Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Diagrams
In physics, computation and mathematics, inputs are related to outputs by compositional processes that compose in series and in parallel. These processes have a natural graphical syntax — string diagrams — and the DiagrammaticComputation`` paclet provides a uniform symbolic representation of them, along with tools for composing, transforming, rewriting, simplifying and visualising diagrams. A is a morphism in a symmetric monoidal category with typed input and output s; everything else in this guide builds on those two primitives.
Wolfram
— — test whether an expression is a valid diagram
— — symbolic diagram with input and output ports
— — convert graphs, trees, hypergraphs, networks and lambda terms to a diagram
— — wrap a diagram as a single opaque node with specified ports
— — diagram with no subdiagrams and identity port mappings
— — additive identity for direct sums
— — identity morphism on a port
— — permutation morphism on a tuple of ports
— — connect two input ports with a cap
— — connect two output ports with a cup
— — duplicate a port onto multiple outputs
— — merge multiple inputs to a single output
— — many-to-many junction at a single point
— — sequential (vertical) composition
— — sequential composition read left-to-right
— — parallel (horizontal) composition / tensor product
— — direct sum of diagrams (additive choice)
— — orderless composition by port name
— — re-express a composite diagram as a network
— — reverse the direction of every port
— — reflect the diagram top-to-bottom (swap inputs and outputs)
— — reflect the diagram left-to-right (reverse port order)
— — permute the ports of a diagram
— — partition the ports of a diagram between inputs and outputs
— — simplify a diagram by absorbing identity wires
— — simplify the underlying port graph
— — render a diagram as a single node
— — render a diagram with its subdiagrams arranged in a grid
— — insert wires, identities and permutations to make a diagram grid-arrangeable
— — decompose a composite diagram into an expression tree of sub-diagrams
— — interactive tool for drawing diagrams
— — arrange diagrams horizontally
— — arrange diagrams vertically
— — construct a diagram port
— — toggle a port between ingoing and outgoing
— — parallel composition of ports
— — direct sum of ports
— — extract a pure function from a diagram
— — extract a symbolic tensor expression from a diagram
— — convert a tensor expression to a diagram
— — list all subdiagrams
— — positions of every subdiagram
— — positions of subdiagrams matching a pattern
— — extract subdiagrams matching a pattern
— — apply a function to every subdiagram
— — apply a function at specific positions
— — extract the subdiagram at a position
— — insert a subdiagram at a position
— — delete the subdiagram at a position
— — replace subdiagrams at specific positions
— — replace the first matching subdiagram
— — list every possible single replacement
— — iteratively apply rewrite rules
— — bidirectional diagram rewrite rule
— — hypergraph view of a diagram for matching
— — hypergraph view of a diagram rewrite rule
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