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Previous: <a href="maxima_259.html#Introduction-to-Units" accesskey="p" rel="previous">Introduction to Units</a>, Up: <a href="maxima_258.html#unit_002dpkg" accesskey="u" rel="up">unit-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_264.html#g_t_0423_043a_0430_0437_0430_0442_0435_043b_044c-_0444_0443_043d_043a_0446_0438_0439-_0438-_043f_0435_0440_0435_043c_0435_043d_043d_044b_0445" title="Index" rel="index">Index</a>]</p>
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<a name="Functions-and-Variables-for-Units-1"></a>
<h3 class="section">72.2 Functions and Variables for Units</h3>
<a name="setunits"></a><a name="Item_003a-unit_002fdeffn_002fsetunits"></a><dl>
<dt><a name="index-setunits"></a>Function: <strong>setunits</strong> <em>(<var>list</var>)</em></dt>
<dd><p>By default, the <em>unit</em> package does not use any derived dimensions, but will
convert all units to the seven fundamental dimensions using MKS units.
</p><div class="example">
<pre class="example">(%i2) N;
kg m
(%o2) ----
2
s
</pre><pre class="example">(%i3) dyn;
1 kg m
(%o3) (------) (----)
100000 2
s
</pre><pre class="example">(%i4) g;
1
(%o4) (----) (kg)
1000
</pre><pre class="example">(%i5) centigram*inch/minutes^2;
127 kg m
(%o5) (-------------) (----)
1800000000000 2
s
</pre></div>
<p>In some cases this is the desired behavior. If the user wishes to use other
units, this is achieved with the <code>setunits</code> command:
</p><div class="example">
<pre class="example">(%i6) setunits([centigram,inch,minute]);
(%o6) done
</pre><pre class="example">(%i7) N;
1800000000000 %in cg
(%o7) (-------------) (------)
127 2
%min
</pre><pre class="example">(%i8) dyn;
18000000 %in cg
(%o8) (--------) (------)
127 2
%min
</pre><pre class="example">(%i9) g;
(%o9) (100) (cg)
</pre><pre class="example">(%i10) centigram*inch/minutes^2;
%in cg
(%o10) ------
2
%min
</pre></div>
<p>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:
</p><div class="example">
<pre class="example">(%i11) setunits([kg,m,s]);
(%o11) done
</pre><pre class="example">(%i12) centigram*inch/minutes^2;
127 kg m
(%o12) (-------------) (----)
1800000000000 2
s
</pre></div>
<p>Derived units are also handled by this command:
</p><div class="example">
<pre class="example">(%i17) setunits(N);
(%o17) done
</pre><pre class="example">(%i18) N;
(%o18) N
</pre><pre class="example">(%i19) dyn;
1
(%o19) (------) (N)
100000
</pre><pre class="example">(%i20) kg*m/s^2;
(%o20) N
</pre><pre class="example">(%i21) centigram*inch/minutes^2;
127
(%o21) (-------------) (N)
1800000000000
</pre></div>
<p>Notice that the <em>unit</em> 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:
</p><div class="example">
<pre class="example">(%i22) setunits(dyn);
(%o22) done
</pre><pre class="example">(%i23) kg*m/s^2;
(%o23) (100000) (dyn)
</pre><pre class="example">(%i24) centigram*inch/minutes^2;
127
(%o24) (--------) (dyn)
18000000
</pre></div>
<p>To discontinue simplifying to any force, we use the uforget command:
</p><div class="example">
<pre class="example">(%i26) uforget(dyn);
(%o26) false
</pre><pre class="example">(%i27) kg*m/s^2;
kg m
(%o27) ----
2
s
</pre><pre class="example">(%i28) centigram*inch/minutes^2;
127 kg m
(%o28) (-------------) (----)
1800000000000 2
s
</pre></div>
<p>This would have worked equally well with <code>uforget(N)</code> or
<code>uforget(%force)</code>.
</p>
<p>See also <code><a href="#uforget">uforget</a></code>. To use this function write first <code>load("unit")</code>.
</p>
</dd></dl>
<a name="uforget"></a><a name="Item_003a-unit_002fdeffn_002fuforget"></a><dl>
<dt><a name="index-uforget"></a>Function: <strong>uforget</strong> <em>(<var>list</var>)</em></dt>
<dd><p>By default, the <em>unit</em> package converts all units to the
seven fundamental dimensions using MKS units. This behavior can
be changed with the <code>setunits</code> command. After that, the
user can restore the default behavior for a particular dimension
by means of the <code>uforget</code> command:
</p><div class="example">
<pre class="example">(%i13) setunits([centigram,inch,minute]);
(%o13) done
</pre><pre class="example">(%i14) centigram*inch/minutes^2;
%in cg
(%o14) ------
2
%min
</pre><pre class="example">(%i15) uforget([cg,%in,%min]);
(%o15) [false, false, false]
</pre><pre class="example">(%i16) centigram*inch/minutes^2;
127 kg m
(%o16) (-------------) (----)
1800000000000 2
s
</pre></div>
<p><code>uforget</code> operates on dimensions,
not units, so any unit of a particular dimension will work. The
dimension itself is also a legal argument.
</p>
<p>See also <code><a href="#setunits">setunits</a></code>. To use this function write first <code>load("unit")</code>.
</p>
</dd></dl>
<a name="convert"></a><a name="Item_003a-unit_002fdeffn_002fconvert"></a><dl>
<dt><a name="index-convert"></a>Function: <strong>convert</strong> <em>(<var>expr</var>, <var>list</var>)</em></dt>
<dd><p>When resetting the global environment is overkill, there is the <code>convert</code>
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
(<code>ratprint</code>) is true. This is also useful for spot-checking the
accuracy of a global conversion. Another feature is <code>convert</code> will allow a
user to do Base Dimension conversions even if the global environment is set to
simplify to a Derived Dimension.
</p>
<div class="example">
<pre class="example">(%i2) kg*m/s^2;
kg m
(%o2) ----
2
s
</pre><pre class="example">(%i3) convert(kg*m/s^2,[g,km,s]);
g km
(%o3) ----
2
s
</pre><pre class="example">(%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
</pre><pre class="example">(%i5) convert(kg*m/s^2,[N]);
(%o5) N
</pre><pre class="example">(%i6) convert(kg*m^2/s^2,[N]);
(%o6) m N
</pre><pre class="example">(%i7) setunits([N,J]);
(%o7) done
</pre><pre class="example">(%i8) convert(kg*m^2/s^2,[N]);
(%o8) m N
</pre><pre class="example">(%i9) convert(kg*m^2/s^2,[N,inch]);
`rat' replaced 39.37007874015748 by 5000/127 = 39.37007874015748
5000
(%o9) (----) (%in N)
127
</pre><pre class="example">(%i10) convert(kg*m^2/s^2,[J]);
(%o10) J
</pre><pre class="example">(%i11) kg*m^2/s^2;
(%o11) J
</pre><pre class="example">(%i12) setunits([g,inch,s]);
(%o12) done
</pre><pre class="example">(%i13) kg*m/s^2;
(%o13) N
</pre><pre class="example">(%i14) uforget(N);
(%o14) false
</pre><pre class="example">(%i15) kg*m/s^2;
5000000 %in g
(%o15) (-------) (-----)
127 2
s
</pre><pre class="example">(%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
</pre></div>
<p>See also <code><a href="#setunits">setunits</a></code> and <code><a href="#uforget">uforget</a></code>. To use this function write first <code>load("unit")</code>.
</p>
</dd></dl>
<a name="usersetunits"></a><a name="Item_003a-unit_002fdefvr_002fusersetunits"></a><dl>
<dt><a name="index-usersetunits"></a>Optional variable: <strong>usersetunits</strong></dt>
<dd><p>Default value: none
</p>
<p>If a user wishes to have a default unit behavior other than that described,
they can make use of <em>maxima-init.mac</em> and the <em>usersetunits</em>
variable. The <em>unit</em> 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. <code>uforget</code> will revert to the behavior
defined by usersetunits over its own defaults. For example, if we have a
<em>maxima-init.mac</em> file containing:
</p><div class="example">
<pre class="example">usersetunits : [N,J];
</pre></div>
<p>we would see the following behavior:
</p><div class="example">
<pre class="example">(%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.
</pre><pre class="example">(%i2) kg*m/s^2;
(%o2) N
</pre><pre class="example">(%i3) kg*m^2/s^2;
(%o3) J
</pre><pre class="example">(%i4) kg*m^3/s^2;
(%o4) J m
</pre><pre class="example">(%i5) kg*m*km/s^2;
(%o5) (1000) (J)
</pre><pre class="example">(%i6) setunits([dyn,eV]);
(%o6) done
</pre><pre class="example">(%i7) kg*m/s^2;
(%o7) (100000) (dyn)
</pre><pre class="example">(%i8) kg*m^2/s^2;
(%o8) (6241509596477042688) (eV)
</pre><pre class="example">(%i9) kg*m^3/s^2;
(%o9) (6241509596477042688) (eV m)
</pre><pre class="example">(%i10) kg*m*km/s^2;
(%o10) (6241509596477042688000) (eV)
</pre><pre class="example">(%i11) uforget([dyn,eV]);
(%o11) [false, false]
</pre><pre class="example">(%i12) kg*m/s^2;
(%o12) N
</pre><pre class="example">(%i13) kg*m^2/s^2;
(%o13) J
</pre><pre class="example">(%i14) kg*m^3/s^2;
(%o14) J m
</pre><pre class="example">(%i15) kg*m*km/s^2;
(%o15) (1000) (J)
</pre></div>
<p>Without <code>usersetunits</code>, 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 <code>dontusedimension</code>
command can be used. <code>uforget</code> can restore user settings again, but
only if <code>usedimension</code> frees it for use. Alternately,
<code>kill(usersetunits)</code> will completely remove all knowledge of the user defaults
from the session. Here are some examples of how these various options work.
</p><div class="example">
<pre class="example">(%i2) kg*m/s^2;
(%o2) N
</pre><pre class="example">(%i3) kg*m^2/s^2;
(%o3) J
</pre><pre class="example">(%i4) setunits([dyn,eV]);
(%o4) done
</pre><pre class="example">(%i5) kg*m/s^2;
(%o5) (100000) (dyn)
</pre><pre class="example">(%i6) kg*m^2/s^2;
(%o6) (6241509596477042688) (eV)
</pre><pre class="example">(%i7) uforget([dyn,eV]);
(%o7) [false, false]
</pre><pre class="example">(%i8) kg*m/s^2;
(%o8) N
</pre><pre class="example">(%i9) kg*m^2/s^2;
(%o9) J
</pre><pre class="example">(%i10) dontusedimension(N);
(%o10) [%force]
</pre><pre class="example">(%i11) dontusedimension(J);
(%o11) [%energy, %force]
</pre><pre class="example">(%i12) kg*m/s^2;
kg m
(%o12) ----
2
s
</pre><pre class="example">(%i13) kg*m^2/s^2;
2
kg m
(%o13) -----
2
s
</pre><pre class="example">(%i14) setunits([dyn,eV]);
(%o14) done
</pre><pre class="example">(%i15) kg*m/s^2;
kg m
(%o15) ----
2
s
</pre><pre class="example">(%i16) kg*m^2/s^2;
2
kg m
(%o16) -----
2
s
</pre><pre class="example">(%i17) uforget([dyn,eV]);
(%o17) [false, false]
</pre><pre class="example">(%i18) kg*m/s^2;
kg m
(%o18) ----
2
s
</pre><pre class="example">(%i19) kg*m^2/s^2;
2
kg m
(%o19) -----
2
s
</pre><pre class="example">(%i20) usedimension(N);
Done. To have Maxima simplify to this dimension, use
setunits([unit]) to select a unit.
(%o20) true
</pre><pre class="example">(%i21) usedimension(J);
Done. To have Maxima simplify to this dimension, use
setunits([unit]) to select a unit.
(%o21) true
</pre><pre class="example">(%i22) kg*m/s^2;
kg m
(%o22) ----
2
s
</pre><pre class="example">(%i23) kg*m^2/s^2;
2
kg m
(%o23) -----
2
s
</pre><pre class="example">(%i24) setunits([dyn,eV]);
(%o24) done
</pre><pre class="example">(%i25) kg*m/s^2;
(%o25) (100000) (dyn)
</pre><pre class="example">(%i26) kg*m^2/s^2;
(%o26) (6241509596477042688) (eV)
</pre><pre class="example">(%i27) uforget([dyn,eV]);
(%o27) [false, false]
</pre><pre class="example">(%i28) kg*m/s^2;
(%o28) N
</pre><pre class="example">(%i29) kg*m^2/s^2;
(%o29) J
</pre><pre class="example">(%i30) kill(usersetunits);
(%o30) done
</pre><pre class="example">(%i31) uforget([dyn,eV]);
(%o31) [false, false]
</pre><pre class="example">(%i32) kg*m/s^2;
kg m
(%o32) ----
2
s
</pre><pre class="example">(%i33) kg*m^2/s^2;
2
kg m
(%o33) -----
2
s
</pre></div>
<p>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.
</p>
</dd></dl>
<a name="metricexpandall"></a><a name="Item_003a-unit_002fdeffn_002fmetricexpandall"></a><dl>
<dt><a name="index-metricexpandall"></a>Function: <strong>metricexpandall</strong> <em>(<var>x</var>)</em></dt>
<dd><p>Rebuilds global unit lists automatically creating all desired metric units.
<var>x</var> 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:
</p><div class="example">
<pre class="example"> 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
</pre></div>
<p>Normally, Maxima will not define the full expansion since this results in a
very large number of units, but <code>metricexpandall</code> can be used to
rebuild the list in a more or less complete fashion. The relevant variable
in the <em>unit.mac</em> file is <var>%unitexpand</var>.
</p>
</dd></dl>
<a name="Item_003a-unit_002fdefvr_002f_0025unitexpand"></a><dl>
<dt><a name="index-_0025unitexpand"></a>Variable: <strong>%unitexpand</strong></dt>
<dd><p>Default value: <code>2</code>
</p>
<p>This is the value supplied to <code>metricexpandall</code> during the initial loading
of <em>unit</em>.
</p>
</dd></dl>
<hr>
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<p>
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