This module bundles some of the most important functionality of the AERN-RnToRm package. It is intended to be imported *qualified*.

AERN-RnToRm provides datatypes and abstractions for approximating functions of type D -> R^m where D is a bounded interval in R^n with non-empty interior.

Abstractions are provided via 4 type classes:

• ERUnitFnBase: generalises polynomials with floating point coefficients. (Not exported here, used only internally.)
• ERFnApprox: generalises functions enclosures on a certain unspecified domain.
• ERUnitFnApprox (extends ERFnApprox): generalises function graph enclosures on the domain [-1,1]^n. (Not exported here, used only internally.)
• ERFnDomApprox (extends ERFnApprox): generalises function enclosures over a specified and queriable domain box (instance of class DomainBox).

At all levels, all field operations are supported as well as some elementary operations, namely exp, sin and cos. Log and sqrt are planned to be added soon.

Implementations of ERUnitFnBase:

• ERChebPoly

By using the Chebyshev basis on domain [-1,1]^n, we gain simple and optimally rounding degree reduction as well as relatively simple handling of rounding in other operations.

Implementations of ERUnitFnApprox:

• ERFnInterval

Implementations of ERFnDomApprox:

• ERFnDomTranslApprox: builds a basic implementation using an instance of ERUnitFnApprox.
• ERFnTuple: extends another implementation of ERFnDomApprox to work with lists of functions simultaneously.
• ERFnDomEdgesApprox: separately enclose a function on its domain box as well as on all the domain's hyper-edges (including the corners) using another implementation of ERFnDomApprox.
• ERFnPiecewise: allows the domain box to be bisected to an arbitrary finite depth and uses another implementation of ERFnDomApprox to approximate the function on each segment.