Functions and Variables for Units (Maxima 5.45.1 Manual)

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### 90.2 Functions and Variables for Units

Function: setunits (list)

  By default, the unit package does not use any derived dimensions, but will convert all units to the seven fundamental dimensions using MKS units.

      (%i2) N;
                                           kg m
      (%o2)                                ----
                                             2
                                            s

      (%i3) dyn;
                                         1      kg m
      (%o3)                           (------) (----)
                                       100000     2
                                                 s

      (%i4) g;
                                          1
      (%o4)                             (----) (kg)
                                         1000

      (%i5) centigram*inch/minutes^2;
                                        127        kg m
      (%o5)                       (-------------) (----)
                                   1800000000000     2
                                                    s

  In some cases this is the desired behavior. If the user wishes to use other units, this is achieved with the `setunits` command:

      (%i6) setunits([centigram,inch,minute]);
      (%o6)                                done

      (%i7) N;
                                  1800000000000   %in cg
      (%o7)                      (-------------) (------)
                                       127            2
                                                  %min

      (%i8) dyn;
                                     18000000   %in cg
      (%o8)                         (--------) (------)
                                       127          2
                                                %min

      (%i9) g;
      (%o9)                             (100) (cg)

      (%i10) centigram*inch/minutes^2;
                                          %in cg
      (%o10)                              ------
                                              2
                                          %min

  The setting of units is quite flexible. For example, if we want to get back to kilograms, meters, and seconds as defaults for those dimensions we can do:

      (%i11) setunits([kg,m,s]);
      (%o11)                               done

      (%i12) centigram*inch/minutes^2;
                                        127        kg m
      (%o12)                      (-------------) (----)
                                   1800000000000     2
                                                    s

  Derived units are also handled by this command:

      (%i17) setunits(N);
      (%o17)                               done

      (%i18) N;
      (%o18)                                 N

      (%i19) dyn;
                                          1
      (%o19)                           (------) (N)
                                        100000

      (%i20) kg*m/s^2;
      (%o20)                                 N

      (%i21) centigram*inch/minutes^2;
                                          127
      (%o21)                        (-------------) (N)
                                     1800000000000

  Notice that the unit package recognized the non MKS combination of mass, length, and inverse time squared as a force, and converted it to Newtons. This is how Maxima works in general. If, for example, we prefer dyne to Newtons, we simply do the following:

      (%i22) setunits(dyn);
      (%o22)                               done

      (%i23) kg*m/s^2;
      (%o23)                          (100000) (dyn)

      (%i24) centigram*inch/minutes^2;
                                        127
      (%o24)                         (--------) (dyn)
                                      18000000

  To discontinue simplifying to any force, we use the uforget command:

      (%i26) uforget(dyn);
      (%o26)                               false

      (%i27) kg*m/s^2;
                                           kg m
      (%o27)                               ----
                                             2
                                            s

      (%i28) centigram*inch/minutes^2;
                                        127        kg m
      (%o28)                      (-------------) (----)
                                   1800000000000     2
                                                    s

  This would have worked equally well with `uforget(N)` or `uforget(%force)`.

  See also `uforget`. To use this function write first `load("unit")`.

  Categories: Package unit

Function: uforget (list)

  By default, the unit package converts all units to the seven fundamental dimensions using MKS units. This behavior can be changed with the `setunits` command. After that, the user can restore the default behavior for a particular dimension by means of the `uforget` command:

      (%i13) setunits([centigram,inch,minute]);
      (%o13)                               done

      (%i14) centigram*inch/minutes^2;
                                          %in cg
      (%o14)                              ------
                                              2
                                          %min

      (%i15) uforget([cg,%in,%min]);
      (%o15)                      [false, false, false]

      (%i16) centigram*inch/minutes^2;
                                        127        kg m
      (%o16)                      (-------------) (----)
                                   1800000000000     2
                                                    s

  `uforget` operates on dimensions, not units, so any unit of a particular dimension will work. The dimension itself is also a legal argument.

  See also `setunits`. To use this function write first `load("unit")`.

  Categories: Package unit

Function: convert (expr, list)

  When resetting the global environment is overkill, there is the `convert` command, which allows one time conversions. It can accept either a single argument or a list of units to use in conversion. When a convert operation is done, the normal global evaluation system is bypassed, in order to avoid the desired result being converted again. As a consequence, for inexact calculations "rat" warnings will be visible if the global environment controlling this behavior (`ratprint`) is true. This is also useful for spot-checking the accuracy of a global conversion. Another feature is `convert` will allow a user to do Base Dimension conversions even if the global environment is set to simplify to a Derived Dimension.

      (%i2) kg*m/s^2;
                                           kg m
      (%o2)                                ----
                                             2
                                            s

      (%i3) convert(kg*m/s^2,[g,km,s]);
                                           g km
      (%o3)                                ----
                                             2
                                            s

      (%i4) convert(kg*m/s^2,[g,inch,minute]);

      `rat' replaced 39.37007874015748 by 5000/127 = 39.37007874015748
                                    18000000000   %in g
      (%o4)                        (-----------) (-----)
                                        127           2
                                                  %min

      (%i5) convert(kg*m/s^2,[N]);
      (%o5)                                  N

      (%i6) convert(kg*m^2/s^2,[N]);
      (%o6)                                 m N

      (%i7) setunits([N,J]);
      (%o7)                                done

      (%i8) convert(kg*m^2/s^2,[N]);
      (%o8)                                 m N

      (%i9) convert(kg*m^2/s^2,[N,inch]);

      `rat' replaced 39.37007874015748 by 5000/127 = 39.37007874015748
                                       5000
      (%o9)                           (----) (%in N)
                                       127

      (%i10) convert(kg*m^2/s^2,[J]);
      (%o10)                                 J

      (%i11) kg*m^2/s^2;
      (%o11)                                 J

      (%i12) setunits([g,inch,s]);
      (%o12)                               done

      (%i13) kg*m/s^2;
      (%o13)                                 N

      (%i14) uforget(N);
      (%o14)                               false

      (%i15) kg*m/s^2;
                                      5000000   %in g
      (%o15)                         (-------) (-----)
                                        127       2
                                                 s

      (%i16) convert(kg*m/s^2,[g,inch,s]);

      `rat' replaced 39.37007874015748 by 5000/127 = 39.37007874015748
                                      5000000   %in g
      (%o16)                         (-------) (-----)
                                        127       2
                                                 s

  See also `setunits` and `uforget`. To use this function write first `load("unit")`.

  Categories: Package unit

Optional variable: usersetunits

  Default value: none

  If an user wishes to have a default unit behavior other than that described, they can make use of maxima-init.mac and the usersetunits variable. The unit package will check on startup to see if this variable has been assigned a list. If it has, it will use setunits on that list and take the units from that list to be defaults. `uforget` will revert to the behavior defined by usersetunits over its own defaults. For example, if we have a maxima-init.mac file containing:

      usersetunits : [N,J];

  we would see the following behavior:

      (%i1) load("unit")$
      *******************************************************************
      *                       Units version 0.50                        *
      *          Definitions based on the NIST Reference on             *
      *              Constants, Units, and Uncertainty                  *
      *       Conversion factors from various sources including         *
      *                   NIST and the GNU units package                *
      *******************************************************************

      Redefining necessary functions...
      WARNING: DEFUN/DEFMACRO: redefining function
       TOPLEVEL-MACSYMA-EVAL ...
      WARNING: DEFUN/DEFMACRO: redefining function MSETCHK ...
      WARNING: DEFUN/DEFMACRO: redefining function KILL1 ...
      WARNING: DEFUN/DEFMACRO: redefining function NFORMAT ...
      Initializing unit arrays...
      Done.
      User defaults found...
      User defaults initialized.

      (%i2) kg*m/s^2;
      (%o2)                                  N

      (%i3) kg*m^2/s^2;
      (%o3)                                  J

      (%i4) kg*m^3/s^2;
      (%o4)                                 J m

      (%i5) kg*m*km/s^2;
      (%o5)                             (1000) (J)

      (%i6) setunits([dyn,eV]);
      (%o6)                                done

      (%i7) kg*m/s^2;
      (%o7)                           (100000) (dyn)

      (%i8) kg*m^2/s^2;
      (%o8)                     (6241509596477042688) (eV)

      (%i9) kg*m^3/s^2;
      (%o9)                    (6241509596477042688) (eV m)

      (%i10) kg*m*km/s^2;
      (%o10)                   (6241509596477042688000) (eV)

      (%i11) uforget([dyn,eV]);
      (%o11)                           [false, false]

      (%i12) kg*m/s^2;
      (%o12)                                 N

      (%i13) kg*m^2/s^2;
      (%o13)                                 J

      (%i14) kg*m^3/s^2;
      (%o14)                                J m

      (%i15) kg*m*km/s^2;
      (%o15)                            (1000) (J)

  Without `usersetunits`, the initial inputs would have been converted to MKS, and uforget would have resulted in a return to MKS rules. Instead, the user preferences are respected in both cases. Notice these can still be overridden if desired. To completely eliminate this simplification - i.e. to have the user defaults reset to factory defaults - the `dontusedimension` command can be used. `uforget` can restore user settings again, but only if `usedimension` frees it for use. Alternately, `kill(usersetunits)` will completely remove all knowledge of the user defaults from the session. Here are some examples of how these various options work.

      (%i2) kg*m/s^2;
      (%o2)                                  N

      (%i3) kg*m^2/s^2;
      (%o3)                                  J

      (%i4) setunits([dyn,eV]);
      (%o4)                                done

      (%i5) kg*m/s^2;
      (%o5)                           (100000) (dyn)

      (%i6) kg*m^2/s^2;
      (%o6)                     (6241509596477042688) (eV)

      (%i7) uforget([dyn,eV]);
      (%o7)                          [false, false]

      (%i8) kg*m/s^2;
      (%o8)                                  N

      (%i9) kg*m^2/s^2;
      (%o9)                                  J

      (%i10) dontusedimension(N);
      (%o10)                             [%force]

      (%i11) dontusedimension(J);
      (%o11)                         [%energy, %force]

      (%i12) kg*m/s^2;
                                           kg m
      (%o12)                               ----
                                             2
                                            s

      (%i13) kg*m^2/s^2;
                                               2
                                           kg m
      (%o13)                               -----
                                             2
                                            s

      (%i14) setunits([dyn,eV]);
      (%o14)                               done

      (%i15) kg*m/s^2;
                                           kg m
      (%o15)                               ----
                                             2
                                            s

      (%i16) kg*m^2/s^2;
                                               2
                                           kg m
      (%o16)                               -----
                                             2
                                            s

      (%i17) uforget([dyn,eV]);
      (%o17)                         [false, false]

      (%i18) kg*m/s^2;
                                           kg m
      (%o18)                               ----
                                             2
                                            s

      (%i19) kg*m^2/s^2;
                                               2
                                           kg m
      (%o19)                               -----
                                             2
                                            s

      (%i20) usedimension(N);
      Done.  To have Maxima simplify to this dimension, use
      setunits([unit]) to select an unit.
      (%o20)                               true

      (%i21) usedimension(J);
      Done.  To have Maxima simplify to this dimension, use
      setunits([unit]) to select an unit.
      (%o21)                               true

      (%i22) kg*m/s^2;
                                           kg m
      (%o22)                               ----
                                             2
                                            s

      (%i23) kg*m^2/s^2;
                                               2
                                           kg m
      (%o23)                               -----
                                             2
                                            s

      (%i24) setunits([dyn,eV]);
      (%o24)                               done

      (%i25) kg*m/s^2;
      (%o25)                          (100000) (dyn)

      (%i26) kg*m^2/s^2;
      (%o26)                    (6241509596477042688) (eV)

      (%i27) uforget([dyn,eV]);
      (%o27)                           [false, false]

      (%i28) kg*m/s^2;
      (%o28)                                 N

      (%i29) kg*m^2/s^2;
      (%o29)                                 J

      (%i30) kill(usersetunits);
      (%o30)                               done

      (%i31) uforget([dyn,eV]);
      (%o31)                          [false, false]

      (%i32) kg*m/s^2;
                                           kg m
      (%o32)                               ----
                                             2
                                            s

      (%i33) kg*m^2/s^2;
                                               2
                                           kg m
      (%o33)                               -----
                                             2
                                            s

  Unfortunately this wide variety of options is a little confusing at first, but once the user grows used to them they should find they have very full control over their working environment.

  Categories: Package unit

Function: metricexpandall (x)

  Rebuilds global unit lists automatically creating all desired metric units. x is a numerical argument which is used to specify how many metric prefixes the user wishes defined. The arguments are as follows, with each higher number defining all lower numbers’ units:

                 0 - none. Only base units
                 1 - kilo, centi, milli
      (default)  2 - giga, mega, kilo, hecto, deka, deci, centi, milli,
                     micro, nano
                 3 - peta, tera, giga, mega, kilo, hecto, deka, deci,
                     centi, milli, micro, nano, pico, femto
                 4 - all

  Normally, Maxima will not define the full expansion since this results in a very large number of units, but `metricexpandall` can be used to rebuild the list in a more or less complete fashion. The relevant variable in the unit.mac file is %unitexpand.

  Categories: Package unit

Variable: %unitexpand

  Default value: `2`

  This is the value supplied to `metricexpandall` during the initial loading of unit.

  Categories: Package unit

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