From f0650492811b7e1c57604b9d974e76a305467636 Mon Sep 17 00:00:00 2001
From: Glen Whitney <gwhitney@post.harvard.edu>
Date: Thu, 19 Oct 2017 01:12:31 +0200
Subject: [PATCH] string conversions and showing objects

---
 gap/structure.gi | 117 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 117 insertions(+)

diff --git a/gap/structure.gi b/gap/structure.gi
index b845666..c09f66a 100644
--- a/gap/structure.gi
+++ b/gap/structure.gi
@@ -247,6 +247,123 @@ InstallMethod(IsRSelfDistributive, "for magma",
               M -> IsRightSelfDistributiveTable(MultiplicationTable(M))
 );
 
+## View and print and such
+LeftObjString@ := function(Q)
+  if HasIsLeftRack(Q) and IsLeftRack(Q) then return "LeftRack"; fi;
+  return "LeftQuasigroup";
+end;
+    
+RightObjString@ := function(Q)
+  if HasIsRightRack(Q) and IsRightRack(Q) then return "RightRack"; fi;
+  return "RightQuasigroup";
+end;
+
+InstallMethod(String, "for a left quasigroup",
+              [IsLeftQuasigroup],
+              Q -> Concatenation(LeftObjString@(Q), "(...)");
+
+InstallMethod(String, "for a left quasigroup with generators",
+              [IsLeftQuasigroup and HasGeneratorsOfLeftQuasigroup],
+              Q -> Concatenation(LeftObjString@(Q), "( ", 
+                                 String(GeneratorsOfLeftQuasigroup(Q)), " )"));
+
+InstallMethod(String, "for a left quasigroup with multiplication table",
+              [IsLeftQuasigroup and HasMultiplicationTable],
+              Q -> Concatenation(LeftObjString@(Q), 
+                                 "ByMultiplicationTableNC( ",
+                                 String(MultiplicationTable(Q)), " )"));
+
+InstallMethod(String, "for a right quasigroup",
+              [IsRightQuasigroup],
+              Q -> Concatenation(RightObjString@(Q), "(...)");
+
+InstallMethod(String, "for a right quasigroup with generators",
+              [IsRightQuasigroup and HasGeneratorsOfRightQuasigroup],
+              Q -> Concatenation(RightObjString@(Q), "( ", 
+                                 String(GeneratorsOfRightQuasigroup(Q)), " )"));
+
+InstallMethod(String, "for a right quasigroup with multiplication table",
+              [IsRightQuasigroup and HasMultiplicationTable],
+              Q -> Concatenation(RightObjString@(Q), 
+                                 "ByMultiplicationTableNC( ",
+                                 String(MultiplicationTable(Q)), " )"));
+
+InstallMethod(DisplayString, "for a one-sided quasigroup",
+              [IsLeftQuasigroup or IsRightQuasigroup],
+              Q -> String(Q));
+
+InstallMethod(Display, "for a left quasigroup with multiplication table",
+  [IsLeftQuasigroup and HasMultiplicationTable],
+  function(Q)
+    Print(LeftObjString@, " with ", Size(Q), 
+          " elements, generated by ", 
+          GeneratorsOfLeftQuasigroup(Q), ", with table\n");
+    Display(MultiplicationTable(Q));
+end);
+
+InstallMethod(Display, "for a right quasigroup with multiplication table",
+  [IsRightQuasigroup and HasMultiplicationTable],
+  function(Q)
+    Print(RightObjString@, " with ", Size(Q), 
+          " elements, generated by ", 
+          GeneratorsOfRightQuasigroup(Q), ", with table\n");
+    Display(MultiplicationTable(Q));
+end);
+
+LeftObjView@ := function(Q)
+  if HasIsLeftRack(Q) and IsLeftRack(Q) then return "<left rack"; fi;
+  return "<left quasigroup";
+end;
+    
+RightObjView@ := function(Q)
+  if HasIsRightRack(Q) and IsRightRack(Q) then return "<right rack"; fi;
+  return "<right quasigroup";
+end;
+
+InstallMethod(ViewString, "for a left quasigroup",
+              [IsLeftQuasigroup], 
+              Q -> Concatenation(LeftObjView@(Q), ">");
+
+InstallMethod(ViewString, "for a left quasigroup with generators",
+              [IsLeftQuasigroup and HasGeneratorsOfLeftQuasigroup], 
+              Q -> Concatenation(LeftObjView@(Q), " with ",
+                                 Size(GeneratorsOfLeftQuasigroup), 
+                                 " generators>"));
+
+InstallMethod(ViewString, "for a right quasigroup",
+              [IsRightQuasigroup], 
+              Q -> Concatenation(RightObjView@(Q), ">");
+
+InstallMethod(ViewString, "for a right quasigroup with generators",
+              [IsRightQuasigroup and HasGeneratorsOfRightQuasigroup], 
+              Q -> Concatenation(RightObjView@(Q), " with ",
+                                 Size(GeneratorsOfRightQuasigroup), 
+                                 " generators>"));
+
+# Patch View/Print/Display for magma by mult objects
+InstallMethod(String, "for an element of magma by multiplication table",
+  [IsMagmaByMultiplicationTableObj],
+  function(obj)
+    local fam;
+    fam := FamilyObj(obj);
+    if IsBound(fam!.elmNamePrefix) then 
+      return Concatenation(fam!.elmNamePrefix, String(obj![1]));
+    fi;
+    return Concatenation("m", String(obj![1]));
+end);
+
+InstallMethod(ViewString, "for an element of magma by multiplication table",
+              [IsMagmaByMultiplicationTableObj],
+              obj -> String(obj));
+
+InstallMethod(DisplayString, "for an element of magma by multiplication table",
+              [IsMagmaByMultiplicationTableObj],
+              obj -> String(obj));
+
+InstallMethod(PrintObj, "for an element of magma by multiplication table",
+              [IsMagmaByMultiplicationTableObj],
+              function(obj) Print(String(obj)); end);
+             
 ## Special case the Opposite function from LOOPS package, since the opposite
 ## of a left quasigroup is a right quasigroup and vice versa