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93.2 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 a 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 a unit.
(%o20)                               true
(%i21) usedimension(J);
Done.  To have Maxima simplify to this dimension, use
setunits([unit]) to select a 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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