+ i&Rt^RIHt^RIHt^RIHt^RIHt^RI H t ^RI H t ^RI Ht^RIHt^R IHt^R IHt^R IHt^R IHt^R IHtHt^RIHt^RIHt^RI H!t!^RI"H#t#Rt$RRlt%RRRllt&RRlt'R#)zA Several methods to simplify expressions involving unit objects. )reduce)Iterable)Optional)default_sort_key)Add)Tuple)Mul)Pow)ordered)sympify)Function)NonInvertibleMatrixError) DimensionDimensionSystem)Prefix)Quantity UnitSystem)siftcn^RIHpVP4p\VP V44pVP VRR7pVUu.uFp\VP V44NK ppVUU u.uFqtP VRR7FqNK K p pp \ V4p V P\ V 44'gR#\ 4p V U u.uF&qV 9dK V PV 4'dK$V NK( p p T!V U U u.uF4qU u.uF%qP V RR7PV ^4NK' up NK6 up p 4pT!V Uu.uFqPV^4NK up4pVPV4pV#uupiuup piuup iuup iuup p iuupi \dR#i;i))MatrixTmark_dimensionlessN) sympy.matrices.denserget_dimension_systemrget_dimensional_exprget_dimensional_dependenciessetissubsetaddgetsolver )expr target_units unit_systemrdimension_systemexpr_dimdim_dependenciesx target_dimsicanon_dim_unitscanon_expr_unitsseenjcamatkexprmat res_exponentss&&& V/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/physics/units/util.py_get_conversion_matrix_for_exprr5s+"77999$?@H'DDXbfDgKWX>> from sympy.physics.units import speed_of_light, meter, gram, second, day >>> from sympy.physics.units import mile, newton, kilogram, atomic_mass_constant >>> from sympy.physics.units import kilometer, centimeter >>> from sympy.physics.units import gravitational_constant, hbar >>> from sympy.physics.units import convert_to >>> convert_to(mile, kilometer) 25146*kilometer/15625 >>> convert_to(mile, kilometer).n() 1.609344*kilometer >>> convert_to(speed_of_light, meter/second) 299792458*meter/second >>> convert_to(day, second) 86400*second >>> 3*newton 3*newton >>> convert_to(3*newton, kilogram*meter/second**2) 3*kilogram*meter/second**2 >>> convert_to(atomic_mass_constant, gram) 1.660539060e-24*gram Conversion to multiple units: >>> convert_to(speed_of_light, [meter, second]) 299792458*meter/second >>> convert_to(3*newton, [centimeter, gram, second]) 300000*centimeter*gram/second**2 Conversion to Planck units: >>> convert_to(atomic_mass_constant, [gravitational_constant, speed_of_light, hbar]).n() 7.62963087839509e-20*hbar**0.5*speed_of_light**0.5/gravitational_constant**0.5 rcZ<\P!VV3RlVP44#)c3><"TFp\VSS4xK R#5iN convert_to).0r+r$r%s& r4 2convert_to..handle_Adds..gs$ 'q, DDs)rfromiterargs)r#r$r%s&r4 handle_Addsconvert_to..handle_Addsfs%|| YY   c"\V\4#r9) isinstancer)r)s&r4convert_to..vs jH&=rCc(<VPSS4#r9r:)r)r$r%s&r4rFrGwsall<=rCc X<\V\4'd.\RVPUu.uF pS!V4NK up4#\V\4'd$S!VP 4VP ,#\V\4'dSPV4#V#uupi)cW,#r9)r)ys&&r4rF.get_total_scale_factor..{squrC) rErrr@r baseexprget_quantity_scale_factor)r#r+get_total_scale_factorr%s& r4rQ*convert_to..get_total_scale_factorys dC ,48II>Iq'*I>@ @ c " ")$))4@ @ h ' '88> > ?sB' c3b<"TF$wr^S!V4, V,V,xK& R#5i)NrK)r<uprQs& r4r=convert_to..s2,#!04q !! $ $Q &**!s,/)sympy.physics.unitsrget_unit_systemrErrrr rNrOr r togetherrhasreplacer5rr?zip)r#r$r%rrAdepmatexpr_scale_factorrQs&ff @r4r;r;4s6X/,,[9K lXu$5 6 6$~  $4  D#  :dii#=#=499%11 4=D<(L$!!}} dH % %$((8*<*<||= =?-T< MF ~ .t4 s||,# L&!,# # ##rCNc$V^8dQhR\/#)across_dimensions)bool)formats"r4 __annotate__resAAtArCc VP'g!VP\\4'gV#VP \4pTP VUu/uFq3VP bK up4p\VP \4R4pVFp\WE,4^8XdK\\WE,44pV^,V^,P , pTP VR,Uu/uFqWxP ,bK up4pK V'dVf \R4h\P!V4pVP4p VPV4p V P!V RR7p Rp V P"P%4FwrW8XgK T p M V fV#VP&P)V 4pV'd \+WV4pV#uupiuupi)aReturn an equivalent expression in which prefixes are replaced with numerical values and all units of a given dimension are the unified in a canonical manner by default. `across_dimensions` allows for units of different dimensions to be simplified together. `unit_system` must be specified if `across_dimensions` is True. Examples ======== >>> from sympy.physics.units.util import quantity_simplify >>> from sympy.physics.units.prefixes import kilo >>> from sympy.physics.units import foot, inch, joule, coulomb >>> quantity_simplify(kilo*foot*inch) 250*foot**2/3 >>> quantity_simplify(foot - 6*inch) foot/2 >>> quantity_simplify(5*joule/coulomb, across_dimensions=True, unit_system="SI") 5*volt cVP#r9) dimension)r+s&r4rF#quantity_simplify..sQ[[rC:rTNNNz:unit_system must be specified if across_dimensions is TrueTr)is_Atomr[rratomsxreplace scale_factorrlenlistr ValueErrorrrYrrrdimensional_dependenciesitems derived_unitsr!r;)r#rbr%rVdr1vrefvir&dim_exprdim_depstarget_dimensionds_dim ds_dim_deps target_units&&& r4quantity_simplifyr~s, |||488FH55  6A ==Q7QQ^^+Q7 8D TZZ !#89A  qt9>   d1Q4$$$}}"F"#oo"55FG   YZ Z 00= ,7,L,L,N33D9#@@^b@c04#3#L#L#R#R#T F&#) $U  #K!//334DE d=D KM8Gs G0G5 c ^RIHpVP!V4pRpVP\4pVP 4P pVEF]p\4pVPEF>pVP'dVPR4K).p Rp /p \P!V4Fyp V P\4'd\VP!V 44p V P\4'dV!W!V 44p KcV P"'gKwRp M V P%V P'44V 'dKVP\)\+V \,R744\/V4^8gEK'\1RP3V44h EK` /p VP\4Fp\4;QJd&RVP4F 'gK RM RM!RVP44'gKSVP6!VPU u.uFqP'dKV NK up !W&K VP9V 4#uup i) zWReturn expr if units in addends have the same base dimensions, else raise a ValueError.rc/VCVCpVP4F&wr4W09gK W19gKW@V,,W#&K( VP4UUu/uFwr5V^8wgKW5bK upp#uuppi)zUMerge dictionaries by adding values of common keys and removing keys with value of 0.)rr)dict1dict2dict3keyvaluevals&& r4addDict!check_dimensions..addDictsh#5"E"++-JC| "3Z/ (). B HC BBBs  A.$A.FT)rz(addends have incompatible dimensions: {}c3B"TFp\V\4xK R#5ir9)rEr)r<r+s& r4r=#check_dimensions..s8Az!Y''srK)rXrrYrkrrrrr@ is_numberr r make_argsr[rrr free_symbolsextendrrtuplesortedrrnrprdanyfuncrl)r#r%rraddsDIM_OFadesetaidimsskipdimdictr+repsms&& r4check_dimensionsrs/,,[9KC ::c?D  - - / L LF &&B||| " DDG]]2&55??!+"B"B1"EFA55##%gvay9G^^^D' KK  (4 %t1A BCDu:>$BII%PRR'4 D ZZ_ 38833388 8 8ff666!a667DG == 6s 3I- I- )SI)FN)(__doc__ functoolsrcollections.abcrtypingrsympyrsympy.core.addrsympy.core.containersrsympy.core.mulrsympy.core.powerr sympy.core.sortingr sympy.core.sympifyr sympy.core.functionr sympy.matrices.exceptionsr sympy.physics.units.dimensionsrrsympy.physics.units.prefixesrsympy.physics.units.quantitiesrsympy.physics.units.unitsystemrsympy.utilities.iterablesrr5r;r~rrKrCr4rsW$"' &&(>E/35*8V#rAH8rC