Singular Manual: Letterplace correspondence

| ### 7.9.5 Letterplace correspondence The name letteplace has been inspired by the work of Rota and, independently, Feynman. In [LL09] a natural shifting on letterplace polynomials was introduced and used. Indeed, there is 1-to-1 correspondence between two-sided ideals of a free algebra and so-called letterplace ideals in the letterplace algebra, see [LL09], [LL13], [LSS13] and [L14] for details. Note, that first this correspondence was established for graded ideals, but holds more generally for arbitrary ideals and subbimodules of a free bimodule of a finite rank. All the computations internally take place in the Letterplace algebra. A letterplace monomial of length is a monomial of a letterplace algebra, such that its places are exactly 1,2,..., . In particular, such monomials are multilinear with respect to places (i.e. no place, smaller than the length is omitted or filled more than with one letter). A letterplace polynomial is an element of the -vector space, spanned by letterplace monomials. A letterplace ideal is generated by letterplace polynomials subject to two kind of operations: the Note: Letterplace correspondence naturally extends to the correspondence over ,..., , where is a commutative unital ring. The case is implemented, in addition to being a field.

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