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\brief LinBox uses common object interfaces and archetypical instantiations. This is done for several key concepts including blackbox matrices, fields, random iterators, and vectors.

LinBox objects and algorithms are parameterized by types which must meet the interface requirements described here. Parameterization is via C++ templates. The interface concepts are specified in classes called archetypes.

The archetype classes are similar in spirit to Java interfaces. However most of them are also instantiable and their instances are concrete objects. Originally archetypes were pure virtual classes and algorithms with archetype arguments could be written and separately compiled. However virtual classes cannot also provide templated member functions, and LinBox is moving to greater use of template member functions. In some cases, we forgo the separate complation and code bloat avoidance mechanism in favor of speed and flexibility using template members.

Archetypes exist for fields, field elements, random iterators, vectors, blackbox matrices, dense matrices, and sparse matrices.

• Blackbox matrix archetype LinBox::BlackboxArchetype in linbox/blackbox/archetype.h specifies this interface in detail. It is a parent class from which the various blackbox classes inherit.

• Sparse Matrix interface. This extends the blackbox interface and provides facilities for some direct methods.

• Dense Matrix interface. This extends the blackbox interface and provides facilities for some direct methods and block methods (dense matrices in lieu of vectors as arguments to black box apply).

• Field archetype. This provides the basic arithmetic functionality of a field. The interface is used more generally for representations of commutative rings with 1. LinBox::FieldArchetype in linbox/field/archetype.h specifies this interface in detail and sets it up in such a way that algorithms can be compiled once against the field archetype. Alternatively, and with some performance gain, one can compile an algorithm separately against each field class used. For a listing of the field implementations see LinBox::FieldInterface .

• Random iterator archetype. LinBox fields (and rings) provide a random iterator type. Objects of this type can be used to generate elements at random. RandIterArchetype in linbox/randiter/archetype.h specifies this interface in detail.

• Element archetype. To allow for high performance, it must be possible to use any C++ type to represent elments of fields and rings. This includes the primitive types such as int and float. To support this, our element type requires only: a public default constructor, a copy constructor, an assignment operator, and a destructor. ElementArchetype in linbox/element/archetype.h specifies this interface in detail.

• Dense vector interface. This is the interface for vectors to which blackboxes are applied (the vector of a matrix vector product). This is simply the std::vector<Elt> interface, where Elt is the element type of the field involved. But we do not use the functionality concerning resizing vectors, {\tt resize, push_back}, etc. An example of a class meeting this interface is LinBox::SubVector .

• Sparse vector interfaces. We are experimenting with two or three variant interfaces for manipulation of sparse vectors.

These additional interfaces are under construction.

• Target Domain interface. This extends the field (or ring) interface. It has members dealing with the ring as a module over another. This interface is designed primarily with three applications in mind.
  • finite field extensions .
  • .
  • conversions among isomorphic representations, as used for instance in implementing the Toeplitz matrix class.

• Ring homomorphism interface. This is used by the target rings.

• Polynomial interface. This may become the std::vector interface (including the resizing functionality) together with a handful of functions for manipulating polynomials. LinBox' design intentions are to exploit other software for any serious polynomial manipulation.

In general, there are three uses for the archetypes classes:

• To define the common object interface of the concept, i.e., specify what an classes must have to meet the interface.

• To allow distribution of compiled code and prototype library components. Thus it is possible to compile algorithms with the archetypes as parameters and call the compiled code with objects of other classes meeting the interface.

• To control code bloat. (by means of separate compilation as sketched in the item above)

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