I'm inclined to agree that maybe SymPy should be smarter when it
prints combined units, but there is the question of how it would
resolve ambiguities. For example, the force on a lever arm (Fxr) has
the same units as energy (mgh), but saying that it is in Joules would
be incorrect, because the force on a lever arm is a vector and energy
(and thus Joules) is a scalar. There are other cases when it would
not be as incorrect but might still be confusing if the user was
expecting one unit but got a dimensionally equivalent one. Can't
think of any off the top of my head, but I know I have ran into
several of them, especially in electricity and magnetism.
Aaron Meurer
On Apr 9, 2009, at 1:43 AM, kenji wrote:
>
> Hello Bill and alls.
>
> I claim to use MKSA+V base units system, not MKSA
>
> I know volt unit is derived and "m**2*kg/(A*s**3)" at
> SI:International System
> of Units.
>
> But no electrical/electronics engineers can't understand
> voltage:115*m**2*kg/(A*s**3). They can understand only 115*V.
>
> Similarly they can't understand resistor:1*m**2*kg/(A**2*s**3). They
> can under
> stand 1*ohm or 1*V/A.
>
> SI unit system was constructed compromising with previously
> established
> volt/ampere. Because it compromised with volt/ampere/ohm, it had to
> use kg as
> a unit mass and couldn't use g. It had to use weird value
> 2*10**-7*newton to
> define a unit current and couldn't use 1*newton.
>
> For electrical/electronics engineers, 1*ohm is resistance shedding
> 1*ampere
> between 1*volt. There are two base units for them in electro
> magnetic arear.
>
> ----------------------------------
> Bill wrote
>> In [34]: A*ohm
>> Out[34]: m**2*kg/(A*s**3) <-- Why not 'V'?
>
> I agree with you. The result must be V
>
>> In [35]: V/A
>> Out[35]: m**2*kg/(A**2*s**3) <-- Why not 'ohm'?
>
> I don't agree with you. It is easy to break down to base unit. But
> It is
> uneasy to synthesize unit, because the best synthesized unit is not
> determined
> uniquely and depends on user purposes.
>
> ----------------------------------
> I am dissatisfied that sympy unit module uses MKSA base units and
> V:volt is a
> derived unit.
>
> I am also dissatisfied that sympy.sin etc functions accept physical
> values
> with unit and math, scipy functions can't accept it.
>
> //@@
> import sympy as ts
> import sympy.physics.units as ut
> import math
> import scipy
> print ts.sin(2*ut.s)
> #print math.sin(2*ut.s) #ValueError: Symbolic value, can't compute
> #print scipy.sin(1.5*ut.s) #AttributeError: sin
> //@@@
> sin(2*s)
>
> sin(2*s) is correct as a result of symbolic operations, but is
> nonsence as a
> physical equation. Physically, sin function's parameter must be
> unitless.
>
> ----------------------------------
> I propose to introduce MSKA+V base unit and Float(physicalValue)
> function as
> codes in appendix. V,A,ohm units operations become as below examples
>
> print 1.5* ohm --> 1.50000000000000*V/A
> print 1.5* ohm *(1*A) --> 1.50000000000000*V
>
>
> ****************** Help me out *******************
> Yet I am dissatisfied that one * unit become Unit instance, not a
> Mul
> instance. So the it's str value dosen't have 1 and only unit.e.g
> //@@
> import sympy.physics.units as ut
> print 1*ut.s
> print 1*ut.m/(10*ut.s)
> //@@@
> s
> m/(10*s)
>
> This is not a severe problem. But 1*s, (1/10)*m/s results are
> desirable.
> Is there a countermeasure?
>
> --
> Kenji Kobayashi
>
>
> ============== appendix begin ========================
> //@@
> """
> Physical units and dimensions.
>
> The base class is Unit, where all here defined units (~200) inherit
> from.
> """
>
> import sympy as ts
> from sympy import Rational, pi
> from sympy.core.basic import Basic, Atom
>
> class Unit(Atom):
> """
> Base class for all physical units.
>
> Create own units like:
> m = Unit("meter", "m")
> """
> is_positive = True # make (m**2)**Rational(1,2) --> m
> is_commutative = True
>
> __slots__ = ["name", "abbrev"]
>
> def __new__(cls, name, abbrev, **assumptions):
> #import pdb; pdb.set_trace()
> obj = Basic.__new__(cls, **assumptions)
> assert isinstance(name, str),`type(name)`
> assert isinstance(abbrev, str),`type(abbrev)`
> obj.name = name
> obj.abbrev = abbrev
> return obj
>
> def __eq__(self, other):
> return isinstance(other, Unit) and self.name == other.name
>
> def _hashable_content(self):
> return (self.name,self.abbrev)
>
> # Delete this so it doesn't pollute the namespace
> del Atom
>
> def defunit(value, *names):
> u = value
> g = globals()
> for name in names:
> g[name] = u
>
>
> # Dimensionless
>
> percent = percents = Rational(1,100)
> permille = permille = Rational(1,1000)
>
> ten = Rational(10)
>
> yotta = ten**24
> zetta = ten**21
> exa = ten**18
> peta = ten**15
> tera = ten**12
> giga = ten**9
> mega = ten**6
> kilo = ten**3
> deca = ten**1
> deci = ten**-1
> centi = ten**-2
> milli = ten**-3
> micro = ten**-6
> nano = ten**-9
> pico = ten**-12
> femto = ten**-15
> atto = ten**-18
> zepto = ten**-21
> yocto = ten**-24
>
> rad = radian = radians = 1
> deg = degree = degrees = pi/180
>
>
> # Base units
>
> defunit(Unit('meter', 'm'), 'm', 'meter', 'meters')
> defunit(Unit('kilogram', 'kg'), 'kg', 'kilogram', 'kilograms')
> defunit(Unit('second', 's'), 's', 'second', 'seconds')
> defunit(Unit('ampere', 'A'), 'A', 'ampere', 'amperes')
> defunit(Unit('kelvin', 'K'), 'K', 'kelvin', 'kelvins')
> defunit(Unit('mole', 'mol'), 'mol', 'mole', 'moles')
> defunit(Unit('candela', 'cd'), 'cd', 'candela', 'candelas')
> defunit(Unit('volt', 'V'), 'V', 'volt', 'volts')
>
>
> # Derived units
>
> defunit(1/s, 'Hz', 'hz', 'hertz')
> defunit(m*kg/s**2, 'N', 'newton', 'newtons')
> defunit(N*m, 'J', 'joule', 'joules')
> #defunit(J/s, 'W', 'watt', 'watts')
> defunit(V*A, 'W', 'watt', 'watts')
> defunit(N/m**2, 'Pa', 'pa', 'pascal', 'pascals')
> defunit(s*A, 'C', 'coulomb', 'coulombs')
> defunit(V/A, 'ohm', 'ohms')
> defunit(A/V, 'S', 'siemens', 'mho', 'mhos')
> defunit(C/V, 'F', 'farad', 'farads')
> defunit(J/A, 'Wb', 'wb', 'weber', 'webers')
> defunit(V*s/m**2, 'T', 'tesla', 'teslas')
> defunit(V*s/A, 'H', 'henry', 'henrys')
>
>
> def Float(physicalValAg):
> if isinstance(physicalValAg, ts.Number):
> return float(physicalValAg)
> else:
> assert isinstance(physicalValAg, ts.Mul)
> # covert V to m**2*kg/(A*s**3)
> compensatingUnitAt = 1
> for elmAt in physicalValAg.args:
> if elmAt == V:
> compensatingUnitAt = compensatingUnitAt*(m**2*kg/
> (A*s**3))/V
> elif isinstance(elmAt, ts.Pow):
> if elmAt.args[0] == V:
> powNumAt = elmAt.args[1]
> compensatingUnitAt = (compensatingUnitAt
> *((m**2*kg/(A*s**3))**powNumAt)
> *(V**-powNumAt)
> )
> if compensatingUnitAt == 1:
> assert False, ("At Float(.), you set physical quantity
> parameter"
> +",the unit of which is not cancelled:"
> + str(physicalValAg)
> )
> else:
> valAt = physicalValAg * compensatingUnitAt
> assert isinstance(valAt, ts.Number),("At Floa(.)"
> + " you set physical quantity parameter"
> +",the unit of which is not cancelled:"
> + str(valAt)
> )
>
> return float(valAt)
>
> print 1* W
> print 1* V
> print 1* ohm
> print 1* ohm *(1*A)
>
> print 1.5* W
> print 1.5* V
> print 1.5* ohm
> print 1.5* ohm *(1*A)
>
> print 1*W/(10*V *(5*A))
> print 1*W/(10*J/s)
> print 3.3*F
> print 1*F *(1*V)/(2*C)
>
> print "========== Float ============="
> print Float(1.5*s *(1.1/s) )
> print Float(1*s/s)
> print Float(1.5*V*A /(1.1*W) )
> print Float(1.5*W*s /(1.1*N*m) )
> print Float(1.5* m**2*kg/(A*s**3)/(1.1*V) )
>
> import math
> import scipy
> print math.sin(Float(1.5*V*A /(1.1*W) ))
> print scipy.sin(Float(1.5*V*A /(1.1*W) ))
> print ts.sin(Float(1*V*A /W ))
> //@@@
> //copy \#####.### temp.py /y
>
> A*V
> V
> V/A
> V
> 1.50000000000000*A*V
> 1.50000000000000*V
> 1.50000000000000*V/A
> 1.50000000000000*V
> 1/50
> s**3*A*V/(10*kg*m**2)
> 3.30000000000000*A*s/V
> 1/2
> ========== Float =============
> 1.65
> 1.0
> 1.36363636364
> 1.36363636364
> 1.36363636364
> 0.978619003421
> 0.978619003421
> sin(1.00000000000000)
>
> ============== appendix end ========================
>
> >
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