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Units conversion

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  Units conversion Thomas Dean <tomdean@speakeasy.org> - 2012-01-17 22:12 -0800
    Re: Units conversion acer <maple@rogers.com> - 2012-01-18 06:03 -0800

#316 — Units conversion

I am attempting to convert tesla*meter/second to volts/meter.

I can almost get there.

restart; with(ScientificConstants);
E := 30*10^(-15)*Unit('T')*GetValue(Constant(c))*Unit('m')/Unit('s');
teslaDefn := Unit('V')*Unit('s')/(Unit('m')*Unit('m'));
velocityDefn := Unit('m')/Unit('s');
teslaDefn*velocityDefn;
voltDefn:= 
(Unit('kg')*Unit('m')*Unit('m'))/((Unit('s')*Unit('s'))*Unit('s')*Unit('A')); 
voltDefn/Unit('m');

How to I get E's units to be volts/meter?

Tom Dean

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#317

You can define and use a modified version of the SI system in which volts/meter is the default for expressing items with the same dimensions as of kg*m/s^3*A.

(This is typeset in ascii, but of course the units get printed more nicely with the double [[]] brackets in the GUI.)

restart;

with(ScientificConstants):

E := 30*10^(-15)*Unit('T')*GetValue(Constant(c))*Unit('m')/Unit('s'); 

          449688687 Units:-Unit('T') Units:-Unit('m')
          -------------------------------------------
                50000000000000 Units:-Unit('s')     
 
combine(E,units);

              449688687               /('kg') ('m')\
            -------------- Units:-Unit|------------|
            50000000000000            |     3      |
                                      \('s')  ('A')/

convert(combine(E,units),units,volts/meter);

                  449688687               /'V'\
                -------------- Units:-Unit|---|
                50000000000000            \'m'/

simplify(%); # back to where we started, as it is not special to SI

              449688687               /('kg') ('m')\
            -------------- Units:-Unit|------------|
            50000000000000            |     3      |
                                      \('s')  ('A')/

# define a new version of SI
Units:-AddSystem(newSI,Units:-GetSystem(SI),volts/meter);
Units:-UseSystem(newSI);

combine(E,units); # now done in one step (and `simplify` does not undo it)

                  449688687               /'V'\
                -------------- Units:-Unit|---|
                50000000000000            \'m'/


That should also play reasonably nicely with more automatic simplification of units with arithmetic that one gets after loading Unit:-Standard.

best,
acer

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