Cadabra
a field theory motivated approach to computer algebra

Manual pages

Every algorithm and every property has a manual page with examples, which you can view online, or by pressing F1 in the Cadabra notebook interface.

Algorithms

Aasym Anti-symmetrise or symmetrise an expression in indicated indices or arguments
Ccanonicalise Bring a tensorial expression to canonical form by re-ordering indices.
collect_factors Collect identical factors in a product.
collect_terms Collect identical terms in a sum.
combine Combine two consecutive indexbracket objects
complete Complete a set of substitution rules to cover related objects.
Ddecompose_product Decompose a product of tensors by using Young projectors.
distribute Distribute factors over sums.
drop_weight Drop terms with given weight
Eeliminate_kronecker Eliminate Kronecker delta symbols.
eliminate_metric Eliminate metrics by raising or lowering indices.
epsilon_to_delta Replace a product of two epsilon tensors with a generalised delta
evaluate Evaluate components of a tensor expression.
expand Write out products of objects with implicit indices.
expand_delta Expand generalised Kronecker delta symbols
expand_diracbar Simplify the Dirac bar of a composite object.
expand_power Expand powers into repeated products
Ffactor_in Collect terms in a sum that differ only by given pre-factors.
factor_out Isolate common factors in a sum of products
fierz Perform a Fierz transformation on a product of four spinors
Iintegrate_by_parts Integrate by parts away from the indicated expression
Jjoin_gamma Work out the product of two generalised Dirac gamma matrices.
Kkeep_weight Keep terms with indicated weight
Llr_tensor Compute the tensor project of two Young tableaux
Pproduct_rule Apply the Leibnitz rule to a derivative of a product
Rreduce_delta Simplify a self-contracted generalised delta.
rename_dummies Rename dummy indices.
rewrite_indices Rewrite indices by contracting with vielbein or metric.
Ssort_product Sort factors in a product
sort_spinors Sort Majorana spinor bilinears
sort_sum Sort terms in a sum.
split_gamma Split a Dirac gamma matrix off a generalised product of gamma matrices.
split_index Split the range of an index into two subsets
substitute Generic substitution algorithm.
Uunwrap Move objects out of derivatives or accents.
Vvary Generic variation algorithm for functional derivatives.
Yyoung_project_product Project all tensors in a product with their Young tableau projector.
young_project_tensor Project tensors with their Young projector.

Properties

AAccent Turn a symbol into an accent.
AntiCommuting Make objects anti-commuting.
AntiSymmetric Make an object anti-symmetric in all indices.
CCommuting Make components commuting.
CommutingAsProduct Makes an object behave as a product when commuting.
CommutingAsSum Makes an object behave as a sum when commuting.
Coordinate Declare a symbol to be a coordinate label.
DDAntiSymmetric Gives object the symmetries of the derivative of a fully antisymmetric tensor.
Depends Makes an object implicitly dependent on other objects.
Derivative Declare an operator to satisfy the Leibnitz rule.
Diagonal Declares a tensor to only have non-zero diagonal entries.
DiracBar An accent representing the Dirac conjugation operation.
EEpsilonTensor A fully anti-symmetric tensor with constant components.
FFilledTableau A Young tableau with labelled boxes.
GGammaMatrix A generalised generator of a Clifford algebra.
IImplicitIndex Indicates that an object carries indices which are not written out.
Indices Declare names to be used as indices.
Integer Indicates that an object takes integer values.
InverseMetric Make a two-tensor an inverse metric.
KKroneckerDelta Turns an object into a generalised Kronecker delta symbol.
LLaTeXForm Changes the way in which symbols are displayed.
MMetric Makes a two-tensor a metric.
NNonCommuting Makes components non-commuting.
PPartialDerivative Makes an object a partial derivative.
RRiemannTensor Make an object a Riemann curvature tensor.
SSatisfiesBianchi Make an object satisfy the generalised Bianchi identity.
SelfAntiCommuting Make components of tensors anti-commute.
SelfCommuting Make tensor components commute.
SelfNonCommuting Make tensor components non-commuting.
SortOrder Set sorting order of objects.
Spinor Declares an object to transform as a spinor.
Symmetric Make an object symmetric in all indices.
TTableau Make object a Young tableau
TableauSymmetry Gives a tensor a generic Young tableau symmetry.
WWeightInherit Make object inherit weights from child nodes
Copyright © 2001-2017 Kasper Peeters
Questions? info@cadabra.science