Manual pages

Every algorithm and every property has a manual page with examples, which you can view online here, or by pressing F1 in the Cadabra notebook interface when your cursor is located on an algorithm or property name. Consider this the "dry" version of the documentation: to-the-point, but not very useful if you do not have an understanding of the big picture yet.

For a more introductory description of the basics of Cadabra, you may be better off first reading or skimming through the tutorials or the Cadabra book.

Packages

Cadabra comes with various add-on packages, which can be imported in the usual Python way with import. Their content is listed below.

cdb.core.component
Simple access to component expressions
	get_component	Extract a single component from an expression.
	remove_zero_components	Remove all components of an expression that are equal to zero.
	components_to_subrule	Turn a component expression (the result of a \texttt{evaluate

cdb.core.manip
Manipulating equations, inequalities and similar expressions
	eq_to_subrule	Create substitution rule from an equation.
	multiply_through	Multiply all terms by the same factor.
	add_through	Add a factor to both sides of an equation.
	apply_through	Apply an operator through both sides of an equation.
	get_lhs	Return left-hand side of an expression
	get_rhs	Return right-hand side of an expression
	swap_sides	Swap the left and right-hand sides of an expression.
	get_factor	Get all multiplicative factors of term in node
	get_basis_component	Returns the multiplicative coefficients of \texttt{basis
	to_rhs	Move the indicated term of the expression to the right-hand side.
	to_lhs	Move the indicated term of the expression to the left-hand side.
	isolate	Isolates a term on the left hand side of an equation or inequality

cdb.core.trace
Manipulating Trace objects
	combine_traces	Combine separate trace nodes into one sum.

cdb.graphics.plot
Plotting of functions
	plot	Plot a function of one variable given the range.
	plot3d	Plot a function of two variables given their ranges.

cdb.numeric.evaluate
Numeric evaluation of Cadabra expressions
	evalf	Evaluate an expression to a floating point number
	lambdify	Create a Python function which evaluates an expression with the given parameters

cdb.numeric.integrate
Functions for numeric integration and numeric solutions to differential equations
	integrate_ode	Numerically integrate a system of ODEs over a range of values

cdb.relativity.abstract
Core general relativity package, mainly a library of various standard expressions.
	riemann_from_christoffel	Generates an equality which determines the Riemann tensor in terms of the Christoffel symbols.
	christoffel_from_metric	Generates an equality which determines the Christoffel symbols in terms of the metric.
	riemann_to_ricci	Convert contractions of Riemann tensors to Ricci tensors or scalars.

cdb.sympy.calculus
Use SymPy calculus functionality on Cadabra expressions.
	diff	Differentiate an expression with respect to one or more variables.
	integrate	Integrate a definite or indefinite integral.
	limit	Take the limit of an expression.
	series	Construct a Taylor series.
	factor	Factorise an expression

cdb.sympy.solvers
Access to Sympy solver functions.
	dsolve	Solve (system of) ordinary differential equation(s).
	linsolve	Solve a linear system for unknowns.
	nonlinsolve	Solve a system of non-linear equations.

cdb.utils.develop
Helper functions to aid development, debugging and testing
	class Algorithm	Base class for user defined tree-traversal algorithms
	algo	Decorator for creating tree-traversal algorithms
	time_algo	Simple function to time the execution of an algorithm with given inputs.
	CadabraTestError	Exception derived from AssertionError raised by testing functions when an assertion fails
	test_algo	Decorator to aid defining unit tests for algorithms.
	inherit_kernel	Find a kernel in the stack.

cdb.utils.indices
Additional functionality to deal with indices
	all_index_positions	Generate all possible combinations of covariant and contravariant indices
	replace_index	Rename indices
	get_indices	Return a list of all indices inside \texttt{Node
	get_dummy_indices	Return a list of all dummy indices inside \texttt{Node
	get_free_indices	Return a list of all free indices inside \texttt{Node
	symmetrise_slots	Symmetrise or antisymmetrise an expression in the given slots

cdb.utils.node
Helper functions for working with ExNode objects
	n_indices	Return the number of first-level indices a node has
	nth_index	Gets the nth index of an ExNode object
	n_args	Returns the number of first-level arguments a node has
	nth_arg	Gets the nth first-level argument of an ExNode object
	arg_tuple	Returns a tuple containing the first n arguments of an ExNode object
	n_children	Returns the number of first-level children a node has
	nth_child	Gets the nth first-level child of an ExNode object
	child_tuple	Returns a tuple containing the first n children of an ExNode object
	empty_sum	Returns an Ex object with just one \textbackslash sum node with no children
	empty_product	Returns an Ex object with just one \textbackslash product node with no children

cdb.utils.types
Determining semantic properties of nodes
	is_relational_operator	Returns True for $=$, $<$ and $>$ nodes
	is_relational_expression	Returns True for expressions which contain a top node which is a relational operator and exactly two children

Core algorithms

A	asym	Anti-symmetrise or symmetrise an expression in indicated indices or arguments
C	canonicalise	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.
D	decompose	Decompose a tensor monomial on a given basis of monomials.
	decompose_product	Decompose a product of tensors by using Young projectors.
	distribute	Distribute factors over sums.
	drop_weight	Drop terms with given weight
E	einsteinify	Raise or lower indices of pairs which are both upper or lower.
	eliminate_kronecker	Eliminate Kronecker delta symbols.
	eliminate_metric	Eliminate metrics by raising or lowering indices.
	eliminate_vielbein	Eliminates vielbein objects.
	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
	explicit_indices	Make indices explicit on an expression with implicit indices.
F	factor_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
I	integrate_by_parts	Integrate by parts away from the indicated expression
J	join_gamma	Work out the product of two generalised Dirac gamma matrices.
K	keep_weight	Keep terms with indicated weight
L	lower_free_indices	Make all free indices in an expression subscripts.
	lr_tensor	Compute the tensor product of two Young tableaux
M	map_sympy	Map Sympy algorithms to Cadabra expressions
	meld	Combine terms when allowed by symmetries.
N	nevaluate	Numerically evaluate an expression.
P	product_rule	Apply the Leibnitz rule to a derivative of a product
R	raise_free_indices	Make all free indices in an expression superscripts.
	reduce_delta	Simplify a self-contracted generalised delta.
	rename_dummies	Rename dummy indices, within a set or from one set to another.
	replace_match	Put the result of a sub-computation back into the original expression
	rewrite_indices	Rewrite indices by contracting with vielbein or metric.
S	simplify	Simplify the scalar part of an expression.
	slot_asym	Anti-symmetrise or symmetrise an expression in indicated index slots
	sort_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.
T	take_match	Select a subset of terms in a sum for further computations.
U	untrace	Take objects out of traces
	unwrap	Move objects out of derivatives, accents or exterior products.
V	vary	Generic variation algorithm for functional derivatives.
Y	young_project_product	Project all tensors in a product with their Young tableau projector.
	young_project_tensor	Project tensors with their Young projector.
Z	zoom	Only show selected terms in a sum, and restrict subsequent algorithms to these terms.

Core properties

A	Accent	Turn a symbol into an accent.
	AntiCommuting	Make objects anti-commuting.
	AntiSymmetric	Make an object anti-symmetric in all indices.
C	Commuting	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.
D	DAntiSymmetric	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.
	Determinant	Declares an object to be the determinant of a matrix or metric.
	Diagonal	Declares a tensor to only have non-zero diagonal entries.
	DiracBar	An accent representing the Dirac conjugation operation.
E	EpsilonTensor	A fully anti-symmetric tensor with constant components.
T	Tableau	A Young-tableau object with unlabelled boxes.
G	GammaMatrix	A generalised generator of a Clifford algebra.
I	ImplicitIndex	Indicates that an object carries indices which are not written out.
	IndexInherit	Make an object inherit all indices from its child objects.
	Indices	Declare names to be used as indices.
	Integer	Indicates that an object takes integer values.
	InverseMetric	Make a two-tensor an inverse metric.
K	KroneckerDelta	Turns an object into a generalised Kronecker delta symbol.
L	LaTeXForm	Changes the way in which expressions are displayed.
M	Metric	Makes a two-tensor a metric.
N	NonCommuting	Makes components non-commuting.
P	PartialDerivative	Makes an object a partial derivative.
R	RiemannTensor	Make an object a Riemann curvature tensor.
S	SatisfiesBianchi	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.
	Symbol	Make an object not count as index when it is a sub- or super-script
	Symmetric	Make an object symmetric in all indices.
T	Tableau	A Young-tableau object with unlabelled boxes.
	TableauSymmetry	Gives a tensor a generic Young tableau symmetry.
W	Weight	Attach a labelled weight to an object
	WeightInherit	Make object inherit weights from child nodes