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(* :Title: V3ReducedUnits *)
(* :Context: Miscellaneous`V3ReducedUnits` *)
(* :Author: David J. M. Park Jr. djmp@earthlink.net *)
(* :Summary: 
      This is an auxiliary package to Miscellaneous`ExtendUnits`. It provides 
        for unit conversions when certain physical constants are unitized. *)
(* :Copyright: \[Copyright] 1999 by David J. M. Park Jr. *)
(* :Package Version: 1.0 *)
(* :Mathematica Version: 3.0 *)
(* :Keywords: Units *)
(* :Requirements: Miscellaneous`V3ExtendUnits` *)



BeginPackage["Miscellaneous`V3ReducedUnits`",{"Miscellaneous`V3ExtendUnits`"}]

Miscellaneous`V3ReducedUnits::usage=
  "This is an auxiliary package to Miscellaneous`ExtendUnits` which provides \
for unit conversions when certain physical constants are unitized."

ReducedEquivalent::nosol=
  "There is not a proper solution to the conversion equations.";

ReducedEquivalent::usage=
  "ReducedEquivalent[expr, oldunit, newunit] will attempt to convert oldunit \
in expr to the newunit by multiplying by the right combination of the unit \
quantities in the reduced unit system. If there are no retained units, use 1. \
For this particular function only, ReducedEquivalent[a, 1, b] = a/b if a and \
b are both numbers. SetupReducedUnits must have been previously evaluated.";

ReducedUnitRules::usage=
  "ReducedUnitRules is the generated list of rules which transform the base \
SI units under the reduced unit system.";

ReducedUnits::usage=
  "ReducedUnits[expr] will convert the units in expr to the retained base SI \
units. SetupReducedUnits must have previously been evaluated to establish the \
transformation rules.";

SetupReducedUnits::nosol=
  "The equations for SetUpUnits do not have a proper solution.";

SetupReducedUnits::usage=
  "SetupReducedUnits[unitquantities, retainedunits] establishes a set of \
rules which will convert nonretained base SI quantities to retained base SI \
quantities. The rules are calculated by solving the equations which result \
from setting each of the unitquantities to 1. The retained units must be \
picked from the list {Meter, Kilogram, Second, Ampere, Kelvin}. The number of \
unitquantities plus the number of retainedunits should sum to 5.";

Begin["`Private`"]

baseunits={Miscellaneous`SIUnits`Meter,Miscellaneous`SIUnits`Kilogram,
    System`Second,Miscellaneous`SIUnits`Ampere,Miscellaneous`SIUnits`Kelvin};
numunits=0;
ReducedUnitRules={};

ReducedEquivalent[a_?NumberQ,1,b_?NumberQ]:=a/b

\!\(ReducedEquivalent[expr_, oldunit_, newunit_] := \n\t
    Module[{eqns, e1, k, baseratio, sol, dsol, d}, \n\t\t
      baseratio = BaseSI[newunit/oldunit]; \n\t\t
      e1 = Sum[k[i] Log[pc[i]] // PowerExpand, {i, 1, numunits}] - 
            Log[baseratio] // PowerExpand; \n\t\t
      eqns = \(\((Coefficient[e1, Log[#]] == 0)\)&\)/@baseunits; \n\t\t
      sol = Solve[eqns]; \n\t\t
      If[Length[sol] \[NotEqual] 1 \[Or] 
          Length[sol\[LeftDoubleBracket]1\[RightDoubleBracket]] \[NotEqual] 
            numunits, Message[ReducedEquivalent::nosol]; Return[$Failed]]; \n
      \t\teqns = 
        Product[pc[i]\^k[i], {i, 1, numunits}] == d\ baseratio /. 
          sol\[LeftDoubleBracket]1\[RightDoubleBracket]; \n\t\t
      dsol = \(Solve[eqns, d]\)\[LeftDoubleBracket]1, 1
            \[RightDoubleBracket] // PowerExpand; \n\t\t
      If[oldunit === 1, \n\t\t\t
        \(expr /. a_?NumberQ \[Rule] a\ \ d\ newunit\) /. dsol, \n\t\t\t
        \(expr /. oldunit \[Rule] d\ \ newunit\) /. dsol]\n\t\t]\)

ReducedUnits[expr_]:=BaseSI[expr]/.ReducedUnitRules

SetupReducedUnits[unitquantities_List,retainedunits_List]:=
	Module[{eqns,solvedunits,sols},
		numunits=Length[unitquantities];
		Clear[pc];
    Do[pc[i]=PowerExpand[
          BaseSI[unitquantities\[LeftDoubleBracket]i\[RightDoubleBracket]]],{
        i,1,numunits}];
		solvedunits=Complement[baseunits, retainedunits ];
		eqns=(PowerExpand[BaseSI[#]]==1)&/@unitquantities;
		sols=Solve[eqns,solvedunits];
		If[Length[sols]\[NotEqual]1
          \[Or]Length[sols\[LeftDoubleBracket]1\[RightDoubleBracket]]
            \[NotEqual]numunits,Message[SetupReducedUnits::nosol];
      Return[$Failed]];
		ReducedUnitRules=sols\[LeftDoubleBracket]1\[RightDoubleBracket]
		]

End[]

Protect[ReducedEquivalent,ReducedUnits,SetupReducedUnits]

EndPackage[]