(components->oneform-field components coordinate-system & [name])(coordinate-basis-oneform-field coordinate-system name & i)(coordinate-basis-oneform-field-procedure coordinate-system & i)(coordinate-name->ff-name n)From the name of a coordinate, produce the name of the coordinate basis one-form field (as a symbol)
From the name of a coordinate, produce the name of the coordinate basis one-form field (as a symbol)
(permutation-sequence as)This is an unusual way to go about this in a functional language, but it's fun. Produces an iterable sequence developing the permutations of the input sequence of objects (which are considered distinct) in church-bell-changes order, that is, each permutation differs from the previous by a transposition of adjacent elements (Algorithm P from §7.2.1.2 of Knuth). This has the side-effect of arranging for the parity of the generated permutations to alternate; the first permutation yielded is the identity permutation (which of course is even). Inside, there is a great deal of mutable state, but this cannot be observed by the user.
This is an unusual way to go about this in a functional language, but it's fun. Produces an iterable sequence developing the permutations of the input sequence of objects (which are considered distinct) in church-bell-changes order, that is, each permutation differs from the previous by a transposition of adjacent elements (Algorithm P from §7.2.1.2 of Knuth). This has the side-effect of arranging for the parity of the generated permutations to alternate; the first permutation yielded is the identity permutation (which of course is even). Inside, there is a great deal of mutable state, but this cannot be observed by the user.
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