Correspondence Scrolls generalize rational normal scrolls and K3 Carpets, among other familiar constuctions. Suppose that Z is a subscheme of a product of projective spaces Z ⊂P^{a0} x .. x P^{an-1} The Correspondence Scroll C(Z;b), where b = (b_{0},..,b_{n-1}) is the subscheme of P^{N-1} consisting set theoretically of the planes spanned by the points of the Segre-Veronese embedding corresponding to Z.

More generally, we treat the case of a multi-homogneous subscheme Z’ ⊂A^{a0-1} x .. x A^{an-1-1}.

- Functions and commands
- carpet -- ideal of a K3 carpet
- correspondencePolynomial -- computes the Hilbert polynomial of a correspondence scroll
- correspondenceScroll -- Union of planes joining points of rational normal curves according to a given correspondence
- hankelMatrix -- matrix with constant anti-diagonal entries
- irrelevantIdeal -- returns the irrelevant ideal of a multi-graded ring
- multiHilbertPolynomial -- Multi-graded Hilbert polynomial for a product of projective spaces
- productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)
- schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces
- smallDiagonal -- Ideal of the small diagonal in (P^1)^n

- Symbols
- CoefficientField -- symbol used to define the ground field in many routines
- VariableName -- symbol used to define the variable name in many routines