http://redberry.cc/ 2026-04-09T21:00:15+00:00 http://redberry.cc/ http://redberry.cc/lib/tpl/redberry/images/favicon.ico text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:collect?rev=1448109188&do=diff Collect ---------- Description * Collect[var1, var2] collects together terms involving the same powers of specified vars. * Collect[var1, var2, ..., transformations] or Collect[var1, var2, ..., [Simplifications: transformations]] additionally applies specified transformations to the expression that forms the coefficient of each term obtained. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:collectnonscalars?rev=1448109188&do=diff CollectNonScalars ---------- Description * CollectNonScalars collects terms in sums with same tensorial parts. In contrast to standard Redberry behaviour when factored out tersorial parts with nonzero sized idices, CollectNonScalars tries to factor out parts with nonzero sized free indices. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:collectscalars?rev=1448109188&do=diff CollectScalars ---------- Description * CollectScalars collects similar scalar factors in products. Examples ---------- Collect same scalars in product: ---------- CollectScalars may significantly simplify expression: ---------- CollectScalars text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:conjugate?rev=1448109188&do=diff Conjugate ---------- Description * Conjugate replaces all complex numbers in expression by their complex conjugations Examples See also * Related guides: Applying and manipulating transformations, List of common transformations * JavaDocs: ComplexConjugateTransformation * Source code: ComplexConjugateTransformation.java text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:denominator?rev=1448109188&do=diff Denominator ---------- Description * Denominator gives the denominator of expression. Examples Extract denominator of a rational expression: See also * Related guides: Applying and manipulating transformations, List of common transformations * Related transformations: Numerator * JavaDocs: GetDenominatorTransformation * Source code: GetDenominatorTransformation.java text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:differentiate?rev=1448109188&do=diff Differentiate ---------- Description * Differentiate[var1, var2] differentiates expression successively with respect to var1, var2 ... * Differentiate can differentiate tensorial expressions with respect to tensorial variables. Differentiate takes care about dummies relabelling and symmetries of tensors. The following convention is adopted: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:diracorder?rev=1448109188&do=diff DiracOrder ---------- Description * DiracOrder brings all products of -matrices to alphabetical order * By default DiracOrder works in ; for arbitrary one can use option DiracOrder[[Dimension: D]] * One can directly set trace of identity matrix (e.g. for dimensional regularisation): text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:diracsimplify?rev=1448109188&do=diff DiracSimplify ---------- Description * DiracSimplify simplifies products of gamma matrices * By default DiracSimplify works in ; for arbitrary one can use option DiracSimplify[[Dimension: D]] * One can directly set trace of identity matrix (e.g. for dimensional regularisation): text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:diractrace?rev=1448109188&do=diff DiracTrace ---------- Description * DiracTrace calculates trace of Dirac matrices in dimensions * By default DiracTrace works in ; for arbitrary one can use option DiracTrace[[Dimension: D]] * One can directly set trace of identity matrix (e.g. for dimensional regularisation): text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:eliminateduesymmetries?rev=1448109188&do=diff EliminateDueSymmetries ---------- Description * EliminateDueSymmetries removes parts of expression, which are zero because of the symmetries. * EliminateDueSymmetries does not perform any structural simplifications (expand, eliminate metrics etc.), it is just using symmetries of expression. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:eliminatemetrics?rev=1448109188&do=diff EliminateMetrics ---------- Description * EliminateMetrics eliminates contractions with metric tensors and Kronecker deltas in any part of expression. * EliminateMetrics eliminates metrics for all types of indices, for who metric is defined. * EliminateMetrics eliminates Kroneckers for all types of indices (even if no metric is defined for this type). text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expand?rev=1448109188&do=diff Expand ---------- Description * Expand expands out products and positive integer powers. * Expand[transformations] expands out products and positive integer powers and applies transformations at each level of expand procedure. Examples ---------- text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expandall?rev=1448109188&do=diff ExpandAll ---------- Description * ExpandAll expands out all products and integer powers in any parts of expressions. * ExpandAll[transformations] expands out products and positive integer powers in any parts of expressions and applies transformations text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expandandeliminate?rev=1448109188&do=diff ExpandAndEliminate ---------- Description * ExpandAndEliminate expands out product of sums and positive integer powers and permanently eliminates metric and Kronecker deltas. * ExpandAndEliminate is equivalent to sequential applying Expand & EliminateMetrics text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expanddenominator?rev=1448109188&do=diff ExpandDenominator ---------- Description * ExpandDenominator expands out products and powers that appear as denominators in expressions. * ExpandDenominator[transformations] additionally applies transformations at each level of expand procedure. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expandnumerator?rev=1448109188&do=diff ExpandNumerator ---------- Description * ExpandNumerator expands out products and powers that appear in the numerator of expressions. * ExpandNumerator[transformations] additionally applies transformations at each level of expand procedure. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:expandtensors?rev=1448109188&do=diff ExpandTensors ---------- Description * ExpandTensors expands out products of tensors leaving unexpended all symbolic terms. * ExpandTensors[transformations] or ExpandTensors[[Simplifications: transformations]] applies transformations at each level of expand procedure. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:factor?rev=1448109188&do=diff Factor ---------- Description * Factor factors a symbolic polynomial over the integers. * Factor applies only to scalar parts of expressions. * Factor applies only to the top algebraic level in an expression. * Factor tries to factor all scalar combinations of tensors (like text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:fullyantisymmetrize?rev=1448109188&do=diff FullyAntiSymmetrize ---------- Description * FullyAntiSymmetrize makes expression antisymmetric with respect to all free indices * FullyAntiSymmetrize[indices] makes expression antisymmetric with respect to specified indices Examples ---------- text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:fullysymmetrize?rev=1448109188&do=diff FullySymmetrize ---------- Description * FullySymmetrize makes expression symmetric with respect to all free indices * FullySymmetrize[indices] makes expression symmetric with respect to specified indices Examples ---------- Symmetrize expression: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:generatetensor?rev=1448109188&do=diff GenerateTensor ---------- Description * GenerateTensor(indices, samples) generates tensor of the most general form from a given samples. * The indices of tensor produced by GenerateTensor(indices, samples) are indices. * The symmetries of tensor produced by text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:indextype?rev=1448109188&do=diff IndexType ---------- Description IndexType represents a type of a single index. It encodes mathematical nature of indices with different types (e.g. Lorentz, SU(N) etc.). One can print all available index types as follows: If two indices have different types, then they have different mathematical nature. Thus, for example, two tensors text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:indices?rev=1448109188&do=diff Indices ---------- Basics Indices represents indices of tensor. Indices is a simple container of single indices. For all types of tensors except SimpleTensor and TensorField, Indices are always sorted in some predefined way (e.g. first upper then lower, first Latin then Greek, in each group indices sorted in lexicographical order etc.): text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:invertindices?rev=1448109188&do=diff InvertIndices Description * InvertIndices inverts indices of tensors * InvertIndices[type] inverts indices of specified type Examples ---------- Invert indices of some expression ---------- Invert only indices of certain type: See also text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:kronecker_delta?rev=1448109188&do=diff Kronecker delta ---------- Basics The notation for Kronecked delta used in Redberry is ordinary d^a_b and similarly for other index types (d^A_B, d^\\alpha_\\beta etc.). Kronecker delta are automatically symmetric: Raising and lowering of Kronecker delta indices may produce text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:levicivitasimplify?rev=1448109188&do=diff LeviCivitaSimplify ---------- Description * LeviCivitaSimplify simplifies combinations of Levi-Civita tensors. * LeviCivitaSimplify.euclidean[eps] simplifies combinations of Levi-Civita tensors (denoted as eps) assuming that space is Euclidean. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:metric_tensor?rev=1448109188&do=diff Metric tensor ---------- Basics The notation for metric tensor used in Redberry is ordinary g_ab and similarly for other index types (g_AB, g_\\alpha\\beta etc.). Metric tensors are automatically symmetric: Raising and lowering of metric tensor indices may involve text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:numerator?rev=1448109188&do=diff Numerator ---------- Description * Numerator gives the numerator of expression. Examples Extract numerator of a rational expression: See also * Related guides: Applying and manipulating transformations, List of common transformations * Related transformations: Denominator * JavaDocs: GetNumeratorTransformation * Source code: GetNumeratorTransformation.java text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:numeric?rev=1448109188&do=diff Numeric ---------- Description * Numeric gives the numerical value of expression. Examples Evaluate numerically: See also * Related guides: Applying and manipulating transformations, List of common transformations * JavaDocs: ToNumericTransformation * Source code: ToNumericTransformation.java text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:outputformat?rev=1448109188&do=diff OutputFormat ---------- Description OutputFormat is a enum that defines different formats of string representation of expressions in Redberry. There are several available output formats. In order to specify a particular one one can do: The above result can be directly pasted to Maple system. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:permutation?rev=1448109188&do=diff Permutation ---------- Basics * Permutation represents a mathematical permutation. * Permutation can be inputted in both one-line and cycle notation using .p property. * Permutation can can represent both permutational symmetry or antisymmetry. text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:permutationgroup?rev=1448109188&do=diff PermutationGroup ---------- Basics * PermutationGroup represents a group of permutations. * Redberry can handle permutation groups with degree in the range of a few thousand, hence working with groups with more than elements. * PermutationGroup text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:powerexpand?rev=1448109188&do=diff PowerExpand ---------- Description * PowerExpand expands all powers of products and powers. * PowerExpand[var1, var2, ...] expands only with respect to the variables var1, var2, ... Examples ---------- Expand a power of a product: ---------- text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:powerunfold?rev=1448109188&do=diff PowerUnfold ---------- Description * PowerUnfold expands all powers of products and unfolds powers of indexed arguments into products. * PowerUnfold[var1, var2, ...] expands only with respect to the variables var1, var2, ... * PowerUnfold is similar to text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:product?rev=1448109188&do=diff Product ---------- Basics Product represents a product of terms. Like any other expression, it inherits all properties of Tensor. Product adopts the following convention on its indices: the indices of product are sorted concatenated indices of its multipliers: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:reduce?rev=1448109188&do=diff Reduce ---------- Description * Reduce(equations, vars) reduces a system of tensorial equations to a system of symbolic equations. * Reduce(equations, vars, options) allows to pass additional . * Reduce allows to completely solve a system of equations using external system (Maple or Mathematica). text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:reverse?rev=1448109188&do=diff Reverse ---------- Description * Reverse[type] reverses the order of matrices of specified type. * Reverse[type1, type2, ...] reverses the order of matrices of types type1, type2, ... in expressions. Examples ---------- Reverse product of matrices: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:setmandelstam?rev=1448109188&do=diff setMandelstam ---------- Description * setMandelstam([k1:m1, k2:m2, k3:m3, k4:m4]) generates a list of Mandelstam and mass shell substitutions for incoming particles with momentums k1 and k2 with masses m1 and m2 and outcoming particles with momentums text/html 2016-06-21T09:53:30+00:00 http://redberry.cc/documentation:ref:setmandelstam5?rev=1466502810&do=diff setMandelstam5 ---------- Description * setMandelstam5([k1:m1, k2:m2, k3:m3, k4:m4, k5:m5]) generates a list of generalised Mandelstam and mass shell substitutions for incoming particles with momentums k1 and k2 with masses m1 and m2 and outcoming particles with momentums text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:simpleindices?rev=1448109188&do=diff SimpleIndices ---------- Basics SimpleIndices represents indices of SimpleTensor and TensorField. It inherits all properties of Indices but does not sort indices., so indices in SimpleIndices appear exactly in that order as defined by the user: On the other hand, since indices of different text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:simpletensor?rev=1448109188&do=diff SimpleTensor ---------- Basics SimpleTensor represents a simple tensors like f_mn of symbols like x etc. Like any other expression, it inherits all properties of Tensor. SimpleTensor adopts the following convention on its indices: the indices of SimpleTensor text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:spinorssimplify?rev=1448109188&do=diff SpinorsSimplify ---------- Description * SpinorsSimplify simplifies products of -matrices and Dirac spinors using Dirac equation * By default SpinorsSimplify works in ; for arbitrary one can use option SpinorsSimplify[[Dimension: D]] * One can directly set trace of identity matrix (e.g. for dimensional regularisation): text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:sum?rev=1448109188&do=diff Sum ---------- Basics Sum represents a sum of terms. Like any other expression, it inherits all properties of Tensor. Sum adopts the following convention on its indices: the indices of sum are free sorted indices of its summands: Sum sorts its arguments and reduces any equal terms. Additionally, it reduces terms with same tensorial parts as described in text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:symmetrize?rev=1448109188&do=diff Symmetrize ---------- Description * Symmetrize[indices] makes expression symmetries same to the symmetries of indices * Symmetrize[indices] makes expression symmetric only with respect to specified indices * Symmetrize[indices] will also multiply the result on the symmetric factor text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:tensor?rev=1448109188&do=diff Tensor ---------- Basics Tensor is a parent object type for all mathematical expressions used in Redberry. Thus, all expressions in Redberry are tensors. From the programming point of view that means, that Tensor is a parent class for all types of mathematical expressions used in Redberry (sums, products, etc.). text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:tensorfield?rev=1448109188&do=diff TensorField ---------- Basics TensorField represents a function like f_mn[x_a] or derivative of function like f~(1)_a[x_i]. Like any other expression, it inherits all properties of Tensor. Additionally it inherits all properties of SimpleTensor and adopts same convention on its indices: the indices of text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:together?rev=1448109188&do=diff Together ---------- Description * Together puts terms in a sum over a common denominator * Together cancels only terms that can be canceled without factorisation * TogetherFactor cancels factors in the result Examples Combine terms over a common denominator: text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:transformation?rev=1448109188&do=diff Transformation ---------- Basics * Transformation represents a transformation of expression; it is a super type for all transformations (e.g. Expand or EliminateMetrics). * Transformation can be applied to expression using >> operator. * A list of common useful transformations can be found at text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:unitarysimplify?rev=1448109188&do=diff UnitarySimplify ---------- Description * UnitarySimplify simplifies combinations of SU(N) matrices and SU(N) structural and -constants in expression. * By default UnitarySimplify uses notation T_A for SU(N) matrices, f_ABC for SU(N) structural constants, text/html 2015-11-21T12:33:08+00:00 http://redberry.cc/documentation:ref:unitarytrace?rev=1448109188&do=diff UnitaryTrace ---------- Description * UnitaryTrace calculates the trace of SU(N) matrices in expressions. * By default UnitaryTrace uses notation T_A for SU(N) matrices, f_ABC for SU(N) structural constants, d_ABC for -constatnts and N for dimension.