Redberry

Redberry is an Open Source Java framework that acts like a computer algebra system designed to provide capabilities for tensor manipulation.The framework contains a wide spectrum of algorithms required by tensor algebra. and has the role of finding analytical solutions to complicated mathematical and physical problems.

The framework consists of three central objects that include sub-objects that can share common properties and can be manipulated if they are of the same type. The Tensors are the reference mathematical expression and employ object-oriented programming technology and can be manipulated in a uniform way. The mathematical types in the algebra system are inherited from a base super type Tensor.

The second type of central objects are the Indices, which can be described as a single container of single indices of Tensors. With the exception of TensorField and SimpleTensor, the Indices can be sorted in a pre-defined way, such as lexicographical or first upper than lower, for example. The exceptions represent a subtype of Indices that cannot be sorted in any way.

The third type of central objects are the Transformations that refer to a manipulation of mathematical expressions and include operations like apply index mapping, collect, conjugate, denominator, differentiate, EliminateMetrics, ExpandAndEliminate, FullyAntiSymmetrize or InvertIndices.