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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. Therefore, 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.

Redberry is a mathematics based algebraic software technology, framework and ecosystem. It can be described as a an open-source-based tensor-led mathematics-based framework. Redberry was originally created as a new tensor-based algebraic technology to be based on and to add to the existing mathematics-based technology.
Redberry supports all mathematical operations required by tensor mathematics and also supports all fields of mathematics currently used in the original mathematics-based technology.
The redberry-core algorithm framework consists of three central mathematical objects, Indices, Transformations and Tensors. The Tensors represent mathematical objects and also include the objects in the mathematical algebra system. They are the reference object of Redberry and the sub-objects that can be manipulated in Redberry. The Indices represent a mathematical concept and are the container that stores the indices of the tensors.
The first sub-object in the algorithm framework is the Tensors, which can be described as the reference mathematical objects for Redberry. Tensors can be manipulated in Redberry and can be classified into the ten mathematical types of Tensor; Tensor, EigenTensor, LinearTensor, VectorTensor, MatrixTensor, TensorField, SimpleTensor, ScaledTensor, ScalarTensor and Tensor. The second sub-object in Redberry is the Indices, which are the indices of tensors and the container that stores the indices of the tensors. The Indices can be described as the indices that can be sorted for each mathematical type of tensor. The third sub-object of Redberry is the Transformations, which are the mathematical operations that manipulate mathematical expressions. The Transformations can also be used to manipulate the mathematical objects Tensor and Indices. The Transformations include operations such as apply index mapping, collect, conjugate, denominator, differentiate, EliminateMetrics, ExpandAndEliminate, FullyAntiSymmetrize or InvertIndices.
Redberry applications include:
Tensor analysis: to solve equation systems derived from tensors that have been reduced to tensor algebra.
Advanced data analysis: to find the analytical solutions of such tensor algebra using tensor algebra and tensor solvers.
Tensor simulation: to predict the behavior of dynamical systems that include tensor math elements
Geometrical tensor analysis: to calculate the potential and the energy of tensor math
Geometrical flow analysis: to determine the potential of tensor

Redberry is an Open Source Java framework for tensor algebra and numerical mathematics. The usage of the framework is to provide a set of open source tools for tensor algebra and numerical mathematics.
This framework is the result of a joint effort of a small team of researchers that initially started to build an application focused on simulation tasks in a molecular dynamics environment. After a successful collaboration with the molecular dynamics software packages, they then decided to use this set of tools for numerical task oriented tasks. In this case, they realized that it could help other researchers in numerical and mathematical fields.
Redberry is based on an overall object-oriented architecture and combines the power of Java with the convenience of Open Source. These factors allow the developers to create and distribute the framework for a free of charge. Moreover, the developers can decide where to take the application to to help their community.
Due to the versatility of the framework, the authors have a wide range of ideas for future releases and they encourage the community to participate by submitting their ideas or helping with the development.
The source code of the framework can be downloaded from here:

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A Java API for Redberry is available. This API allows users to access and manipulate Redberry data structures and operations from their own Java programs.The Java API is defined as a group of classes that can be instantiated and manipulated using the Java programming language. The API is implemented using a Collection object, which is the central object in the Redberry framework. Other object types can be classified into a collection based on their characteristic properties. For instance, arrays, strings, sets, maps, and lists are all collections. The classes and interfaces defined in the API include the following.
• RedberryTensors
The RedberryTensor class is a reference class that defines a collection of tensor data. The RedberryTensor class is an abstract class that is the base type for Redberry tensor objects, which are further defined by two sub classes. RedberrySimpleTensor and RedberryTensorField, which extends the RedberryTensor class. The constructor of the RedberryTensor class takes three parameters, including a set of indices representing a collection of indices, the base type of the RedberryTensor object. The set of indices that can be represented includes mathematical types, such as numeric types and string types. In addition, the set includes collections.
• RedberryIndices
The RedberryIndices class is a collection of indices in Redberry tensors. The RedberryIndices class includes three sub classes, including RedberryOrderedIndices, RedberryNoOrderedIndices, and RedberryIndexedIndices. The RedberryOrderedIndices class is a collection of indices that define a numerical order. The RedberryNoOrderedIndices class is a collection of indices that cannot be ordered in any way. The RedberryIndexedIndices class is a collection of indices that define a numerical order, and RedberryIndexedIndices also includes a collection of indices that can be split into indices that define numerical order and indices that do not define numerical order.
• RedberryTransformations
The RedberryTransformations class includes the various mathematical operations for tensors, including apply index mapping, collect, conjugate, eliminate metrics, differentiate, eliminate homogeneous part, expand, eliminate metrics, eliminate homogeneous part, expand and eliminate, fully anti-symmetrize, and invert indices. The class includes numerous methods and static variables that include the following:
• MathTypeEnum.
MathTypeEnum is a set of predefined enumer

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. Therefore, 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.

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. Therefore, 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,

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