ó ~9­\c@ sídZddlmZddlmZddlmZmZmZm Z m Z m Z m Z ddl mZmZmZddlmZmZddlmZddlmZdd lmZd „Zd „Zd „Zd „Zd„ZdS(sA Several methods to simplify expressions involving unit objects. iÿÿÿÿ(tdivision(tSymPyDeprecationWarning(tAddtFunctiontMultPowtRationaltTupletsympify(treducetIterabletordered(t Dimensiontdimsys_default(tQuantity(tPrefix(tsiftc C s>tddddddddƒjƒtj|ƒ\}}|S( s¯ NOTE: this function could be deprecated in the future. Simplify expression by recursively evaluating the dimension arguments. This function proceeds to a very rough dimensional analysis. It tries to simplify expression with dimensions, and it deletes all what multiplies a dimension without being a dimension. This is necessary to avoid strange behavior when Add(L, L) be transformed into Mul(2, L). tdeprecated_since_versions1.2tfeatures#dimensional simplification functiontissuei4t useinsteads don't use(RtwarnRt_collect_factor_and_dimension(texprt_((s7lib/python2.7/site-packages/sympy/physics/units/util.pyt dim_simplifys  c C s2ddlm}ttj|ƒƒ}tj|dtƒ}g|D]}ttj|ƒƒ^qA}d„|Dƒ}d„|Dƒ}|j|ƒs•dSt |ƒ}|g|D]:} g|D]'} tj| dtƒj | dƒ^q¸^q«ƒ} |g|D]} |j | dƒ^qøƒ} | j | ddƒ}|S(Niÿÿÿÿ(tMatrixtmark_dimensionlesscS s2h|](}tj|dtƒD] }|’qqS(R(R tget_dimensional_dependenciestTrue(t.0txti((s7lib/python2.7/site-packages/sympy/physics/units/util.pys .s cS sh|] }|’qS(((RR ((s7lib/python2.7/site-packages/sympy/physics/units/util.pys /s itmethod( tsympyRR Rtget_dimensional_exprR RRtissubsettNonetsortedtgettsolve_least_squares(Rt target_unitsRtexpr_dimtdim_dependenciesRt target_dimstcanon_dim_unitstcanon_expr_unitstjR tcamattktexprmatt res_exponents((s7lib/python2.7/site-packages/sympy/physics/units/util.pyt_get_conversion_matrix_for_expr(s( M+c stˆttfƒs!ˆg‰nt|tƒrPtj‡fd†|jDƒƒSt|ƒ}t|tƒ rœ|jtƒrœ|j d„‡fd†ƒ}n‡fd†‰t |ˆƒ}|dkrÊ|Sˆ|ƒ}|t j‡fd†t ˆ|ƒDƒƒS(sÞ 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 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) 1.66053904e-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: >>> from sympy.physics.units import gravitational_constant, hbar >>> convert_to(atomic_mass_constant, [gravitational_constant, speed_of_light, hbar]).n() 7.62950196312651e-20*gravitational_constant**(-0.5)*hbar**0.5*speed_of_light**0.5 c3 s|]}t|ˆƒVqdS(N(t convert_to(RR (R)(s7lib/python2.7/site-packages/sympy/physics/units/util.pys mscS s t|tƒS(N(t isinstanceR(R((s7lib/python2.7/site-packages/sympy/physics/units/util.pytrtc s |jˆƒS(N(R5(R(R)(s7lib/python2.7/site-packages/sympy/physics/units/util.pyR7rR8c sxt|tƒr;td„g|jD]}ˆ|ƒ^q"ƒSt|tƒr^ˆ|jƒ|jSt|tƒrt|jS|S(NcS s||S(N((Rty((s7lib/python2.7/site-packages/sympy/physics/units/util.pyR7vR8( R6RR targsRtbasetexpRt scale_factor(RR (tget_total_scale_factor(s7lib/python2.7/site-packages/sympy/physics/units/util.pyR>ts,c3 s-|]#\}}dˆ|ƒ||VqdS(iN((Rtutp(R>(s7lib/python2.7/site-packages/sympy/physics/units/util.pys ‚sN(R6R RRtfromiterR:RRthastreplaceR4R%Rtzip(RR)tdepmattexpr_scale_factor((R>R)s7lib/python2.7/site-packages/sympy/physics/units/util.pyR5=s,   !   c sâ|js|jttƒ r |S|jtƒ}|jd„|Dƒƒ}t|jtƒd„ƒ}xx|D]p}t||ƒdkrŒqjntt ||ƒƒ}|d|dj ‰|j‡fd†|dDƒƒ}qjW|S(sßReturn 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. Examples ======== >>> from sympy.physics.units.util import quantity_simplify >>> from sympy.physics.units.prefixes import kilo >>> from sympy.physics.units import foot, inch >>> quantity_simplify(kilo*foot*inch) 250*foot**2/3 >>> quantity_simplify(foot - 6*inch) foot/2 cS si|]}|j|“qS((R=(RR@((s7lib/python2.7/site-packages/sympy/physics/units/util.pys ›s cS s|jS(N(t dimension(R ((s7lib/python2.7/site-packages/sympy/physics/units/util.pyR7ŸR8iic s i|]}ˆ|j|“qS((R=(Rtvi(tref(s7lib/python2.7/site-packages/sympy/physics/units/util.pys ¥s ( tis_AtomRBRRtatomstxreplaceRtlentlistR R=(RR@tdR1tv((RIs7lib/python2.7/site-packages/sympy/physics/units/util.pytquantity_simplify…s 'c C s»ddlm}|jtƒ}tj}x|D] }tƒ}xû|jD]ð}|jrj|j dƒqHng}t }x|t j |ƒD]k} | j tƒr³ttj| ƒƒ} n| j tƒrÞ|j|| ƒjƒƒq†| jr†t}Pq†q†W|sH|j tt|ƒƒƒt|ƒdkr8tdƒ‚q8qHqHWq/Wi} xe|jt ƒD]T} td„| jDƒƒrV| jg| jD]} | js…| ^q…Œ| | Ðs((tsympy.solvers.solvesetRRRKRR RtsetR:t is_numbertaddtFalseRt make_argsRBRR R#textendtitemst free_symbolsRttupleR&RMt ValueErrortanytfuncRL( RRRtaddstDIM_OFtatdesettaitdimstskipR trepstm((s7lib/python2.7/site-packages/sympy/physics/units/util.pytcheck_dimensionsªs<      3N(t__doc__t __future__Rtsympy.utilities.exceptionsRR"RRRRRRRtsympy.core.compatibilityR R R tsympy.physics.units.dimensionsR R tsympy.physics.units.quantitiesRtsympy.physics.units.prefixesRtsympy.utilities.iterablesRRR4R5RQRi(((s7lib/python2.7/site-packages/sympy/physics/units/util.pyts4   H %