Diagram

class discopy.ribbon.Diagram(inside, dom, cod, _scan=True)

Bases: discopy.pivotal.Diagram, discopy.balanced.Diagram, discopy.abc.RibbonCategory

A ribbon diagram is a pivotal diagram and a balanced diagram.

Parameters:

• inside (Layer) – The layers of the diagram.

• dom (pivotal.Ty) – The domain of the diagram, i.e. its input.

• cod (pivotal.Ty) – The codomain of the diagram, i.e. its output.

trace(n=1, left=False)

The trace of a ribbon diagram.

Parameters:

n – The number of wires to trace.

cup(x, y)

Post-compose a ribbon diagram with a cup between wires i and j by introducing braids.

Parameters:

• i – The wire on the left of the cup.

• j – The wire on the right of the cup.

to_ribbons(width=None)

Doubles every object and sends the twist to the braid, folding cups and caps into a single box.

Parameters:

width (float) – The width of a ribbon, i.e. the gap between the two wires encoding each object, defaults to the ribbon_width in discopy.config.DRAWING_DEFAULT. Set to 0 to return the diagram as is, i.e. without doubling it into dual rails.

Example

>>> x = Ty('x')
>>> braided_twist = Diagram.twist(x).to_ribbons()

braid_factory

alias of Braid

cap_factory

alias of Cap

cup_factory

alias of Cup

dual_rail_factory

alias of DualRail

factory

alias of Diagram

twist_factory

alias of Twist