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s also form a , but the binary operation issuperposition (just like that of diagrams). Paths withmultiple components can be used, for example, to create shapes withholes:

To make use of the diagrams libraries in the sandbox, you can usecommands such as

The wrapper can be used to create "scale-invariant"objects. (Note that is not exported from; to use it, import.) In the diagram below, the sametransformation is applied to each pair of arrows.

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You can also use  in the case that you want to rotateabout some point other than the origin.

It is quite convenient to be able to use, say, as adiagram, path, trail, list of vertices, etc., whichever suits one'sneeds. Otherwise, either a long list of functions would be needed foreach primitive (like , , ,, , , ... ugh!),or else explicit conversion functions would have to be inserted whenyou wanted something other than what the function gave you bydefault.

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This function takes a name and a diagram, and returns the firstsubdiagram associated to that name if any are found, and otherwise. (Note that is implemented in terms of thelower-level lookup functions and ; occasionally itmay be useful to directly access these lower-level functions, but thehope is that you shouldn't need to.)

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For even more low-level access, the class provides the method, which can be used to directly access the tracefunction for an object. Given inputs and , it returns asorted list of scalars such that is a pointof intersection between the ray and an edge of thediagram.

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Envelopes are useful for placing diagrams relative to one another, butthey are not particularly useful for finding actual points on theboundary of a diagram. Finding points on the boundary of a diagramcan be useful for things like drawing lines or arrows between twoshapes, or deciding how to position another diagram relative to agiven one.

Have you chosen the diagrams or photographs carefully ..

In addition, the list type is an instance of whenever is. The envelope for a list is simply thecombination of all the individual envelopes of the list'selements—that is, an envelope that contains all of the listelements. In conjunction with the instance for lists(see ), this can be used to do things suchas apply an alignment to a list of diagrams considered as a group.For some examples and an explanation of why this might be useful, see.

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takes a single name and makes available a list ofall subdiagrams associated with that name.(, by contrast, returns only the most recent.) This isuseful when you want to work with a collection of named subdiagrams allat once.