DisplayCharTable( tbl )
DisplayCharTable( tbl, arec )
DisplayCharTable prepares the data contained in the character table
tbl for a pretty columnwise output.
In the first form
DisplayCharTable prints all irreducible characters
of the table tbl, together with the orders of the centralizers in
factorized form and the available powermaps.
Thus it can be used to echo character tables in interactive use, being
the value of the record field
of tbl (see Character Table Records,
Operations Records for Character Tables).
Each displayed character is given a name
The number of columns printed at one time depends on the actual
linelength, which is restored by the function
The first lines of the output describe the order of the centralizer of an element of the class factorized into its prime divisor.
The next line gives the name of the class. If the record field
classnames of the table tbl is not bound,
calls the function
ClassNamesCharTable to determine the class names
and to store them on the table tbl (see ClassNamesCharTable).
Preceded by a name
Pn the next lines show the nth powermaps
of tbl in terms of the former shown class names.
Every ambiguous or unknown (see Unknown) value of the table is
displayed as a question mark
Irrational character values are not printed explicitly because the lengths of their printed representation might disturb the view. Instead of that every irrational value is indicated by a name, which is a string of a least one capital letter.
Once a name for an irrational number is found, it is used all over the
printed table. Moreover the complex conjugate and the star of an
irrationality are represented by that very name preceded by a
The printed character table is then followed by a legend, a list identifying the occurred symbols with their actual irrational value. Occasionally this identity is supplemented by a quadratic representation of the irrationality together with the corresponding ATLAS--notation.
gap> a5:= CharTable("A5");; gap> DisplayCharTable(a5); A5
2 2 2 . . . 3 1 . 1 . . 5 1 . . 1 1
1a 2a 3a 5a 5b 2P 1a 1a 3a 5b 5a 3P 1a 2a 1a 5b 5a 5P 1a 2a 3a 1a 1a
X.1 1 1 1 1 1 X.2 3 -1 . A *A X.3 3 -1 . *A A X.4 4 . 1 -1 -1 X.5 5 1 -1 . .
A = -E(5)-E(5)^4 = (1-ER(5))/2 = -b5
In the second form
DisplayCharTable takes an argument record arec as
an additional argument. This record can be used to change the default
style for displaying a character as shown above. Its relevant fields
"X"is replaced by
falseto suppress the powermaps,
"P"for permutation characters) to replace
trueenables the printing of the second Schur indicator, a list of integers enables the printing of the corresponding indicators.
gap> arec:= rec( chars:= 4, classes:= [a5.3a..a5.5a], > centralizers:= false, indicator:= true, powermap:=  );; gap> Indicator( a5, 2 );; gap> DisplayCharTable( a5, arec ); A5
3a 5a 2P 3a 5b 2 X.4 + 1 -1
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