ó ¡¼™\c@sìddlmZmZddlmZmZddlm Z ddl m Z m ZmZddlmZmZmZmZddlmZdefd„ƒYZd eefd „ƒYZd eefd „ƒYZd efd„ƒYZdS(iÿÿÿÿ(tsimplifyttrigsimp(tcall_highest_priorityt _sympifyit(t StdFactKB(tfactortdifftIntegral(tStAddtMult count_ops(tExprtBasisDependentcBsâeZdZedƒd„ƒZedƒd„ƒZedƒd„ƒZedƒd„ƒZed e ƒed ƒd „ƒƒZ ed e ƒed ƒd „ƒƒZ d„Z ed e ƒedƒd„ƒƒZ edƒd„ƒZe ZeZd!d„Zejejj7_eZdeeed„Zejej7_d„Zejej7_d„Zd„Zd„Zd„Zd„Zd„Z e je!j7_ed„Z"d„Z#d„Z$e$je%j7_d „Z&RS("sÒ Super class containing functionality common to vectors and dyadics. Named so because the representation of these quantities in sympy.vector is dependent on the basis they are expressed in. t__radd__cCs|j||ƒS(N(t _add_func(tselftother((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__add__sRcCs|j||ƒS(N(R(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRst__rsub__cCs|j|| ƒS(N(R(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__sub__sRcCs|j|| ƒS(N(R(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRsRt__rmul__cCs|j||ƒS(N(t _mul_func(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__mul__!sRcCs|j||ƒS(N(R(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR&scCs|jtdƒ|ƒS(Niÿÿÿÿ(RR(R((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__neg__+st__rdiv__cCs |j|ƒS(N(t _div_helper(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__div__.sRcCs tdƒS(NsInvalid divisor for division(t TypeError(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR3scKsG|j}x7|jjƒD]&\}}||j|||7}qW|S(s… Implements the SymPy evalf routine for this quantity. evalf's documentation ===================== (tzerot componentstitemstevalf(Rtprectoptionstvectktv((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR :s g333333û?c CsWg|jjƒD]4\}}t|d|d|d|d|ƒ|^q}|j|ŒS(sŽ Implements the SymPy simplify routine for this quantity. simplify's documentation ======================== tratiotmeasuretrationaltinverse(RRtsimpR(RR&R'R(R)R$R%tsimp_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRKsGcKsBg|jjƒD]\}}t|||^q}|j|ŒS(s Implements the SymPy trigsimp routine, for this quantity. trigsimp's documentation ======================== (RRttsimpR(RtoptsR$R%ttrig_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRZs2c Cs"|jd|d|d|d|ƒS(NR&R'R(R)(R(RR&R'R(R)((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt_eval_simplifyhscKs |j|S(N(R(RR-((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt_eval_trigsimpkscCs |j|ƒS(N(R(Rtwrt((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt_eval_derivativenscOsEg|jjƒD]"\}}t|||Ž|^q}|j|ŒS(N(RRRR(Rtsymbolst assumptionsR$R%tintegral_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt_eval_Integralqs5cCs |tjfS(s‚ Returns the expression as a tuple wrt the following transformation - expression -> a/b -> a, b (RtOne(R((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pytas_numer_denomvscOsEg|jjƒD]"\}}t|||Ž|^q}|j|ŒS(sµ Implements the SymPy factor routine, on the scalar parts of a basis-dependent expression. factor's documentation ======================== (RRtfctrR(RtargstkwargsR$R%tfctr_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR€s 5cCstdƒ|fS(s2Efficiently extract the coefficient of a product. i(R(RR(((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt as_coeff_MulscGs7g|jD]}||j|^q }dt|ƒfS(s4Efficiently extract the coefficient of a summation. i(Rttuple(Rtdepstxtl((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt as_coeff_add“s'cOstx,|D]$}t|tƒrtdƒ‚qqWg|jjƒD]"\}}t|||Ž|^q?}|j|ŒS(s Implements the SymPy diff routine, for vectors. diff's documentation ======================== sInvalid arg for differentiation(t isinstanceR RRRtdfR(RR:R;R@R$R%tdiff_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR˜s  5cKs=g|jD] }|j|j||^q }|j|ŒS(s(Calls .doit() on each term in the Dyadic(RtdoitR(RthintsR@tdoit_components((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRF©s-N('t__name__t __module__t__doc__RRRRRRtNotImplementedRRRRRt __truediv__t __rtruediv__tNoneR R tnR tFalseRR*RR,R/R0R2R6R8RR9R=RBRRDRF(((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR sD               tBasisDependentAddcBs eZdZd„ZejZRS(st Denotes sum of basis dependent quantities such that they cannot be expressed as base or Mul instances. c Osëi}xét|ƒD]Û\}}t||jƒs’t|tƒrU|j|jŒ}q’t|tƒry|j|jŒ}q’tt |ƒdƒ‚n||j kr§qnt |dƒrx5|j D]'}|j |dƒ|j |||Rt__hash__t_hash(RbRg((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR]6s!cCs|jS(N(R†(R((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR…=st__req__cCst||jƒS(N(RCRo(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt__eq__@sRcCs&t||jƒr|Stdƒ‚dS(Ns#Invalid argument types for addition(RCRUR(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRFsRcCs&t||jƒr|Stdƒ‚dS(Ns#Invalid argument types for addition(RCRUR(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRMsRcCs't||jƒr| Stdƒ‚dS(Ns&Invalid argument types for subtraction(RCRUR(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRTsRcCs&t||jƒr|Stdƒ‚dS(Ns&Invalid argument types for subtraction(RCRUR(RR((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR[scCs|S(N((R((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRbscCs|S(s@ Returns the normalized version of this vector. ((R((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyt normalizeescCsdS(Nt0((RR€((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyRksN(RIRJRKRR]R…RRˆR‡RRRRRR‰RORR‚Rƒ(((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyR„0s     N(tsympy.simplifyRR*RR,tsympy.core.decoratorsRRtsympy.core.assumptionsRtsympyRR9RRDRt sympy.coreRR R R tsympy.core.exprR R RRRiR„(((s:lib/python2.7/site-packages/sympy/vector/basisdependent.pyts"§4L