The "higher CI operators" complete the structure of the ordinary CI operators on (sometimes called "Eisenbud operators") on a resolution over a complete intersection in the same sense that the "higher homotopies" complete the structure of homotopies on with respect to a sequence of elements. Details will appear in a preprint in preparation by Burke, Eisenbud and Schreyer.

The higher CI operators are constructed by the routine higherCIOperators.

Just as a system of higher homotopies for a regular sequence f_{1}..f_{c} on a resolution over a ring S allow one to construct the Shamash resolution over R = S/(f_{1}..f_{c}), the higher CI operators are involved in a sort of dual construction: from a resolution F over R, lifted to a sequence of maps A over S, and lifted higher CI operators on A⊗L, where L is the Koszul complex on f, one can construct a nonminimal resolution AL over S using the routine ciOperatorResolution.

- Functions and commands
- ciOperatorResolution -- "lift resolution from complete intersection using higher ci-operators"
- exteriorMultiplication -- "multiplication maps in the exterior algebra"
- higherCIOperators -- "creates the HashTable of higher CI operators on a lifted resolution"
- makeALDifferential -- "makes the differential used in ciOperatorResolution"
- trueKoszul -- "Makes Koszul complex, with bases sorted in lex"