Overview

Expressions

Symbolica expression classes

`Expression`	A Symbolica expression
`Transformer`	Operations that transform an expression.
`HeldExpression`	A deferred symbolic computation
`TermStreamer`	A term streamer that can handle large expressions, by streaming terms to and from disk.
`Series`	A series expansion class
`Evaluator`	An optimized evaluator of an expression.
`FunctionDefinition`	A function definition and its evaluator registration settings.
`EvaluatorInstructions`	A portable instruction stream for evaluating an expression.
`EvaluatorFunction`	A non-inlined function evaluator referenced by an instruction stream.
`CompiledRealEvaluator`	A compiled evaluator of an expression.
`CompiledComplexEvaluator`	A compiled evaluator of an expression.
`CompiledSimdRealEvaluator`	A compiled evaluator of an expression that packs 4 double using SIMD.
`CompiledSimdComplexEvaluator`	A compiled evaluator of an expression that packs 4 double using SIMD.
`CompiledCudaRealEvaluator`	A compiled evaluator of an expression that uses CUDA for GPU acceleration.
`CompiledCudaComplexEvaluator`	A compiled evaluator of an expression that uses CUDA for GPU acceleration.
`Replacement`	A replacement of a pattern by a right-hand side.
`Condition`	A deferred relation or logical combination consumed by Transformers, matching, and solve.
`PatternRestriction`	A restriction on wildcards.
`MatchIterator`	An iterator over matches.
`ReplaceIterator`	An iterator over single replacements.
`Symbol`	Built-in Symbolica symbols.
`SymbolAttribute`	Specifies the attributes of a symbol.
`AtomType`	Specifies the type of the atom.
`AtomTree`	A Python representation of a Symbolica expression.
`ParseMode`	Specifies the parse mode.
`PrintMode`	Specifies the print mode.
`FormattedOutput`	A formatted string with rich notebook display representations.
`CompareOp`	One of the following comparison operators: `<`,`>`,`<=`,`>=`,`==`,`!=`.
`IntegrationStep`	One accepted transformation in a symbolic integration derivation.

Polynomials

Symbolica polynomial classes

`Polynomial`	A Symbolica polynomial with rational coefficients.
`IsolatedRoot`	A certified isolated root in the complex plane.
`RootLocation`	Proven location of an isolated root relative to the coordinate axes.
`FiniteFieldPolynomial`	A Symbolica polynomial with finite field coefficients.
`NumberFieldPolynomial`	A Symbolica polynomial with coefficients in an algebraic number field.
`RationalPolynomial`	A Symbolica rational polynomial.
`FiniteFieldRationalPolynomial`	A Symbolica rational polynomial.

Solving

Exact solutions, domains, and coverage

`SolutionSet`	Exact solutions returned by `Expression.solve`
`Solution`	One equality-solution branch: Expression assignments and validity conditions
`SolutionCondition`	A formula or domain restriction under which a solution branch is valid.
`SolveDomain`	A domain supported by the exact equation solver.
`Integers`	The integer solving domain, an alias for `SolveDomain.Integers`
`Rationals`	The rational solving domain, an alias for `SolveDomain.Rationals`
`Reals`	The real solving domain, an alias for `SolveDomain.Reals`
`Complexes`	The complex solving domain, an alias for `SolveDomain.Complexes`
`SolveError`	Base exception for invalid solve requests or failures to obtain the requested result.
`UnsupportedProblem`	The equations require a solving method that is not supported.
`IncompleteCoverage`	The requested conclusion cannot be established for all relevant cases.

Numbers

Exact integers and arbitrary-precision numeric values

`Integer`	Number-theoretic operations on Python integers, including factoring and primality testing.
`Float`	An immutable real number with arbitrary binary precision.
`ComplexFloat`	An immutable complex number with arbitrary-precision Float components.

Linear algebra

Linear algebra classes

Matrix A matrix with rational polynomial coefficients.

Graph theory

Graph theory classes

`Graph`	A graph that supported directional edges, parallel edges, self-edges and expression data on the nodes and edges
`HalfEdge`	A half-edge in a graph that connects to one vertex, consisting of a direction (or `None` if undirected) and edge data.

Numerical integration

Numerical integration classes

`NumericalIntegrator`	A numerical integrator for high-dimensional integrals.
`Sample`	A sample from the Symbolica integrator
`Probe`	A probe that is used to access the Jacobian weight of a point or region of interest
`RandomNumberGenerator`	A reproducible, fast, non-cryptographic random number generator suitable for parallel Monte Carlo simulations

Miscellaneous

Miscellaneous functions

`S`	Create new symbols from `names`
`N`	Create a new Symbolica number from an int, a float, or a string
`E`	Parse a Symbolica expression from a string.
`T`	Create a new transformer that maps an expression.
`P`	Parse a string a polynomial, optionally, with the variable ordering specified in `vars`
`use_custom_logger`	Enable logging using Python’s logging module instead of using the default logging
`get_namespace`	Get the Symbolica namespace for the calling module
`set_namespace`	Set the Symbolica namespace for the calling module
`get_version`	Get the current Symbolica version.
`is_licensed`	Check if the current Symbolica instance has a valid license key set.
`set_license_key`	Set the Symbolica license key for this computer
`request_hobbyist_license`	Request a key for non-professional use for the user `name`, that will be sent to the e-mail address `email`.
`request_trial_license`	Request a key for a trial license for the user `name` working at `company`, that will be sent to the e-mail address `email`.
`request_sublicense`	Request a sublicense key for the user `name` working at `company` that has the site-wide license `super_license`
`get_license_key`	Get the license key for the account registered with the provided email address.
`set_library_key`	Set the Symbolica library key for this Python package