(maxima.info)Functions and Variables for Units
87.2 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")'.
-- 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")'.
-- 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")'.
-- 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.
-- 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>.
-- Variable: %unitexpand
Default value: '2'
This is the value supplied to 'metricexpandall' during the initial
loading of _unit_.
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