o *ήc%@sdZddlmZddlmZddlmZddlmZddl m Z ddl m Z ddl mZdd lmZdd lmZdd lmZdd lmZdd lmZmZddlmZddlmZddlmZddl m!Z!ddZ"dddZ#dde$fddZ%dddZ&dS) zA Several methods to simplify expressions involving unit objects. )reduce)Iterable)Optional)default_sort_key)Add)Tuple)Mul)Pow)ordered)sympify)NonInvertibleMatrixError) DimensionDimensionSystem)Prefix)Quantity UnitSystem)siftc sddlm}t|}j|ddfdd|DfddD}dd D}|t|s:dStfd d|D}|fd d|D}|fd d|D}z||} W| St yoYdSw) Nr)MatrixTmark_dimensionlesscsg|] }t|qS)r get_dimensional_expr).0x) unit_systemr?/tmp/pip-target-vg8gfxp4/lib/python/sympy/physics/units/util.py sz3_get_conversion_matrix_for_expr..cs$g|]}j|ddD]}|q qS)Tr)get_dimensional_dependencies)rri)dimension_systemrrrs$cSsh|]}|qSrrrrrrr sz2_get_conversion_matrix_for_expr..cs"g|] }|vs|s|qSr)addr!)seenrrr&"cs g|] fddDqS)cs"g|] }j|dddqS)Trr)rgetr!)r jrrr(r%z>_get_conversion_matrix_for_expr...r)r)r target_dims)r'rr(s csg|]}|dqSr)r&)rk)dim_dependenciesrrr)) sympy.matrices.denserget_dimension_systemr rrissubsetsetsolver ) expr target_unitsrrexpr_dimcanon_dim_unitscanon_expr_unitscamatexprmat res_exponentsr)r+r r$r(rr_get_conversion_matrix_for_exprs&   r:SIcsddlm}|tttfsgt|tr(tfdd|jDSt |}t t|t sG| t rG| ddfdd}fdd t |}|d urZ|S|}|tfd dt|DS) a Convert ``expr`` to the same expression with all of its units and quantities represented as factors of ``target_units``, whenever the dimension is compatible. ``target_units`` may be a single unit/quantity, or a collection of units/quantities. Examples ======== >>> 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 rrc3s|] }t|VqdSN convert_tor!r3rrr fszconvert_to..cSs t|tSr<) isinstancerrrrrms zconvert_to..cs |Sr<r=rBr?rrrCns csZt|trtddfdd|jDSt|tr!|j|jSt|tr+|S|S)NcSs||Sr<r)ryrrrrCrsz.get_total_scale_factor..csg|]}|qSrrr!get_total_scale_factorrrrsz>convert_to..get_total_scale_factor..) rArrargsr baseexprget_quantity_scale_factor)r2)rFrrrrFps    z*convert_to..get_total_scale_factorNc3s(|]\}}d|||VqdS)Nr)ruprErrr@s )sympy.physics.unitsrget_unit_systemrArrrfromiterrHr rhasreplacer:rzip)r2r3rrdepmatexpr_scale_factorr)rFr3rrr>3s, ,      r>FNacross_dimensionscs8|js |tts |S|t}|dd|D}t|tdd}|D],}t||dkr1q&tt ||}|d|dj |fdd|ddD}q&|r|dur]t d t |}|}||}|j|d d } d} |jD] \} } | | kr| } nqy| dur|S|j| } | rt|| |}|S) 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 cSsi|]}||jqSr scale_factor)rrNrrr rGz%quantity_simplify..cSs|jSr<) dimension)rrrrrCsz#quantity_simplify..rLrcsi|]}||jqSrrX)rvirefrrrZr,Nz:unit_system must be specified if across_dimensions is TrueTr)is_AtomrRrratomsxreplacerlenlistr rY ValueErrorrrPr.rrdimensional_dependenciesitems derived_unitsr&r>)r2rWrrNdr*vr dim_exprdim_depstarget_dimensionds_dim ds_dim_deps target_unitrr]rquantity_simplifys< "    rpc CsJddlm}||}dd}|t}|j}|D]c}t}|jD]Z}|j r.| dq#g} d} i} t |D]"} | trGt|| } | trT|| || } q9| jr[d} nq9| | | s}| tt| tdt|d kr}td |q#qi} |t D]}td d |jDr|jd d|jD| |<q|| S)z[Return expr if units in addends have the same base dimensions, else raise a ValueError.rrcSsPi||}|D]\}}||vr||vr|||||<q dd|DS)z]Merge dictionaries by adding values of common keys and removing keys with value of 0.cSsi|] \}}|dkr||qSr)r)rkeyvalrrrrZsz5check_dimensions..addDict..)rf)dict1dict2dict3rqvaluerrraddDicts z!check_dimensions..addDictrFT)rqrLz(addends have incompatible dimensions: {}css|]}t|tVqdSr<)rAr r!rrrr@sz#check_dimensions..cSsg|]}|js|qSr) is_numberr!rrrrs z$check_dimensions..)rOrrPr`rr.rr0rHrxr#r make_argsrRrr r free_symbolsextendrftuplesortedrrbrdformatanyfuncra)r2rrrwaddsDIM_OFadesetaidimsskipdimdictrrepsmrrrcheck_dimensionssP          r)r;)FN)'__doc__ functoolsrcollections.abcrtypingrsympyrsympy.core.addrsympy.core.containersrsympy.core.mulrsympy.core.powerr sympy.core.sortingr sympy.core.sympifyr sympy.matrices.commonr sympy.physics.units.dimensionsr rsympy.physics.units.prefixesrsympy.physics.units.quantitiesrsympy.physics.units.unitsystemrsympy.utilities.iterablesrr:r>boolrprrrrrs*                QD