combine

pagan — Mon, 06 Feb 2012 08:13:15 Z

Here is one way. I'm pasting as plain text, which is why the units show below as function calls to Units:-Unit() instead of the nice 2D Math output way involving the fenced [[]] brackets.

> restart:
> with(ScientificConstants):

> L:=[seq(1/10^(-i)*Unit(nanometer),i=11..13)];

[100000000000 Units:-Unit('nm'), 1000000000000 Units:-Unit('nm'), 

  10000000000000 Units:-Unit('nm')]

> c := evalf(GetValue(Constant('c'))*GetUnit(Constant('c')));

                             8            /'m'\
                2.99792458 10  Units:-Unit|---|
                                          \'s'/

> newL := map2(`/`,c,L);

              [                          /'m'\  
              [0.002997924580 Units:-Unit|---|  
              [                          \'s'/  
              [-------------------------------, 
              [       Units:-Unit('nm')         

                                           /'m'\  
                0.0002997924580 Units:-Unit|---|  
                                           \'s'/  
                --------------------------------, 
                       Units:-Unit('nm')          

                                            /'m'\]
                0.00002997924580 Units:-Unit|---|]
                                            \'s'/]
                ---------------------------------]
                        Units:-Unit('nm')        ]

> newL := c /~ L;

              [                          /'m'\  
              [0.002997924580 Units:-Unit|---|  
              [                          \'s'/  
              [-------------------------------, 
              [       Units:-Unit('nm')         

                                           /'m'\  
                0.0002997924580 Units:-Unit|---|  
                                           \'s'/  
                --------------------------------, 
                       Units:-Unit('nm')          

                                            /'m'\]
                0.00002997924580 Units:-Unit|---|]
                                            \'s'/]
                ---------------------------------]
                        Units:-Unit('nm')        ]

> map(combine,newL,units);

[              6            / 1 \  
[2.997924580 10  Units:-Unit|---|, 
[                           \'s'/  


                5            / 1 \                         / 1 \]
  2.997924580 10  Units:-Unit|---|, 29979.24580 Units:-Unit|---|]
                             \'s'/                         \'s'/]

Another way could be to rely on the automatic combining of units when the Units:-Standard package is loaded. (I use `map` slightly differently here. Due to the manner of the programming of Units:-Standard:-`/` as a unary procedure, it is a little awkward to `map` it.)

> restart:
> with(ScientificConstants):
> with(Units:-Standard):

> L:=[seq(1/10^(-i)*Unit(nanometer),i=11..13)];

[100000000000 Units:-Unit('nm'), 1000000000000 Units:-Unit('nm'), 

  10000000000000 Units:-Unit('nm')]

> c := evalf(GetValue(Constant('c'))*GetUnit(Constant('c')));

                             8            /'m'\
                2.99792458 10  Units:-Unit|---|
                                          \'s'/

> newL := map(t->c/t,L);

[              6            / 1 \  
[2.997924580 10  Units:-Unit|---|, 
[                           \'s'/  

                5            / 1 \                         / 1 \]
  2.997924580 10  Units:-Unit|---|, 29979.24580 Units:-Unit|---|]
                             \'s'/                         \'s'/]

MaplePrimes - answers and comments on Question, Operating on a list of values with units

combine