ó ~9­\c@ södZddlmZddlZddlmZmZmZmZm Z m Z m Z m Z m Z ddlmZmZddlm Z ddlmZddlmZdd lmZd efd „ƒYZed d ddƒZed dddƒZed dddƒZed dddƒZeddƒZedƒZedƒZed dƒZ ed dƒZ!ed dƒZ"ed dddƒZ#ed dddƒZ$ed d ƒZ%ed d!ƒZ&ed d"dd#ƒZ'ed d$dd%ƒZ(ed&ƒZ)ed d'dd(ƒZ*ed d)dd*ƒZ+ed d+dd,ƒZ,ed d-ƒZ-ed d.ƒZ.ed d/dd0ƒZ/ed d1dd2ƒZ0ed d3ƒZ1ed d4ƒZ2d5e fd6„ƒYZ3e3eeegd7e4de4d d8ddƒde4d d8dd9ƒde4dd8d d8ddƒde4dd8d d8dd9ƒde4dd8d d:dd9ƒd e4d d:dd8dd;ƒd!e4dd8d ddd9ƒd"e4ddƒd$e4d d:dd8ddƒd&e4d d<ƒƒ ƒZ5e5j6egd=e4d'e4dd8d d:dddd;ƒd)e4dd8d d:dd9dd;ƒd+e4ddd d9dd:dd<ƒd-e4ddd d9dd:dd>ƒd.e4dd8d d:dd9dd9ƒd/e4dd8dd8ƒd1e4dd8dddd9ƒd3e4d d:dd8dddd9ƒƒƒZ7e7j6eeegƒZ8e8j6e2gƒZ9dS(?sÉ Definition of physical dimensions. Unit systems will be constructed on top of these dimensions. Most of the examples in the doc use MKS system and are presented from the computer point of view: from a human point, adding length to time is not legal in MKS but it is in natural system; for a computer in natural system there is no time dimension (but a velocity dimension instead) - in the basis - so the question of adding time to length has no meaning. iÿÿÿÿ(tdivisionN( tIntegertMatrixtStSymboltsympifytBasictTupletDicttdefault_sort_key(treducet string_types(R(tExpr(tPow(tSymPyDeprecationWarningt DimensioncB s@eZdZdZeƒZeZeZ eZ eZ dd„Z ed„ƒZed„ƒZd„Zd„Zd„Zd„Zd „Zd „Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Z eZ!e Z"ed„Z#e$d„ƒZ%e$d„ƒZ&edd„ƒZ'd„Z(RS(s• This class represent the dimension of a physical quantities. The ``Dimension`` constructor takes as parameters a name and an optional symbol. For example, in classical mechanics we know that time is different from temperature and dimensions make this difference (but they do not provide any measure of these quantites. >>> from sympy.physics.units import Dimension >>> length = Dimension('length') >>> length Dimension(length) >>> time = Dimension('time') >>> time Dimension(time) Dimensions can be composed using multiplication, division and exponentiation (by a number) to give new dimensions. Addition and subtraction is defined only when the two objects are the same dimension. >>> velocity = length / time >>> velocity Dimension(length/time) It is possible to use a dimension system object to get the dimensionsal dependencies of a dimension, for example the dimension system used by the SI units convention can be used: >>> from sympy.physics.units.dimensions import dimsys_SI >>> dimsys_SI.get_dimensional_dependencies(velocity) {'length': 1, 'time': -1} >>> length + length Dimension(length) >>> l2 = length**2 >>> l2 Dimension(length**2) >>> dimsys_SI.get_dimensional_dependencies(l2) {'length': 2} g*@cC sÖt|tƒrt|ƒ}n t|ƒ}t|tƒsHtdƒ‚nt|tƒrft|ƒ}n$|dk rŠt|tƒsŠt‚n|dk r®tj|||ƒ}ntj||ƒ}||_ ||_ |S(Ns2Dimension name needs to be a valid math expression( t isinstanceR RRR t TypeErrortNonetAssertionErrort__new__t_namet_symbol(tclstnametsymboltobj((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRQs     cC s|jS(N(R(tself((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRiscC s|jS(N(R(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRmscC s tj|ƒS(N(R t__hash__(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRqscC s#t|tƒr|j|jkStS(N(RRRtFalse(Rtother((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__eq__tscC s2|jdkrd|jSd|j|jfSdS(sE Display the string representation of the dimension. s Dimension(%s)sDimension(%s, %s)N(RRR(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__str__ys cC s |jƒS(N(R (R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__repr__‚scC s|S(N((R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__neg__…sc C s®tddddddddƒjƒ|jjs@td ƒ‚n|j}|tjkrgtd ƒ‚nttjƒ}t id |6ƒ||¹s cC s||S(N((RR((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__rmul__ÅscC s|t|dƒS(Niÿÿÿÿ(R (RR((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__div__ÈscC s|t|dƒS(Niÿÿÿÿ(tpow(RR((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__rdiv__Ësc C sntddddddddƒjƒ|j}tj|ƒ}|rZ|ikrZid d 6Sd „|jƒDƒS( NR#s1.2R$i4R%s do not callR&R'it dimensionlesscS s%i|]\}}|t|ƒ“qS((tstr(t.0titj((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys Üs (RR(RR*tget_dimensional_dependenciestitems(Rtmark_dimensionlessRtdimdep((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRHÑs   cC s td„d„|jƒDƒƒS(NcS s||S(N((txty((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytàtcs s%|]\}}t|ƒ|VqdS(N(R(RER0te((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys ás(R RI(Rt dependencies((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt_from_dimensional_dependenciesÞs c C s2tddddddddƒjƒtj|ƒS( NR#s1.2R$i4R%s%do not call from `Dimension` objects.R&R'(RR(R*RH(RR((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt&_get_dimensional_dependencies_for_nameäs  cC sZ|jdkrtS|dkrGtddddddƒjƒt}n|j|ƒikS( s” Check if the dimension object really has a dimension. A dimension should have at least one component with non-zero power. iR#s1.2R$i4R%s wrong classN(RtTrueRRR(R*RH(RR+((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytis_dimensionlessîs   cC sAx:|j|ƒjƒD]}t|ttfƒstSqWtSdS(s  Check if the dimension object has only integer powers. All the dimension powers should be integers, but rational powers may appear in intermediate steps. This method may be used to check that the final result is well-defined. N(RHtvaluesRtintRRRT(Rtdim_systdpow((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pythas_integer_powerss N()t__name__t __module__t__doc__t _op_priorityR-t_dimensional_dependenciesRTtis_commutativeRt is_numbert is_positivetis_realRRtpropertyRRRRR R!R"R1R7R8R9R:R<R;R>R?R@RBt __truediv__t __rtruediv__RHt classmethodRRRSRURZ(((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRsD*                 RtlengthRtLtmasstMttimetTtcurrenttIt temperaturetamount_of_substancetluminous_intensitytvelocityt accelerationtmomentumtforcetFtenergytEtpowertpressuret frequencytftactiontAtvolumetvoltagetUt impedancetZt conductancetGt capacitancet inductancetchargetQtmagnetic_densitytBt magnetic_fluxt informationR'cB seZdZgiddd„Zed„ƒZed„ƒZed„ƒZd„Z e d„Z d„Z giddd„Z ed „ƒZd „Zd „Zd „Zed „ƒZed„ƒZed„ƒZd„Zd„Zd„Zed„ƒZed„ƒZRS(sä DimensionSystem represents a coherent set of dimensions. The constructor takes three parameters: - base dimensions; - derived dimensions: these are defined in terms of the base dimensions (for example velocity is defined from the division of length by time); - dependency of dimensions: how the derived dimensions depend on the base dimensions. Optionally either the ``derived_dims`` or the ``dimensional_dependencies`` may be omitted. c  sYt|ƒ}|dk s$|dk rFtddddddƒjƒnd„}g|D]}||ƒ^qV}g|D]}||ƒ^qu}x{|D]s}|j}||krðt||ƒdksá||j|dƒdkrðtd ƒ‚ntid|6ƒ||{s (RRI(R0(R’(s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt parse_dictzsc s+i|]!\}}ˆ|ƒˆ|ƒ“qS(((RERFRG(R“R’(s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys ~s s%Dimension %s both in base and derivedtkeycS s%i|]\}}t|ƒ|“qS((R(RERFRG((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys s (R-RRR(RtlentgetR,RtkeystappendRIt ValueErrortsortR RRR( Rt base_dimst derived_dimsR+RtdescrRRFRR((R“R’s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRKsH         !  cC s |jdS(Ni(R.(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyR›‘scC s |jdS(Ni(R.(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRœ•scC s |jdS(Ni(R.(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyR+™sc  sjˆjr"t|jjˆiƒƒSˆjr/iStj‰ˆjrÄtj t ƒ}gˆj D]}ˆ|ƒ^qZ}x;|D]3}x*|j ƒD]\}}||c|7­s c s&i|]\}}|ˆj|“qS((texp(RERžRŸ(R(s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys ±s c3 s$|]}tjˆ|ƒƒVqdS(N(RRR(REtarg(t get_for_name(s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys ´s(R)R-R+R–t is_NumberR*RStis_Mult collectionst defaultdictRWR.RItis_Powtbaset is_FunctiontfuncRRRH( RRtretRFtdictsR0RžRŸRR.tresult((R¢Rs=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRSs0    "      cC syt|tƒr|j}nt|tƒr9t|ƒ}n|j|ƒ}|re|ikreidd6Sd„|jƒDƒS(NiRCcS s%i|]\}}|t|ƒ“qS((RD(RERFRG((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pys Ès (RRRR RRSRI(RRRJRK((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRH¿s  cC s(|j|ƒ}|j|ƒ}||kS(N(RH(Rtdim1tdim2tdeps1tdeps2((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytequivalent_dimsÊsc C s’|dk s|dk r@tddddddddƒjƒnt|jƒ}|j|ƒtt|jƒt|ƒt|j ƒt|ƒ|ƒS( NR#s1.2R$i4R%s(name and descriptions of DimensionSystemR&s&do not specify `name` or `description`( RRR(R-R+tupdateR'ttupleR›Rœ(Rt new_base_dimstnew_derived_dimst new_dim_depsRt descriptiontdeps((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytextendÏs c C s;tddddddddƒjƒtt|d tƒƒS( s Useless method, kept for compatibility with previous versions. DO NOT USE. Sort dimensions given in argument using their str function. This function will ensure that we get always the same tuple for a given set of dimensions. R#s1.2R$i4R%t sort_dimsR&s!sorted(..., key=default_sort_key)R”(RR(R´tsortedRD(tdims((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyR»ás  c C sStddddddddƒjƒ|j|ƒ}|d krOt|ƒ‚n|S( s  Useless method, kept for compatibility with previous versions. DO NOT USE. Shortcut to the get_dim method, using key access. R#s1.2R$i4R%sthe get [ ] operatorR&sthe dimension definitionN(RR(tget_dimRtKeyError(RR”R0((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt __getitem__õs  c C s2tddddddddƒjƒ|j|ƒS( s“ Useless method, kept for compatibility with previous versions. DO NOT USE. Wrapper to the method print_dim_base R#s1.2R$i4R%scall DimensionSystemR&sthe dimension definition(RR(tprint_dim_base(Rtunit((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt__call__ s  cC s&|jdkrtS|j|ƒikS(s” Check if the dimension object really has a dimension. A dimension should have at least one component with non-zero power. i(RRTRH(Rt dimension((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRUscC sXtgƒ}x3|jD](}|jttj|ƒjƒƒƒqWtt|dtƒƒS(s’ Useless method, kept for compatibility with previous versions. DO NOT USE. List all canonical dimension names. R”( tsetR›R³R*RHR—R´R¼RD(RtdimsetRF((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt list_can_dims#s &cC s5td„g|jD]}|j|ƒ^qƒ}|S(sp Useless method, kept for compatibility with previous versions. DO NOT USE. Compute the inverse transformation matrix from the base to the canonical dimension basis. It corresponds to the matrix where columns are the vector of base dimensions in canonical basis. This matrix will almost never be used because dimensions are always defined with respect to the canonical basis, so no work has to be done to get them in this basis. Nonetheless if this matrix is not square (or not invertible) it means that we have chosen a bad basis. cS s |j|ƒS(N(trow_join(RLRM((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRNCRO(R R›tdim_can_vector(RR0tmatrix((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytinv_can_transf_matrix1s (cC sAtd„gt|jdtƒD]}|j|ƒ^qƒjƒS(s! Useless method, kept for compatibility with previous versions. DO NOT USE. Return the canonical transformation matrix from the canonical to the base dimension basis. It is the inverse of the matrix computed with inv_can_transf_matrix(). cS s |j|ƒS(N(RÈ(RLRM((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRNVROR”(R R¼R›RDRÉtinv(RR0((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pytcan_transf_matrixGs cC sFg}x3|jD](}|jtj|ƒj|dƒƒqWt|ƒS(s´ Useless method, kept for compatibility with previous versions. DO NOT USE. Dimensional representation in terms of the canonical base dimensions. i(RÇR˜R*RHR–R(RRtvecR0((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRÉZs &cC s|jt|j|ƒƒS(s¦ Useless method, kept for compatibility with previous versions. DO NOT USE. Vector representation in terms of the base dimensions. (RÍRRÉ(RR((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt dim_vectorhs cC s|j|ƒ}g|jD]'}|jdk r7|jn|j^q}tj}x+t||ƒD]\}}|||9}q_W|S(sY Give the string expression of a dimension in term of the basis symbols. N(RÏR›RRRRtOnetzip(RRR½RFtsymbolstreststp((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyRÁss 7 cC s t|jƒS(sÔ Useless method, kept for compatibility with previous versions. DO NOT USE. Give the dimension of the system. That is return the number of dimensions forming the basis. (R•R›(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyR~s cC s |jjS(s“ Useless method, kept for compatibility with previous versions. DO NOT USE. Check if the system is well defined. (RËt is_square(R((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt is_consistent‹s N(R[R\R]RRRdR›RœR+RSRRHR²Rºt staticmethodR»RÀRÃRURÇRËRÍRÉRÏRÁRR×(((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyR';s*F "       R+iiþÿÿÿiiýÿÿÿiR·i(:R]t __future__RR¥tsympyRRRRRRRRR tsympy.core.compatibilityR R tsympy.core.basictsympy.core.exprR tsympy.core.powerR tsympy.utilities.exceptionsRRRhRjRlRnRpRqRrRsRtRuRvRxRzR{R|R~R€RRƒR…R‡RˆR‰R‹RRŽR'R-t dimsys_MKSRºt dimsys_MKSAt dimsys_SIR*(((s=lib/python2.7/site-packages/sympy/physics/units/dimensions.pyt sŠ @ö   ÿa  !!!!!'