Merge pull request #148 from ThomasBreuer/TB_show_complex_conj_via_ov…

…erline

show the complex conjugate value via overline

examples/GroupCharacters.jl

@@ -30,9 +30,17 @@ show(t)                            # call `labelled_matrix_formatted`
 GAP.Globals.Display( t.GAPTable )  # compare with GAP's Display
 show(stdout, MIME("text/html"), t) # produce LaTeX output
 
-# show a legend of irrationalities instead of self-explanatory values
+# show a legend of irrationalities instead of self-explanatory values,
+# in the screen format ...
 show(IOContext(stdout, :with_legend => true), t)
 
+# ... and in LaTeX format
+show(IOContext(stdout, :with_legend => true), MIME("text/html"), t)
+
+# show the screen format for a table with real and non-real irrationalities
+show(IOContext(stdout, :with_legend => true),
+  Main.GroupCharacters.character_table("L2(11)"))
+
 # show some separating lines, in the screen format ...
 show(IOContext(stdout, :column_separators => [0,5],
                        :row_separators => [0,5]), t)
@@ -172,6 +180,8 @@ function gap_cyclotomic(elm::QabModule.QabElem)
     return GAP.Globals.CycList(GAP.julia_to_gap(coeffs))
 end
 
+complex_conjugate(elm::QabModule.QabElem) = elm^QabModule.QabAutomorphism(-1)
+
 
 #############################################################################
 ##
@@ -218,21 +228,18 @@ function character_table(G::Oscar.GAPGroup, p::Int = 0)
 end
 
 function character_table(id::String, p::Int = 0)
-    if GAP.Globals.IsBoundGlobal(GAP.julia_to_gap("CTblLib"))
-      tbl = GAP.Globals.CharacterTable(GAP.julia_to_gap(id))
+    hasproperty(GAP.Globals, :CTblLib) || error("no character table library available")
+    tbl = GAP.Globals.CharacterTable(GAP.julia_to_gap(id))
+    if tbl == GAP.Globals.fail
+      return nothing
+    elseif p != 0
+      isprime(p) || error("p must be 0 or a prime integer")
+      tbl = GAP.Globals.mod(tbl, GAP.julia_to_gap(p))
       if tbl == GAP.Globals.fail
         return nothing
-      elseif p != 0
-        isprime(p) || error("p must be 0 or a prime integer")
-        tbl = GAP.Globals.mod(tbl, GAP.julia_to_gap(p))
-        if tbl == GAP.Globals.fail
-          return nothing
-        end
       end
-      return GAPGroupCharacterTable(tbl, p)
-    else
-      error("no character table library available")
     end
+    return GAPGroupCharacterTable(tbl, p)
 end
 
 
@@ -299,6 +306,10 @@ function matrix_of_strings(tbl::GAPGroupCharacterTable; alphabet::String = "")
           else
             name, state = iterate(iter, state)
             push!(legend, val => name)
+            valbar = complex_conjugate(val)
+            if valbar != val
+              push!(legend, valbar => "\\overline{"*name*"}")
+            end
             m[i,j] = name
           end
         end
@@ -487,16 +498,19 @@ function group_class_function(tbl::GAPGroupCharacterTable, values::Vector{QabMod
     return GAPGroupClassFunction(tbl, GAP.Globals.ClassFunction(tbl.GAPTable, GAP.julia_to_gap([gap_cyclotomic(x) for x in values])))
 end
 
-#function group_class_function(G::Oscar.GAPGroup, values::Vector{QabModule.QabElem})
-#end
+function group_class_function(G::Oscar.GAPGroup, values::Vector{QabModule.QabElem})
+    return group_class_function(character_table(G), values)
+end
 
 function trivial_character(tbl::GAPGroupCharacterTable)
     val = QabModule.QabElem(1)
     return group_class_function(tbl, [val for i in 1:ncols(tbl)])
 end
 
-#function trivial_character(G::Oscar.GAPGroup)
-#end
+function trivial_character(G::Oscar.GAPGroup)
+    val = QabModule.QabElem(1)
+    return group_class_function(G, [val for i in 1:GAP.Globals.NrConjugacyClasses(G.X)])
+end
 
 Base.length(chi::GAPGroupClassFunction) = length(chi.values)
 
@@ -556,3 +570,5 @@ function Base.:^(chi::GAPGroupClassFunction, n::Int)
 end
 
 end  # module
+
+using .GroupCharacters

examples/MatrixDisplay.jl

@@ -17,13 +17,18 @@
 #T TODO:
 #T - Support left/centered/right alignment of columns and of the whole table.
 #T - Concerning irrational values in character tables:
-#T   in `matrix_of_strings`, identify also complex conjugates (mark with
-#T   overline) and unique Galois conjugates (mark with superscript *);
+#T   in `matrix_of_strings`,
+#T   identify also unique Galois conjugates (mark with superscript *);
 #T   show both values in the footer.
 #T   (For elements in quadratic fields, show also an expression in terms of
 #T   square roots.)
 
 
+# `lpad` is wrong for example for strings containing overlined characters,
+# such as "A̅".
+# (This had been observed already by Jean Michel.)
+mylpad(s::String,n::Int) = " "^(n-textwidth(s))*s
+
 # for conversions from \LaTeX format to unicode format,
 # deals with subscripts and superscripts in braces `{}`,
 # character values, character names
@@ -37,6 +42,7 @@ function replace_TeX(str::String)
   str = replace(str, "\\zeta" => "ζ")
   str = replace(str, r"\^\{[-0123456789]*\}" => (s -> map(x->sup[x], s[3:end-1])))
   str = replace(str, r"_\{[-0123456789]*\}" => (s -> map(x->sub[x], s[3:end-1])))
+  str = replace(str, r"\\overline\{(?<nam>[A-Z]*)\}" => s"\g<nam>\u0305")
   return str
 end
 
@@ -261,9 +267,9 @@ function labelled_matrix_formatted(io::IO, mat::Matrix{String})
               println(io, "\\hline")
             end
           else
-            println(io, join(map(lpad, leftpart[i,:], widths_leftpart), " "),
+            println(io, join(map(mylpad, leftpart[i,:], widths_leftpart), " "),
                         cprefix,
-                        join(join.(collect(zip(map(lpad, rightpart[i,:][crange], widths_rightpart[crange]), cpattern)))))
+                        join(join.(collect(zip(map(mylpad, rightpart[i,:][crange], widths_rightpart[crange]), cpattern)))))
             if i in row_separators
               println(io, hline)
             end