SurrealNumbers

canonicalise(s::SurrealFinite)

Convert a surreal number form into its equivalent canonical form. It performs the conversion by converting to a Rational and then back to a Surreal.

Examples

julia> pf( canonicalise( convert(SurrealFinite, 1) - convert(SurrealFinite, 1) ) )
{ ∅ | ∅ }

expand(x::SurrealFinite; level=0)

Writes a surreal as a string with varying levels of expansion.

Arguments

• x::SurrealFinite: the number of elements to expand
• level=0: the amount of expansion
  • 0 : write shorthand if it exists, or $\{ X_L \| X_R \}$ if not
  • 1 : $\{ X_L \| X_R \}$
  • 2 : expand out $X_L$ and $X_R$ recursively

Examples

julia> expand( convert(SurrealFinite, 2))
"2"
julia> expand( convert(SurrealFinite, 2); level=1)
"{ 1 | ∅ }"
julia> expand( convert(SurrealFinite, 2); level=2)
"{ { { ∅ | ∅ } | ∅ } | ∅ }"

generation(x::SurrealFinite)

Finds the birthday of a surreal number, which is 1 + the max of any of its components.

Arguments

• x::SurrealFinite: the number to operate on

julia> generation( convert(SurrealFinite, 1) )
1

surreal2dag(x::SurrealFinite; direction::String="forward")
surreal2dag(io::IO, x::SurrealFinite; direction::String="forward")

Writes a surreal representation as a DAG out in DOT format for drawing using GraphVis, and returns the number of nodes in the graph. Returns the number of nodes in the graph.

Arguments

• io::IO: output stream, default is stdout
• x::SurrealFinite: the number to write out
• direction::String="forward": by default arrows point towards parents ("forward"), to go other way use "back"

Examples

julia> surreal2dag(convert(SurrealFinite, 0))
digraph "0.0" {
   node_1 [shape=none,margin=0,label=
         <<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
         <TR><TD  CELLPADDING="5pt" COLSPAN="2"><o>0</o></TD></TR>
         <TR><TD PORT="L"> Ø </TD><TD PORT="R"> Ø </TD></TR>
         </TABLE>>,
         ];
}
1

surreal2dot(x::SurrealFinite)
surreal2dot(io::IO, x::SurrealFinite)

Writes a surreal representation as a tree out in DOT format for drawing using GraphVis, and returns the number of nodes in the graph.

Arguments

• io::IO: output stream, default is stdout
• x::SurrealFinite: the number to write out
• direction::String="forward": by default arrows point towards parents ("forward"), to go other way use "back"

Examples

julia> surreal2dot(convert(SurrealFinite, 1))
digraph "1.0" {
   node_1 [shape=none,margin=0,label=
         <<TABLE BORDER="0" CELLBORDER="1" CELLSPACING="0" CELLPADDING="4">
         <TR><TD  CELLPADDING="5pt" COLSPAN="2"><o>1</o></TD></TR>
         <TR><TD PORT="L"> <TABLE BORDER="0" CELLBORDER="0" CELLPADDING="0"><TR><TD CELLPADDING="1pt" PORT="0,1"> <o>0</o> </TD> &nbsp; </TR></TABLE> </TD><TD PORT="R"> Ø </TD></TR>
         </TABLE>>,
         ];
   node_1:"0,1" -> node_2 [color="red3", dir=forward];
   node_2 [shape=none,margin=0,label=<<B>0</B>>]
}
2