactorsÚgcd_listÚgcdÚlcm_listÚlcmÚ	terms_gcdÚtruncÚmonicÚcontentÚ	primitiveÚcomposeÚ	decomposeÚsturmÚgff_listÚgffÚsqf_normÚsqf_partÚsqf_listÚsqfÚfactor_listÚfactorÚ	intervalsÚrefine_rootÚcount_rootsÚ	all_rootsÚ
real_rootsÚnrootsÚground_rootsÚnth_power_roots_polyÚcancelÚreducedÚgroebnerÚis_zero_dimensionalÚGroebnerBasisÚpolyÚ
symmetrizeÚhornerÚinterpolateÚrational_interpolateÚvieteÚtogetherÚBasePolynomialErrorÚExactQuotientFailedÚPolynomialDivisionFailedÚOperationNotSupportedÚHeuristicGCDFailedÚHomomorphismFailedÚIsomorphismFailedÚExtraneousFactorsÚEvaluationFailedÚRefinementFailedÚCoercionFailedÚNotInvertibleÚNotReversibleÚNotAlgebraicÚDomainErrorÚPolynomialErrorÚUnificationFailedÚGeneratorsErrorÚGeneratorsNeededÚComputationFailedÚUnivariatePolynomialErrorÚMultivariatePolynomialErrorÚPolificationFailedÚOptionErrorÚ	FlagErrorÚminpolyÚminimal_polynomialÚprimitive_elementÚfield_isomorphismÚto_number_fieldÚisolateÚ	round_twoÚprime_decompÚprime_valuationÚgalois_groupÚitermonomialsÚMonomialÚlexÚgrlexÚgrevlexÚilexÚigrlexÚigrevlexÚCRootOfÚrootofÚRootOfÚComplexRootOfÚRootSumÚrootsÚDomainÚFiniteFieldÚIntegerRingÚRationalFieldÚ	RealFieldÚComplexFieldÚPythonFiniteFieldÚGMPYFiniteFieldÚPythonIntegerRingÚGMPYIntegerRingÚPythonRationalÚGMPYRationalFieldÚAlgebraicFieldÚPolynomialRingÚFractionFieldÚExpressionDomainÚ	FF_pythonÚFF_gmpyÚ	ZZ_pythonÚZZ_gmpyÚ	QQ_pythonÚQQ_gmpyÚGFÚFFÚZZÚQQÚZZ_IÚQQ_IÚRRÚCCÚEXÚEXRAWÚconstruct_domainÚswinnerton_dyer_polyÚcyclotomic_polyÚsymmetric_polyÚrandom_polyÚinterpolating_polyÚjacobi_polyÚchebyshevt_polyÚchebyshevu_polyÚhermite_polyÚhermite_prob_polyÚlegendre_polyÚlaguerre_polyÚapartÚ
apart_listÚassemble_partfrac_listÚOptionsÚringÚxringÚvringÚsringÚfieldÚxfieldÚvfieldÚsfield)ÚOrderÚOÚlimitÚLimitÚgruntzÚseriesÚapproximantsÚresidueÚEmptySequenceÚSeqPerÚ
SeqFormulaÚsequenceÚSeqAddÚSeqMulÚfourier_seriesÚfpsÚdifference_deltaÚ	limit_seq)±Ú	factorialÚ
factorial2ÚrfÚffÚbinomialÚRisingFactorialÚFallingFactorialÚsubfactorialÚ
carmichaelÚ	fibonacciÚlucasÚmotzkinÚ
tribonacciÚharmonicÚ	bernoulliÚbellÚeulerÚcatalanÚgenocchiÚandreÚ	partitionÚdivisor_sigmaÚlegendre_symbolÚjacobi_symbolÚkronecker_symbolÚmobiusÚprimenuÚ
primeomegaÚtotientÚreduced_totientÚprimepiÚsqrtÚrootÚMinÚMaxÚIdÚ	real_rootÚRemÚcbrtÚreÚimÚsignÚAbsÚ	conjugateÚargÚ
polar_liftÚperiodic_argumentÚunbranched_argumentÚprincipal_branchÚ	transposeÚadjointÚpolarifyÚ
unpolarifyÚsinÚcosÚtanÚsecÚcscÚcotÚsincÚasinÚacosÚatanÚasecÚacscÚacotÚatan2Ú	exp_polarÚexpÚlnÚlogÚLambertWÚsinhÚcoshÚtanhÚcothÚsechÚcschÚasinhÚacoshÚatanhÚacothÚasechÚacschÚfloorÚceilingÚfracÚ	PiecewiseÚpiecewise_foldÚpiecewise_exclusiveÚerfÚerfcÚerfiÚerf2ÚerfinvÚerfcinvÚerf2invÚEiÚexpintÚE1ÚliÚLiÚSiÚCiÚShiÚChiÚfresnelsÚfresnelcÚgammaÚ
lowergammaÚ
uppergammaÚ	polygammaÚloggammaÚdigammaÚtrigammaÚ
multigammaÚdirichlet_etaÚzetaÚlerchphiÚpolylogÚ	stieltjesÚEijkÚ
LeviCivitaÚKroneckerDeltaÚSingularityFunctionÚ
DiracDeltaÚ	HeavisideÚbspline_basisÚbspline_basis_setÚinterpolating_splineÚbesseljÚbesselyÚbesseliÚbesselkÚhankel1Úhankel2ÚjnÚynÚjn_zerosÚhn1Úhn2ÚairyaiÚairybiÚairyaiprimeÚairybiprimeÚmarcumqÚhyperÚmeijergÚappellf1ÚlegendreÚassoc_legendreÚhermiteÚhermite_probÚ
chebyshevtÚ
chebyshevuÚchebyshevu_rootÚchebyshevt_rootÚlaguerreÚassoc_laguerreÚ
gegenbauerÚjacobiÚjacobi_normalizedÚYnmÚYnm_cÚZnmÚ
elliptic_kÚ
elliptic_fÚ
elliptic_eÚelliptic_piÚbetaÚmathieusÚmathieucÚmathieusprimeÚmathieucprimeÚ
riemann_xiÚbetaincÚbetainc_regularized)5Ú	nextprimeÚ	prevprimeÚprimeÚ
primerangeÚ	randprimeÚSieveÚsieveÚ	primorialÚcycle_lengthÚ	compositeÚcompositepiÚisprimeÚdivisorsÚproper_divisorsÚ	factorintÚmultiplicityÚperfect_powerÚfactor_cacheÚpollard_pm1Úpollard_rhoÚprimefactorsÚdivisor_countÚproper_divisor_countÚ	factorratÚmersenne_prime_exponentÚ
is_perfectÚis_mersenne_primeÚis_abundantÚis_deficientÚis_amicableÚis_carmichaelÚ	abundanceÚnpartitionsÚis_primitive_rootÚis_quad_residueÚn_orderÚsqrt_modÚquadratic_residuesÚprimitive_rootÚnthroot_modÚis_nthpow_residueÚsqrt_mod_iterÚdiscrete_logÚquadratic_congruenceÚbinomial_coefficientsÚbinomial_coefficients_listÚmultinomial_coefficientsÚcontinued_fraction_periodicÚcontinued_fraction_iteratorÚcontinued_fraction_reduceÚcontinued_fraction_convergentsÚcontinued_fractionÚegyptian_fraction)ÚproductÚProductÚ	summationÚSum)ÚfftÚifftÚnttÚinttÚfwhtÚifwhtÚmobius_transformÚinverse_mobius_transformÚconvolutionÚcovering_productÚintersecting_product) ÚsimplifyÚ	hypersimpÚhypersimilarÚ
logcombineÚseparatevarsÚposifyÚ
besselsimpÚkroneckersimpÚsignsimpÚ	nsimplifyÚFUÚfuÚ
sqrtdenestÚcseÚepathÚEPathÚhyperexpandÚcollectÚrcollectÚradsimpÚcollect_constÚfractionÚnumerÚdenomÚtrigsimpÚexptrigsimpÚpowsimpÚ	powdenestÚcombsimpÚ	gammasimpÚratsimpÚratsimpmodprime)ÚSetÚIntervalÚUnionÚEmptySetÚ	FiniteSetÚ
ProductSetÚIntersectionÚDisjointUnionÚimagesetÚ
ComplementÚSymmetricDifferenceÚImageSetÚRangeÚComplexRegionÚ	ComplexesÚRealsÚContainsÚConditionSetÚOrdinalÚ
OmegaPowerÚord0ÚPowerSetÚNaturalsÚ	Naturals0ÚUniversalSetÚIntegersÚ	Rationals)*ÚsolveÚsolve_linear_systemÚsolve_linear_system_LUÚsolve_undetermined_coeffsÚnsolveÚsolve_linearÚchecksolÚ	det_quickÚ	inv_quickÚcheck_assumptionsÚfailing_assumptionsÚdiophantineÚrsolveÚrsolve_polyÚrsolve_ratioÚrsolve_hyperÚcheckodesolÚclassify_odeÚdsolveÚhomogeneous_orderÚsolve_poly_systemÚfactor_systemÚsolve_triangulatedÚpde_separateÚpde_separate_addÚpde_separate_mulÚpdsolveÚclassify_pdeÚcheckpdesolÚ	ode_orderÚreduce_inequalitiesÚreduce_abs_inequalityÚreduce_abs_inequalitiesÚsolve_poly_inequalityÚsolve_rational_inequalitiesÚsolve_univariate_inequalityÚ
decompogenÚsolvesetÚlinsolveÚlinear_eq_to_matrixÚnonlinsolveÚsubstitution)FÚ
ShapeErrorÚNonSquareMatrixErrorÚGramSchmidtÚ
casoratianÚdiagÚeyeÚhessianÚjordan_cellÚ
list2numpyÚmatrix2numpyÚmatrix_multiply_elementwiseÚonesÚ
randMatrixÚ	rot_axis1Ú	rot_axis2Ú	rot_axis3ÚsymarrayÚ	wronskianÚzerosÚMutableDenseMatrixÚDeferredVectorÚ
MatrixBaseÚMatrixÚMutableMatrixÚMutableSparseMatrixÚbandedÚImmutableDenseMatrixÚImmutableSparseMatrixÚImmutableMatrixÚSparseMatrixÚMatrixSliceÚBlockDiagMatrixÚBlockMatrixÚFunctionMatrixÚIdentityÚInverseÚMatAddÚMatMulÚMatPowÚ
MatrixExprÚMatrixSymbolÚTraceÚ	TransposeÚ
ZeroMatrixÚ	OneMatrixÚblockcutÚblock_collapseÚmatrix_symbolsÚAdjointÚhadamard_productÚHadamardProductÚHadamardPowerÚDeterminantÚdetÚdiagonalize_vectorÚ
DiagMatrixÚDiagonalMatrixÚ
DiagonalOfÚtraceÚ
DotProductÚkronecker_productÚKroneckerProductÚPermutationMatrixÚMatrixPermuteÚ	PermanentÚperÚrot_ccw_axis1Úrot_ccw_axis2Úrot_ccw_axis3Ú
rot_givens)ÚPointÚPoint2DÚPoint3DÚLineÚRayÚSegmentÚLine2DÚ	Segment2DÚRay2DÚLine3DÚ	Segment3DÚRay3DÚPlaneÚEllipseÚCircleÚPolygonÚRegularPolygonÚTriangleÚradÚdegÚare_similarÚcentroidÚconvex_hullÚidiffÚintersectionÚclosest_pointsÚfarthest_pointsÚGeometryErrorÚCurveÚParabola)ÚflattenÚgroupÚtakeÚsubsetsÚ
variationsÚnumbered_symbolsÚcartesÚcaptureÚ
dict_mergeÚprefixesÚ	postfixesÚsiftÚtopological_sortÚ	unflattenÚhas_dupsÚhas_varietyÚreshapeÚ	rotationsÚ
filldedentÚlambdifyÚthreadedÚ	xthreadedÚpublicÚmemoize_propertyÚtimed)Ú	integrateÚIntegralÚline_integrateÚmellin_transformÚinverse_mellin_transformÚMellinTransformÚInverseMellinTransformÚlaplace_transformÚlaplace_correspondenceÚlaplace_initial_condsÚinverse_laplace_transformÚLaplaceTransformÚInverseLaplaceTransformÚfourier_transformÚinverse_fourier_transformÚFourierTransformÚInverseFourierTransformÚsine_transformÚinverse_sine_transformÚSineTransformÚInverseSineTransformÚcosine_transformÚinverse_cosine_transformÚCosineTransformÚInverseCosineTransformÚhankel_transformÚinverse_hankel_transformÚHankelTransformÚInverseHankelTransformÚsingularityintegrate)ÚIndexedBaseÚIdxÚIndexedÚget_contraction_structureÚget_indicesÚshapeÚMutableDenseNDimArrayÚImmutableDenseNDimArrayÚMutableSparseNDimArrayÚImmutableSparseNDimArrayÚ	NDimArrayÚtensorproductÚtensorcontractionÚtensordiagonalÚderive_by_arrayÚpermutedimsÚArrayÚDenseNDimArrayÚSparseNDimArray)Ú
parse_expr)Úeuler_equationsÚsingularitiesÚis_increasingÚis_strictly_increasingÚis_decreasingÚis_strictly_decreasingÚis_monotonicÚfinite_diff_weightsÚapply_finite_diffÚdifferentiate_finiteÚperiodicityÚnot_empty_inÚAccumBoundsÚ	is_convexÚstationary_pointsÚminimumÚmaximum)Ú
Quaternion))Úpager_printÚprettyÚpretty_printÚpprintÚpprint_use_unicodeÚpprint_try_use_unicodeÚlatexÚprint_latexÚmultiline_latexÚmathmlÚprint_mathmlÚpythonÚprint_pythonÚpycodeÚccodeÚprint_ccodeÚsmtlib_codeÚ	glsl_codeÚ
print_glslÚcxxcodeÚfcodeÚprint_fcodeÚrcodeÚprint_rcodeÚjscodeÚprint_jscodeÚ
julia_codeÚmathematica_codeÚoctave_codeÚ	rust_codeÚ	print_gtkÚpreviewÚsreprÚ
print_treeÚ
StrPrinterÚsstrÚsstrreprÚ	TableFormÚdotprintÚ
maple_codeÚprint_maple_codezsympy.testing.runtests_pytestÚtestzsympy.testing.runtestsÚdoctest)ÚplotÚtextplotÚplot_backendsÚplot_implicitÚplot_parametric)Úinit_sessionÚinit_printingÚinteractive_traversal(†  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‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r�   rŽ   r�   r�   r‘   r’   r“   r”   r•   r–   r—   r˜   r™   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r³   r´   rµ   r¶   r·   r¸   r¹   rº   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   ré   rê   rë   rì   rí   rî   rï   rð   rñ   rò   ró   rô   rõ   rö   r÷   rø   rù   rú   rû   rü   rý   rþ   rÿ   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rq  rp  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r�  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r�  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  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  rp  ro  rq  rr  rs  rt  ru  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r�  r‚  rv  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r�  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r4  r5  r2  r3  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r�  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r™  rš  r›  rœ  r�  rž  rŸ  r   r—  r˜  )ÚalgebrasÚassumptionsÚcalculusÚconcreteÚdiscreteÚexternalÚ	functionsÚgeometryÚinteractiveÚmultipledispatchÚntheoryÚparsingÚplottingÚpolysÚprintingÚreleaseÚ
strategiesÚtensorÚ	utilities(©  Ú__doc__ÚsysÚversion_infoÚImportErrorÚmpmathÚsympy.releaser   Úsympy.core.cacher   r   r   r   Úcorer   r   r   r   r    r!   r"   r#   r$   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   Úlogicrz   r{   r|   r}   r~   r   r€   r�   r‚   rƒ   r„   r…   r†   r‡   rˆ   r‰   rŠ   r‹   rŒ   r¢  r�   rŽ   r�   r�   r‘   r’   r“   r”   r•   r®  r–   r—   r˜   r™   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   r¥   r¦   r§   r¨   r©   rª   r«   r¬   r­   r®   r¯   r°   r±   r²   r³   r´   rµ   r¶   r·   r¸   r¹   rº   r»   r¼   r½   r¾   r¿   rÀ   rÁ   rÂ   rÃ   rÄ   rÅ   rÆ   rÇ   rÈ   rÉ   rÊ   rË   rÌ   rÍ   rÎ   rÏ   rÐ   rÑ   rÒ   rÓ   rÔ   rÕ   rÖ   r×   rØ   rÙ   rÚ   rÛ   rÜ   rÝ   rÞ   rß   rà   rá   râ   rã   rä   rå   ræ   rç   rè   ré   rê   rë   rì   rí   rî   rï   rð   rñ   rò   ró   rô   rõ   rö   r÷   rø   rù   rú   rû   rü   rý   rþ   rÿ   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rF  rA  rB  rC  rD  rE  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  r§  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r�  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r�  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  r­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r«  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r¤  r9  r:  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  Úsetsrh  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‚  Úsolversrƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r—  r˜  r™  rš  r›  rœ  r�  rž  rŸ  r   r¡  r¢  r£  r¤  r¥  r¦  r§  r¨  r©  rª  r«  r¬  Úmatricesr­  r®  r¯  r°  r±  r²  r³  r´  rµ  r¶  r·  r¸  r¹  rº  r»  r¼  r½  r¾  r¿  rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rÇ  rÈ  rÉ  rÊ  rË  rÌ  rÍ  rÎ  rÏ  rÐ  rÑ  rÒ  rÓ  rÔ  rÕ  rÖ  r×  rØ  rÙ  rÚ  rÛ  rÜ  rÝ  rÞ  rß  rà  rá  râ  rã  rä  rå  ræ  rç  rè  ré  rê  rë  rì  rí  rî  rï  rð  rñ  rò  r¨  ró  rô  rõ  rö  r÷  rø  rù  rú  rû  rü  rý  rþ  rÿ  r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r³  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  Ú	integralsr*  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  r²  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`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  r¡  rm  r¯  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r€  r�  r‚  rƒ  r„  r…  r†  r‡  rˆ  r‰  rŠ  r‹  rŒ  r�  rŽ  r�  r�  r‘  r’  r“  r”  r•  r–  r—  r˜  r­  r™  rš  r›  rœ  r�  r©  rž  rŸ  r   Ú_create_evalf_tableÚ__all__Úextend© r   r   Ú<module>rÅ     sÝ	  ðñó Ø×Ñ�fÒÙ
ÐJÓ
KÐKØðSÛð
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