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<html><head><title>[CTblLib] 4 Interfaces to Other Data Formats for Character Tables</title></head>
<body text="#000000" bgcolor="#ffffff">
[<a href = "chapters.htm">Up</a>] [<a href ="CHAP003.htm">Previous</a>] [<a href = "theindex.htm">Index</a>]
<h1>4 Interfaces to Other Data Formats for Character Tables</h1><p>
<P>
<H3>Sections</H3>
<oL>
<li> <A HREF="CHAP004.htm#SECT001">Interface to the CAS System</a>
<li> <A HREF="CHAP004.htm#SECT002">Interface to the MOC System</a>
<li> <A HREF="CHAP004.htm#SECT003">Interface to GAP 3</a>
</ol><p>
<p>
This chapter describes data formats for character tables that can be read
or created by <font face="Gill Sans,Helvetica,Arial">GAP</font>.
Currently these are the formats used by
the <font face="Gill Sans,Helvetica,Arial">CAS</font> system (see <a href="CHAP004.htm#SECT001">Interface to the CAS System</a>),
the <font face="Gill Sans,Helvetica,Arial">MOC</font> system (see <a href="CHAP004.htm#SECT002">Interface to the MOC System</a>),
and <font face="Gill Sans,Helvetica,Arial">GAP</font> 3 (see <a href="CHAP004.htm#SECT003">Interface to GAP 3</a>).
<p>
<p>
<h2><a name="SECT001">4.1 Interface to the CAS System</a></h2>
<p><p>
The interface to <font face="Gill Sans,Helvetica,Arial">CAS</font> is thought just for printing the <font face="Gill Sans,Helvetica,Arial">CAS</font>
data to a file.
The function <code>CASString</code> is available mainly in order to document the
data format.
<strong>Reading</strong> <font face="Gill Sans,Helvetica,Arial">CAS</font> tables is not supported; note that the tables
contained in the <font face="Gill Sans,Helvetica,Arial">CAS</font> Character Table Library have been migrated to
<font face="Gill Sans,Helvetica,Arial">GAP</font> using a few <code>sed</code> scripts and <code>C</code> programs.
<p>
<a name = "SSEC001.1"></a>
<li><code>CASString( </code><var>tbl</var><code> ) F</code>
<p>
is a string that encodes the <font face="Gill Sans,Helvetica,Arial">CAS</font> library format of the character
table <var>tbl</var>.
This string can be printed to a file which then can be read into the
<font face="Gill Sans,Helvetica,Arial">CAS</font> system using its <code>get</code> command (see <a href="biblio.htm#NPP84"><cite>NPP84</cite></a>).
<p>
The used line length is <code>SizeScreen()[1]</code>
(see <a href="../../../doc/htm/ref/CHAP006.htm#SSEC011.1">SizeScreen</a> in the <font face="Gill Sans,Helvetica,Arial">GAP</font> Reference Manual).
<p>
Only the known values of the following attributes are used.
<code>ClassParameters</code> (for partitions only), <code>ComputedClassFusions</code>,
<code>ComputedPowerMaps</code>, <code>Identifier</code>, <code>InfoText</code>, <code>Irr</code>,
<code>ComputedPrimeBlocks</code>, <code>ComputedIndicators</code>,
<code>OrdersClassRepresentatives</code>, <code>Size</code>, <code>SizesCentralizers</code>.
<p>
<a name = "I0"></a>
<a name = "I0"></a>
<a name = "I1"></a>
<a name = "I2"></a>
<pre>
gap> Print( CASString( CharacterTable( "Cyclic", 2 ) ), "\n" );
'C2'
00/00/00. 00.00.00.
(2,2,0,2,-1,0)
text:
(#computed using generic character table for cyclic groups#),
order=2,
centralizers:(
2,2
),
reps:(
1,2
),
powermap:2(
1,1
),
characters:
(1,1
,0:0)
(1,-1
,0:0);
/// converted from GAP
</pre>
<p>
<p>
<h2><a name="SECT002">4.2 Interface to the MOC System</a></h2>
<p><p>
The interface to <font face="Gill Sans,Helvetica,Arial">MOC</font> can be used to print <font face="Gill Sans,Helvetica,Arial">MOC</font> input.
Additionally it provides an alternative representation of (virtual)
characters.
<p>
The <font face="Gill Sans,Helvetica,Arial">MOC</font> 3 code of a 5 digit number in <font face="Gill Sans,Helvetica,Arial">MOC</font> 2 code is given by the
following list.
(Note that the code must contain only lower case letters.)
<p>
<pre>
ABCD for 0ABCD
a for 10000
b for 10001 k for 20001
c for 10002 l for 20002
d for 10003 m for 20003
e for 10004 n for 20004
f for 10005 o for 20005
g for 10006 p for 20006
h for 10007 q for 20007
i for 10008 r for 20008
j for 10009 s for 20009
tAB for 100AB
uAB for 200AB
vABCD for 1ABCD
wABCD for 2ABCD
yABC for 30ABC
z for 31000
</pre>
<p>
<strong>Note</strong> that any long number in <font face="Gill Sans,Helvetica,Arial">MOC</font> 2 format is divided into packages
of length 4, the first (!) one filled with leading zeros if necessary.
Such a number with decimals <i>d</i><sub>1</sub>, <i>d</i><sub>2</sub>, <font face="symbol"></font>, <i>d</i><sub>4<i>n</i>+<i>k</i></sub> is the sequence
<br clear="all" /><table border="0" width="100%"><tr><td><table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> 0<i>d</i><sub>1</sub><i>d</i><sub>2</sub><i>d</i><sub>3</sub><i>d</i><sub>4</sub> <font face="symbol"></font>0<i>d</i><sub>4<i>n</i><font face="symbol">-</font>3</sub><i>d</i><sub>4<i>n</i><font face="symbol">-</font>2</sub><i>d</i><sub>4<i>n</i><font face="symbol">-</font>1</sub><i>d</i><sub>4<i>n</i></sub> <i>xd</i><sub>4<i>n</i>+1</sub><font face="symbol"></font><i>d</i><sub>4<i>n</i>+<i>k</i></sub> </td></tr></table></td></tr></table>
where 0 <font face="symbol"></font> <i>k</i> <font face="symbol"></font> 3,
the first digit of <i>x</i> is 1 if the number is positive and 2 if the
number is negative,
and then follow (4<font face="symbol">-</font><i>k</i>) zeros.
<p>
<a href="biblio.htm#HJLP92"><cite>HJLP92</cite></a> explains details about the <font face="Gill Sans,Helvetica,Arial">MOC</font> system,
a brief description can be found in <a href="biblio.htm#LP91"><cite>LP91</cite></a>.
<p>
<a name = "SSEC002.1"></a>
<li><code>MAKElb11( </code><var>listofns</var><code> ) F</code>
<p>
<code>MAKElb11</code> prints field information for all number fields with conductor
<i>n</i> where the positive integer <i>n</i> is in the list <var>listofns</var>.
<p>
The output of <code>MAKElb11</code> is used by the <font face="Gill Sans,Helvetica,Arial">MOC</font> system.
<code>MAKElb11( [ 3 .. 189 ] )</code> will print something very similar to
Richard Parker's file <code>lb11</code>.
<p>
<pre>
gap> MAKElb11( [ 3, 4 ] );
3 2 0 1 0
4 2 0 1 0
</pre>
<p>
<a name = "SSEC002.2"></a>
<li><code>MOCTable( </code><var>gaptbl</var><code> ) F</code>
<li><code>MOCTable( </code><var>gaptbl</var><code>, </code><var>basicset</var><code> ) F</code>
<p>
<code>MOCTable</code> returns the <font face="Gill Sans,Helvetica,Arial">MOC</font> table record of the <font face="Gill Sans,Helvetica,Arial">GAP</font> character table
<var>gaptbl</var>.
<p>
The first form can be used only if <var>gaptbl</var> is an ordinary (<i>G</i>.0) table.
For Brauer (<i>G</i>.<i>p</i>) tables one has to specify a basic set <var>basicset</var> of
ordinary irreducibles.
<var>basicset</var> must be a list of positions of the basic set characters in the
<code>Irr</code> list of the ordinary table of <var>gaptbl</var>.
<p>
The result is a record that contains the information of <var>gaptbl</var>
in a format similar to the <font face="Gill Sans,Helvetica,Arial">MOC</font> 3 format.
This record can, e.g., easily be printed out or be used to print out
characters using <code>MOCString</code> (see <a href="CHAP004.htm#SSEC002.3">MOCString</a>).
<p>
The components of the result are
<p>
<dl compact>
<dt><code>identifier</code> <dd>
the string <code>MOCTable(</code><var>name</var><code>)</code> where <var>name</var> is the <code>Identifier</code>
value of <var>gaptbl</var>,
<p>
<dt><code>GAPtbl</code> <dd>
<var>gaptbl</var>,
<p>
<dt><code>prime</code> <dd>
the characteristic of the field (label <code>30105</code> in <font face="Gill Sans,Helvetica,Arial">MOC</font>),
<p>
<dt><code>centralizers</code> <dd>
centralizer orders for cyclic subgroups (label <code>30130</code>)
<p>
<dt><code>orders</code> <dd>
element orders for cyclic subgroups (label <code>30140</code>)
<p>
<dt><code>fieldbases</code> <dd>
at position <i>i</i> the Parker basis of the number field generated
by the character values of the <i>i</i>-th cyclic subgroup.
The length of <code>fieldbases</code> is equal to the value of label <code>30110</code>
in <font face="Gill Sans,Helvetica,Arial">MOC</font>.
<p>
<dt><code>cycsubgps</code> <dd>
<code>cycsubgps[i] = j</code> means that class <code>i</code> of the <font face="Gill Sans,Helvetica,Arial">GAP</font> table
belongs to the <code>j</code>-th cyclic subgroup of the <font face="Gill Sans,Helvetica,Arial">GAP</font> table,
<p>
<dt><code>repcycsub</code> <dd>
<code>repcycsub[j] = i</code> means that class <code>i</code> of the <font face="Gill Sans,Helvetica,Arial">GAP</font> table
is the representative of the <code>j</code>-th cyclic subgroup of the
<font face="Gill Sans,Helvetica,Arial">GAP</font> table.
<strong>Note</strong> that the representatives of <font face="Gill Sans,Helvetica,Arial">GAP</font> table and <font face="Gill Sans,Helvetica,Arial">MOC</font> table
need not agree!
<p>
<dt><code>galconjinfo</code> <dd>
a list [ <i>r</i><sub>1</sub>, <i>c</i><sub>1</sub>, <i>r</i><sub>2</sub>, <i>c</i><sub>2</sub>, <font face="symbol"></font>, <i>r</i><sub><i>n</i></sub>, <i>c</i><sub><i>n</i></sub> ]
which means that the <i>i</i>-th class of the <font face="Gill Sans,Helvetica,Arial">GAP</font> table is
the <i>c</i><sub><i>i</i></sub>-th conjugate of the representative of
the <i>r</i><sub><i>i</i></sub>-th cyclic subgroup on the <font face="Gill Sans,Helvetica,Arial">MOC</font> table.
(This is used to translate back to <font face="Gill Sans,Helvetica,Arial">GAP</font> format,
stored under label <code>30160</code>)
<p>
<dt><code>30170</code> <dd>
(power maps) for each cyclic subgroup (except the trivial one)
and each prime divisor of the representative order store four values,
namely the number of the subgroup, the power,
the number of the cyclic subgroup containing the image,
and the power to which the representative must be raised to yield
the image class.
(This is used only to construct the <code>30230</code> power map/embedding
information.)
In <code>30170</code> only a list of lists (one for each cyclic subgroup)
of all these values is stored, it will not be used by <font face="Gill Sans,Helvetica,Arial">GAP</font>.
<p>
<dt><code>tensinfo</code> <dd>
tensor product information, used to compute the coefficients
of the Parker base for tensor products of characters
(label <code>30210</code> in <font face="Gill Sans,Helvetica,Arial">MOC</font>).
For a field with vector space basis (<i>v</i><sub>1</sub>,<i>v</i><sub>2</sub>,<font face="symbol"></font>,<i>v</i><sub><i>n</i></sub>)
the tensor product information of a cyclic subgroup in <font face="Gill Sans,Helvetica,Arial">MOC</font>
(as computed by <code>fct</code>) is either 1 (for rational classes)
or a sequence
<br clear="all" /><table border="0" width="100%"><tr><td><table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> <i>n</i> <i>x</i><sub>1,1</sub> <i>y</i><sub>1,1</sub> <i>z</i><sub>1,1</sub> <i>x</i><sub>1,2</sub> <i>y</i><sub>1,2</sub> <i>z</i><sub>1,2</sub> <font face="symbol"></font><i>x</i><sub>1,<i>m</i><sub>1</sub></sub> <i>y</i><sub>1,<i>m</i><sub>1</sub></sub> <i>z</i><sub>1,<i>m</i><sub>1</sub></sub> 0 <i>x</i><sub>2,1</sub> <i>y</i><sub>2,1</sub> <i>z</i><sub>2,1</sub> <i>x</i><sub>2,2</sub> <i>y</i><sub>2,2</sub> <i>z</i><sub>2,2</sub> <font face="symbol"></font><i>x</i><sub>2,<i>m</i><sub>2</sub></sub> <i>y</i><sub>2,<i>m</i><sub>2</sub></sub> <i>z</i><sub>2,<i>m</i><sub>2</sub></sub> 0 <font face="symbol"></font><i>z</i><sub><i>n</i>,<i>m</i><sub><i>n</i></sub></sub> 0 </td></tr></table></td></tr></table>
which means that the coefficient of <i>v</i><sub><i>k</i></sub> in the product
<br clear="all" /><table border="0" width="100%"><tr><td><table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> </td><td align="left" class="cl"><font face="symbol"><br /></font> </td><td nowrap="nowrap" align="center"><small><i>n</i></small><!--sup--><br /><font size="+3"><font face="symbol"><br /></font></font><small><i>i</i>=1</small> <br /></td><td nowrap="nowrap" align="center"><i>a</i><sub><i>i</i></sub> <i>v</i><sub><i>i</i></sub> </td><td align="left" class="cl"><font face="symbol"><br /></font></td><td nowrap="nowrap" align="center"></td><td align="left" class="cl"><font face="symbol"><br /></font> </td><td nowrap="nowrap" align="center"><small><i>n</i></small><!--sup--><br /><font size="+3"><font face="symbol"><br /></font></font><small><i>j</i>=1</small> <br /></td><td nowrap="nowrap" align="center"><i>b</i><sub><i>j</i></sub> <i>v</i><sub><i>j</i></sub> </td><td align="left" class="cl"><font face="symbol"><br /></font></td><td nowrap="nowrap" align="center"></td></tr></table></td></tr></table>
is equal to
<br clear="all" /><table border="0" width="100%"><tr><td><table align="center" cellspacing="0" cellpadding="2"><tr><td nowrap="nowrap" align="center"> </td><td nowrap="nowrap" align="center"><small><i>m</i><sub><i>k</i></sub></small><!--sup--><br /><font size="+3"><font face="symbol"><br /></font></font><small><i>i</i>=1</small> <br /></td><td nowrap="nowrap" align="center"><i>x</i><sub><i>k</i>,<i>i</i></sub> <i>a</i><sub><i>y</i><sub><i>k</i>,<i>i</i></sub></sub> <i>b</i><sub><i>z</i><sub><i>k</i>,<i>i</i></sub></sub>. </td></tr></table></td></tr></table>
On a <font face="Gill Sans,Helvetica,Arial">MOC</font> table in <font face="Gill Sans,Helvetica,Arial">GAP</font> the <code>tensinfo</code> component is
a list of lists, each containing exactly the sequence mentioned
above.
<p>
<dt><code>invmap</code> <dd>
inverse map to compute complex conjugate characters,
label <code>30220</code> in <font face="Gill Sans,Helvetica,Arial">MOC</font>.
<p>
<dt><code>powerinfo</code> <dd>
field embeddings for <i>p</i>-th symmetrizations,
<i>p</i> a prime integer not larger than the largest element order,
label <code>30230</code> in <font face="Gill Sans,Helvetica,Arial">MOC</font>.
<p>
<dt><code>30900</code> <dd>
basic set of restricted ordinary irreducibles in the
case of nonzero characteristic,
all ordinary irreducibles otherwise.
</dl>
<p>
<a name = "SSEC002.3"></a>
<li><code>MOCString( </code><var>moctbl</var><code> ) F</code>
<li><code>MOCString( </code><var>moctbl</var><code>, </code><var>chars</var><code> ) F</code>
<p>
Let <var>moctbl</var> be a <font face="Gill Sans,Helvetica,Arial">MOC</font> table record as returned by <code>MOCTable</code>
(see <a href="CHAP004.htm#SSEC002.2">MOCTable</a>).
<code>MOCString</code> returns a string describing the <font face="Gill Sans,Helvetica,Arial">MOC</font> 3 format of <var>moctbl</var>.
<p>
If the second argument <var>chars</var> is specified, it must be a list of <font face="Gill Sans,Helvetica,Arial">MOC</font>
format characters as returned by <code>MOCChars</code> (see <a href="CHAP004.htm#SSEC002.6">MOCChars</a>).
In this case, these characters are stored under label <code>30900</code>.
If the second argument is missing then the basic set of ordinary
irreducibles is stored under this label.
<p>
<pre>
gap> moca5:= MOCTable( CharacterTable( "A5" ) );
rec( identifier := "MOCTable(A5)", prime := 0, fields := [ ],
GAPtbl := CharacterTable( "A5" ), cycsubgps := [ 1, 2, 3, 4, 4 ],
repcycsub := [ 1, 2, 3, 4 ], galconjinfo := [ 1, 1, 2, 1, 3, 1, 4, 1, 4, 2 ]
, centralizers := [ 60, 4, 3, 5 ], orders := [ 1, 2, 3, 5 ],
fieldbases := [ CanonicalBasis( Rationals ), CanonicalBasis( Rationals ),
CanonicalBasis( Rationals ),
Basis( NF(5,[ 1, 4 ]), [ 1, E(5)+E(5)^4 ] ) ],
30170 := [ [ ], [ 2, 2, 1, 1 ], [ 3, 3, 1, 1 ], [ 4, 5, 1, 1 ] ],
tensinfo :=
[ [ 1 ], [ 1 ], [ 1 ], [ 2, 1, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 1, -1, 2,
2, 0 ] ],
invmap := [ [ 1, 1, 0 ], [ 1, 2, 0 ], [ 1, 3, 0 ], [ 1, 4, 0, 1, 5, 0 ] ],
powerinfo :=
[ , [ [ 1, 1, 0 ], [ 1, 1, 0 ], [ 1, 3, 0 ], [ 1, 4, -1, 5, 0, -1, 5, 0 ]
],
[ [ 1, 1, 0 ], [ 1, 2, 0 ], [ 1, 1, 0 ], [ 1, 4, -1, 5, 0, -1, 5, 0 ] ],
, [ [ 1, 1, 0 ], [ 1, 2, 0 ], [ 1, 3, 0 ], [ 1, 1, 0, 0 ] ] ],
30900 := [ [ 1, 1, 1, 1, 0 ], [ 3, -1, 0, 0, -1 ], [ 3, -1, 0, 1, 1 ],
[ 4, 0, 1, -1, 0 ], [ 5, 1, -1, 0, 0 ] ] )
gap> str:= MOCString( moca5 );;
gap> str{[1..70]};
"y100y105ay110fey130t60edfy140bcdfy150bbbfcabbey160bbcbdbebecy170ccbbdd"
gap> moca5mod3:= MOCTable( CharacterTable( "A5" ) mod 3, [ 1 .. 4 ] );;
gap> MOCString( moca5mod3 ){ [ 1 .. 70 ] };
"y100y105dy110edy130t60efy140bcfy150bbfcabbey160bbcbdbdcy170ccbbdfbby21"
</pre>
<p>
<a name = "SSEC002.4"></a>
<li><code>ScanMOC( </code><var>list</var><code> ) F</code>
<p>
returns a record containing the information encoded in the list <var>list</var>.
The components of the result are the labels that occur in <var>list</var>.
If <var>list</var> is in <font face="Gill Sans,Helvetica,Arial">MOC</font> 2 format (10000-format),
the names of components are 30000-numbers;
if it is in <font face="Gill Sans,Helvetica,Arial">MOC</font> 3 format the names of components have <code>yABC</code>-format.
<p>
<a name = "SSEC002.5"></a>
<li><code>GAPChars( </code><var>tbl</var><code>, </code><var>mocchars</var><code> ) F</code>
<p>
Let <var>tbl</var> be a character table or a <font face="Gill Sans,Helvetica,Arial">MOC</font> table record,
and <var>mocchars</var> either a list of <font face="Gill Sans,Helvetica,Arial">MOC</font> format characters
(as returned by <code>MOCChars</code> (see <a href="CHAP004.htm#SSEC002.6">MOCChars</a>)
or a list of positive integers such as a record component encoding
characters, in a record produced by <code>ScanMOC</code> (see <a href="CHAP004.htm#SSEC002.4">ScanMOC</a>).
<p>
<code>GAPChars</code> returns translations of <var>mocchars</var> to <font face="Gill Sans,Helvetica,Arial">GAP</font> character values
lists.
<p>
<a name = "SSEC002.6"></a>
<li><code>MOCChars( </code><var>tbl</var><code>, </code><var>gapchars</var><code> ) F</code>
<p>
Let <var>tbl</var> be a character table or a <font face="Gill Sans,Helvetica,Arial">MOC</font> table record,
and <var>gapchars</var> a list of (<font face="Gill Sans,Helvetica,Arial">GAP</font> format) characters.
<code>MOCChars</code> returns translations of <var>gapchars</var> to <font face="Gill Sans,Helvetica,Arial">MOC</font> format.
<p>
<pre>
gap> scan:= ScanMOC( str );
rec( y105 := [ 0 ], y110 := [ 5, 4 ], y130 := [ 60, 4, 3, 5 ],
y140 := [ 1, 2, 3, 5 ], y150 := [ 1, 1, 1, 5, 2, 0, 1, 1, 4 ],
y160 := [ 1, 1, 2, 1, 3, 1, 4, 1, 4, 2 ],
y170 := [ 2, 2, 1, 1, 3, 3, 1, 1, 4, 5, 1, 1 ],
y210 := [ 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 1, -1, 2, 2, 0 ],
y220 := [ 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 4, 0, 1, 5, 0 ],
y230 := [ 2, 1, 1, 0, 1, 1, 0, 1, 3, 0, 1, 4, -1, 5, 0, -1, 5, 0 ],
y050 := [ 5, 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 1, 0, 0 ],
y900 := [ 1, 1, 1, 1, 0, 3, -1, 0, 0, -1, 3, -1, 0, 1, 1, 4, 0, 1, -1, 0,
5, 1, -1, 0, 0 ] )
gap> gapchars:= GAPChars( moca5, scan.y900 );
[ [ 1, 1, 1, 1, 1 ], [ 3, -1, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ],
[ 3, -1, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ], [ 4, 0, 1, -1, -1 ],
[ 5, 1, -1, 0, 0 ] ]
gap> mocchars:= MOCChars( moca5, gapchars );
[ [ 1, 1, 1, 1, 0 ], [ 3, -1, 0, 0, -1 ], [ 3, -1, 0, 1, 1 ],
[ 4, 0, 1, -1, 0 ], [ 5, 1, -1, 0, 0 ] ]
gap> Concatenation( mocchars ) = scan.y900;
true
</pre>
<p>
<p>
<h2><a name="SECT003">4.3 Interface to GAP 3</a></h2>
<p><p>
The following functions are used to read and write character tables in
<font face="Gill Sans,Helvetica,Arial">GAP</font> 3 format.
<p>
<a name = "SSEC003.1"></a>
<li><code>GAP3CharacterTableScan( </code><var>string</var><code> ) F</code>
<p>
Let <var>string</var> be a string that contains the output of the <font face="Gill Sans,Helvetica,Arial">GAP</font> 3
function <code>PrintCharTable</code>.
In other words, <var>string</var> describes a <font face="Gill Sans,Helvetica,Arial">GAP</font> record whose components
define an ordinary character table object in <font face="Gill Sans,Helvetica,Arial">GAP</font> 3.
<code>GAP3CharacterTableScan</code> returns the corresponding <font face="Gill Sans,Helvetica,Arial">GAP</font> 4
character table object.
<p>
The supported record components are given by the list
<code>GAP3CharacterTableData</code>.
<p>
<a name = "SSEC003.2"></a>
<li><code>GAP3CharacterTableString( </code><var>tbl</var><code> ) F</code>
<p>
For an ordinary character table <var>tbl</var>, <code>GAP3CharacterTableString</code> returns
a string that when read into <font face="Gill Sans,Helvetica,Arial">GAP</font> 3 evaluates to a character table
corresponding to <var>tbl</var>.
A similar format is printed by the <font face="Gill Sans,Helvetica,Arial">GAP</font> 3 function <code>PrintCharTable</code>.
<p>
The supported record components are given by the list
<code>GAP3CharacterTableData</code>.
<p>
<pre>
gap> tbl:= CharacterTable( "Alternating", 5 );;
gap> str:= GAP3CharacterTableString( tbl );;
gap> Print( str );
rec(
centralizers := [ 60, 4, 3, 5, 5 ],
fusions := [ rec( name := "Sym(5)", map := [ 1, 3, 4, 7, 7 ] ) ],
identifier := "Alt(5)",
irreducibles := [
[ 1, 1, 1, 1, 1 ],
[ 4, 0, 1, -1, -1 ],
[ 5, 1, -1, 0, 0 ],
[ 3, -1, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ],
[ 3, -1, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ]
],
orders := [ 1, 2, 3, 5, 5 ],
powermap := [ , [ 1, 1, 3, 5, 4 ], [ 1, 2, 1, 5, 4 ], , [ 1, 2, 3, 1, 1 ] ],
size := 60,
text := "computed using generic character table for alternating groups",
operations := CharTableOps )
gap> scan:= GAP3CharacterTableScan( str );
CharacterTable( "Alt(5)" )
gap> TransformingPermutationsCharacterTables( tbl, scan );
rec( columns := (), rows := (), group := Group([ (4,5) ]) )
</pre>
<p>
<a name = "SSEC003.3"></a>
<li><code>GAP3CharacterTableData V</code>
<p>
This is a list of pairs, the first entry being the name of a component in
a <font face="Gill Sans,Helvetica,Arial">GAP</font> 3 character table and the second entry being the corresponding
attribute name in <font face="Gill Sans,Helvetica,Arial">GAP</font> 4.
The variable is used by <code>GAP3CharacterTableScan</code>
(see <a href="CHAP004.htm#SSEC003.1">GAP3CharacterTableScan</a>) and <code>GAP3CharacterTableString</code>
(see <a href="CHAP004.htm#SSEC003.2">GAP3CharacterTableString</a>).
<p>
<p>
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<P>
<address>CTblLib manual<br>March 2004
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