Magma

Initialisations

x:Symbol :='x
  x
                       Type: Symbol

y:Symbol :='y
  y
                       Type: Symbol

z:Symbol :='z
  z
                       Type: Symbol

word := OrderedFreeMonoid(Symbol)
  OrderedFreeMonoid Symbol
                       Type: Domain

tree := Magma(Symbol)
  Magma Symbol
                       Type: Domain

Let’s make some trees

a:tree := x*x
  [x,x]
                       Type: Magma Symbol

b:tree := y*y
  [y,y]
                       Type: Magma Symbol

c:tree := a*b
  [[x,x],[y,y]]
                       Type: Magma Symbol

Query the trees

left c
  [x,x]
                       Type: Magma Symbol

right c
  [y,y]
                       Type: Magma Symbol

length c
  4
                       Type: PositiveInteger

Coerce to the monoid

c::word
   2 2
  x y
                       Type: OrderedFreeMonoid Symbol

Check ordering

a < b
  true
                       Type: Boolean

a < c
  true
                       Type: Boolean

b < c
  true
                       Type: Boolean

Navigate the tree

first c
  x
                       Type: Symbol

rest c
  [x,[y,y]]
                       Type: Magma Symbol

rest rest c
  [y,y]
                       Type: Magma Symbol

Check ordering

ax:tree := a*x
  [[x,x],x]
                       Type: Magma Symbol

xa:tree := x*a
  [x,[x,x]]
                       Type: Magma Symbol

xa < ax
  true
                       Type: Boolean

lexico(xa,ax)
  false
                       Type: Boolean

See Also:

• )show Magma