7^(hQdZddlmZddlZddlmZddlmZddlm Z m Z ddl m Z ddl mZdd lmZdd lmZdd lmZdd lmZdd lmZddlmZGddZGddeZGddeeZy)a 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. ) annotationsN)reduce)Basic)DictTuple)S)default_sort_key)Symbol)sympify)Matrix)TrigonometricFunction)ExprPowcVeZdZUiZded<iZded<iZded<dZdZdZ dZ d Z y ) _QuantityMapperzdict[Expr, Expr]_quantity_scale_factors_global,_quantity_dimensional_equivalence_map_global_quantity_dimension_globalc i|_i|_yN)_quantity_dimension_map_quantity_scale_factors)selfargskwargss \/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/physics/units/dimensions.py__init__z_QuantityMapper.__init__$s')$')$cddlm}t|}t|ts|dk(r t d}n(t dt||r|j |}||j|<y)z Set the dimension for the quantity in a unit system. If this relation is valid in every unit system, use ``quantity.set_global_dimension(dimension)`` instead. rQuantityzexpected dimension or 1N)sympy.physics.unitsr"r isinstance Dimension ValueErrorget_quantity_dimensionr)rquantity dimensionr"s rset_quantity_dimensionz&_QuantityMapper.set_quantity_dimension(sa 1I& )Y/A~%aL  !:;;  8 ,33I>I1:$$X.rcddlmddlmt |}|j fdd}|j fdfd}|j |<y) a Set the scale factor of a quantity relative to another quantity. It should be used only once per quantity to just one other quantity, the algorithm will then be able to compute the scale factors to all other quantities. In case the scale factor is valid in every unit system, please use ``quantity.set_global_relative_scale_factor(scale_factor)`` instead. rr!)Prefixct|Srr%)xr-s rz;_QuantityMapper.set_quantity_scale_factor..JsjF+rc|jSr) scale_factor)r0s rr1z;_QuantityMapper.set_quantity_scale_factor..Ks annrct|Srr/)r0r"s rr1z;_QuantityMapper.set_quantity_scale_factor..OsjH-rc&j|Sr)get_quantity_scale_factor)r0rs rr1z;_QuantityMapper.set_quantity_scale_factor..Psd44Q7rN)r$r"sympy.physics.units.prefixesr-r replacer)rr)r3r-r"s` @@rset_quantity_scale_factorz)_QuantityMapper.set_quantity_scale_factor:sU 17|, #++ + $ $++ - 7 2>$$X.rcddlm}||jvr|j|S||jvr|j|S||jvrF|j|}t ||r|j |St|j|St ||rt|jStdS)Nrr!r#) r$r"rrrr%r(r&get_dimensional_exprname)runitr"dep_units rr(z&_QuantityMapper.get_quantity_dimensionTs0 4// ///5 5 422 22248 8 4DD DHHNH(H-228<< !:!:8!DEE dH %TYY' 'Q< rc||jvr|j|S||jvr&|j|\}}||j|zStjSr)rrr6rOne)rr= mul_factor other_units rr6z)_QuantityMapper.get_quantity_scale_factorfsc 4// ///5 5 466 6%)%H%H%N "J d<4 $rrceZdZdZdZiZdZdZdZdZ ddZ e dZ e dZ dZd Zd Zfd Zd Zd ZdZdZdZfdZdZdZdZedZdZxZS)r&a 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 quantities. >>> 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.systems.si import dimsys_SI >>> dimsys_SI.get_dimensional_dependencies(velocity) {Dimension(length, L): 1, Dimension(time, T): -1} >>> length + length Dimension(length) >>> l2 = length**2 >>> l2 Dimension(length**2) >>> dimsys_SI.get_dimensional_dependencies(l2) {Dimension(length, L): 2} g*@TFc2t|tr t|}n t|}t|ts t dt|tr t|}n|t|tsJt j ||}||_||_|S)Nz2Dimension name needs to be a valid math expression) r%strr r r TypeError__new___name_symbol)clsr<symbolobjs rrLzDimension.__new__s dC $.s 1q5rc3,K|] \}}||zywrrG).0des r z;Dimension._from_dimensional_dependencies..s+ QAqD+ sr#)ritems)rO dependenciess r_from_dimensional_dependenciesz(Dimension._from_dimensional_dependenciess+(+ )//1+  rc`td|j|jDS)a  Check if the dimension object has only integer powers. All the dimension powers should be integers, but rational powers may appear in intermediate steps. This method may be used to check that the final result is well-defined. c34K|]}|jywr) is_Integer)rdpows rrz/Dimension.has_integer_powers..sct4??cs)allget_dimensional_dependenciesvalues)rdim_syss rhas_integer_powerszDimension.has_integer_powers s*cw/S/STX/Y/`/`/bcccrr)rCrDrE__doc__ _op_priority_dimensional_dependenciesis_commutative is_number is_positiveis_realrLpropertyr<rPrWrYr[rargrjrmrprortrvrzr} classmethodrr __classcell__)rds@rr&r&os)VL!#NIKG*B #  '+ ##% drr&ceZdZdZdifdZedZedZedZdZ ddZ d Z dd Z d Z ed ZedZedZdZdZdZedZedZy )DimensionSystema DimensionSystem represents a coherent set of dimensions. The constructor takes three parameters: - base dimensions; - derived dimensions: these are defined in terms of the base dimensions (for example velocity is defined from the division of length by time); - dependency of dimensions: how the derived dimensions depend on the base dimensions. Optionally either the ``derived_dims`` or the ``dimensional_dependencies`` may be omitted. rGc  t|}d}|Dcgc] }|| }}|Dcgc] }|| }}|D]J}||vr4t||dk7s||j|ddk7r tdt |di||<Ld |j D]%}||}||vs||vs|j |' fd}|jDcic]\}} |||}}}|D])}||vrtd|z||vst |di||<+|jt|jtt|}t|}t |jDcic]\}}|t |c}}}tj||||} | Scc}wcc}wcc}}wcc}}w)Nct|trtt|}|St|tr |St|tr t|}|St d|z)Nz %s wrong type)r%rJr&r rKdims r parse_dimz*DimensionSystem.__new__..parse_dim0se#s#s ,J C+ J C(nJ # 566rr#z!Repeated value in base dimensionsct|tr|St|trtt|St|tr t|St dt |d|)Nzunrecognized type z for )r%r&rJr rKtypers rparse_dim_namez/DimensionSystem.__new__..parse_dim_nameEsR#y) C% --C( ~%cC PQQrc vt|jDcic]\}}||c}}Scc}}wr)rr)rijrs r parse_dictz+DimensionSystem.__new__..parse_dictTs0!'')D$!Q*A-DE EDs5 z%Dimension %s both in base and derivedkey)dictlenget IndexErrorrkeysappendrr'sortr rrrL) rO base_dims derived_dimsdimensional_dependenciesrrrrrrQrs @rrLzDimensionSystem.__new__-s#'(@#A  ,55aYq\5 5.:; ! ; ; ;C//1#671<(-11#t<A !DEE,0#qN $S )  ; R,002 )CC.C<'c.B##C( )  F %=$B$B$D$FAN1$5z!}$D$F $F  ?Ci !H3!NOO2204c1X(-  ? +,./9% l+ #'@X@^@^@`(a1DG(a#b mmCL:RS ]6;8$F)bsF2F7F<:G c |jdS)NrrrSs rrzDimensionSystem.base_dimskyy|rc |jdSNr#rrSs rrzDimensionSystem.derived_dimsorrc |jdS)NrrSs rrz(DimensionSystem.dimensional_dependenciessrrcD t|trtt|}nt|ts t|}|jj r't |jj||diS|jjs|jjriS|j |jjrtjt}|jj Dcgc] } | c} D]'}|j#D]\}}||xx|z cc<)|j#Dcic]\}}|dk7s ||c}}S|jj$rQ|jj Dcgc] } | c} t' fd ddDr dSt)d|jj*r |jj,} |jj.}|ik(s |jj.j r;|j#Dcic]\}}|||jj.z!c}}St)d|jj0r: fd|jj D} |jj2| } |jj Dcgc] } | c} t| tr|j5| S| j2|jj2k(rt|jt6r: ditddifvriSt)dj9|j2t'd DriSt)d j9|j2 | St)d j9t;|jcc}wcc}}wcc}wcc}}wcc}w) Nr#rc3.K|] }|dk(yw)rNrG)rrdictss rrzIDimensionSystem._get_dimensional_dependencies_for_name..s4Q1a=4sz6Only equivalent dimensions can be added or subtracted.zFThe exponent for the power operator must be a Symbol or dimensionless.c3TK|]}tj|!ywr)r&r)rarg get_for_names rrzIDimensionSystem._get_dimensional_dependencies_for_name..s.C'*<<S!#Cs%(anglezYThe input argument for the function {} must be dimensionless or have dimensions of angle.c3&K|] }|ik( ywrrG)ritems rrzIDimensionSystem._get_dimensional_dependencies_for_name..s8$42:8sz>The input arguments for the function {} must be dimensionless.z8Type {} not implemented for get_dimensional_dependencies)r%rJr&r r< is_Symbolrrrris_NumberSymbol&_get_dimensional_dependencies_for_nameis_Mul collections defaultdictintrris_AddrrKis_Powbaseexp is_Functionfuncrr formatr) rr*retrrkvdim_basedim_exprresultrrs @@rrz6DimensionSystem._get_dimensional_dependencies_for_namews| i %!&"34IIy1!),I >> # #5599)iQR^TU U >> # #y~~'E'EIBB >> ))#.C.7nn.A.AB\!_BE GGI DAqFaKF  (+yy{=Vaa1fAqD= = >> .7nn.A.AB\!_BE4%)44QxTU U >> #INN$7$78H"9>>#5#56G"}  2 2 < <@H@PQfq!1y~~1111QQ hii >> % %C.7nn.A.ACD(Y^^(($/F.7nn.A.AB\!_BE&),88@@  3 33inn.CDQxB7);Q(?#@@! ')D)K)KLULZLZ)[\\8%88! '(h(o(opyp~p~(AA#F++RYYZ^_h_m_mZnoppWC>CRCs$P P  P P$P0Pc~|j|}|r|ik(r tddiSt|jSr)rr&rr)rr<mark_dimensionlessdimdeps rrz,DimensionSystem.get_dimensional_dependenciess;<>""rc.|jjS)z Useless method, kept for compatibility with previous versions. DO NOT USE. Check if the system is well defined. )r is_squarerSs r is_consistentzDimensionSystem.is_consistentAs))333r)F)rGN)rCrDrErrLrrrrrrrrrrrrrrr rrrGrrrrs .0"<|=q~$  B . .*$  I  # # 4 4rr)r __future__rr functoolsrsympy.core.basicrsympy.core.containersrrsympy.core.singletonrsympy.core.sortingr sympy.core.symbolr sympy.core.sympifyr sympy.matrices.denser (sympy.functions.elementary.trigonometricr sympy.core.exprrsympy.core.powerrrr&rrGrrrsa #"/"/$&'J NNbfdfd\q4e_q4r