 AL Lesser values for elbnumbers
 
  	AL manually updates two values for lower
  	bounds for e, from "Theoretical and
	computational aspects of Ramsey Theory".
   	Other values which may be influenced
 	are not updated, use UPDATEE.


 DISPE display an e number structure
 
 	DISPE(X,Y,N) displays the entry
 	in position (X,Y,N) in the global 
 	variable ETABLE


 DISPR display a Ramsey number structure
 
 	DISPR(X,Y) displays the entry
 	in position (X,Y) in the global 
 	variable RTABLE


 EELBTABLE Lower bounds for E numbers
 
  	T=EELBTABLE(X) extracts a y-by-n table 
 	of lower bounds for E numbers E(X,y,n)
 	from the global variable ETABLE


 EEUBTABLE Upper bounds for E numbers
 
  	T=EEUBTABLE(X) extracts a y-by-n table 
 	of upper bounds for E numbers E(X,y,n)
 	from the global variable ETABLE


 EEXETABLE Exact values of E numbers
 
  	T=EEXETABLE(X) extracts a y-by-n table 
 	of exact values for E numbers E(X,y,n)
 	from the global variable ETABLE


 ELBTABLE Lower bounds for e numbers
 
  	T=ELBTABLE(X) extracts a y-by-n table 
 	of lower bounds for e numbers e(X,y,n)
 	from the global variable ETABLE


 ENUMBERTABLE create global variable RTABLE
 
 	ENUMBERTABLE(xmax,ymax,nmax) creates
 	the global variable ETABLE: 
 	an xmax-by-ymax-by-nmax matrix of structures
 	of e-numbers and E-numbers for two-color 
 	classical Ramsey numbers. 
 	The structrures have twelve fields:
  	et.x, et.y and et.n are the parameters e(x,y,n). 
 	et.elb is the largest known lower bound for e. 
 	et.eub is the upper bound for e.
 	et.Elb and et.Eub are lower and upper bounds for E.
 	et.exact is true if elb=eub.
 	et.Exact is true if Elb=Eub.
 	et.info is a text string 
 	with information on how the values
  	were calculated.
 	et.graph is a graph object
 	et.minmaxval is a vector containing the minimum 
 	and maximum possible valences for a realiser.


 EUBTABLE Upper bounds for e numbers
 
  	T=EUBTABLE(X) extracts a y-by-n table 
 	of upper bounds for e numbers e(X,y,n)
 	from the global variable ETABLE


 EXETABLE Exact table of e numbers
 
  	T=EXETABLE(X) extracts a y-by-n table 
 	of exact values for e numbers e(X,y,n)
 	from the global variable ETABLE


 EXRTABLE Exact table of ramsey numbers
	
	T=EXRTABLE creates a table of exact bounds 
	for traditional two-color Ramsey numbers 
	R(x,y) from the global variable RTABLE


 GR Grinstead-Roberts values for e-numbers
 
  	GR manually updates values for lower
  	bounds for e, Grinstead-Roberts' 1988
  	paper. Other values which may be influenced
 	are not updated, use UPDATEE.


 GY Graver-Yackel values for elbnumbers
 
  	GY manually updates values for lower
  	bounds for e, from Graver-Yackel's 1968
  	paper. Other values which may be influenced
 	are not updated, use UPDATEE.


 JB Backelin values for elbnumbers
 
  	JB manually updates values for lower
  	bounds for e, from Backelin's 2000
  	manuscript. Other values which may be 
	influenced are not updated, use UPDATEE.


 LORTABLE Lower table of Ramsey numbers
 
  	T=LORTABLE extracts a table of lower 
 	bounds for Ramsey numbers R(x,y)
 	from the global variable RTABLE


 MANUALELB manually update a value of elb
 
  	MANUALELB(X,Y,N,ELB,INFO) sets 
  	ETABLE(X,Y,N).elb to ELB and adds 
 	the string INFO to ETABLE(X,Y,N).info  


 MANUALR manually change a value in the ramsey table RTABLE
 
 	MANUALR(X,Y,N) changes the value of 
 	R(X,Y) (AND R(Y,X)!) to be exactly N
  	MANUALR(X,Y,LB,UB) changes the lower
 	and upper bounds to LB and UB.
  	The exact field and the info-fields are updated.


 RAMEYTABLE create global variable RTABLE
 
 	RAMSEYTABLE(xmax,ymax) creates
 	the global variable RTABLE: 
 	an xmax-by-ymax matrix of structures
 	of two-color classical Ramsey numbers. 
 	The structrures have seven fields:
  	rt.x and rt.y are the parameters R(x,y), 
 	rt.lb is the largest known lower bound, 
 	rt.ub is the upper bound, and rt.exact is true if 
  	lb=ub. rt.ubinfo and rt.lbinfo are text strings 
 	with information on how the values
  	were calculated.


 RK Radziszowski-Kreher values for elbnumbers
 
  	RK manually updates values for lower
  	bounds for e, from Radziszowski and
   	Kreher's 1988 paper. Other values which 
   	may be influenced are not updated, use UPDATEE.


 THEOREM7 exact values for enumbers

  	THEOREM7 uses theorem 7 from "Theoretical 
  	and computational aspects of Ramsey Theory"
  	to calculate exact values of e(3,i+1,n).


 THEOREM8 lower bounds for enumbers

 	THEOREM8 uses theorem 8 from "Theoretical
	and computational aspects of Ramsey Theory",
	which is from Radzisowski/Krehers 1991 
	paper, and an improvement proved by Backelin


 THEOREM9 lower bounds for enumbers
  	
	THEOREM9 uses Backelins as yet unpublished 
  	theorem, theorem 9 from "Theoretical and 
	Computational aspects of Ramsey Theory" to 
	improve lower bounds for e-numbers.


 TURAN upper bounds for E-numbers
 
  	TURAN uses Turan's theorem to improve 
  	values of Eub in the global variable
  	ETABLE


  UPDATEE Update the global enumbertable ETABLE
 
 	UPDATEE uses several recursive techniques
 	to improve bounds for e- and E-numbers.
 	theorem 4 and the delta inequality
 	are used to calculate lower bounds for e.
 	The bounds for E are adjusted so that 
  	they agree with the bounds for e, for
 	example if elb=n then we know that
 	Elb must be greater than or equal to n.
 	Updatee also checks whether any new values
 	have become exact by upper and lower bounds
 	coinciding, and whether any values have 
 	lower bounds that are greater than upper
  	bounds, in which case the number cannot 
  	exist and is set to Inf.


 UPDATER update the global ramsey table
 
  	UPDATER performs a number of simple checks 
 	to improve bounds: First RTABLE is compared 
 	to ETABLE to see if any new bounds have been
 	found, then all values are tested with the simplest 
   	upper- and lower bound recursions.
 	Finally, a check is performed to see if any 
        new exact values have been produced.


 UPRTABLE upper table of Ramsey numbers
 
  	T=UPRTABLE extracts a table of upper 
 	bounds for Ramsey numbers R(x,y)
 	from the global variable RTABLE
