symengine: symengine: R interface to SymEngine C++ library for symbolic...

In symengine: Interface to the 'SymEngine' Library

symengine: R interface to SymEngine C++ library for symbolic computation

Description

symengine is a R package for symbolic computation.

Details

SymEngine library is a standalone fast symbolic manipulation library written in C++. It allows computation over mathematical expressions in a way which is similar to the traditional manual computations of mathematicians and scientists. The R interface of the library tries to provide a user-friendly way to do symbolic computation in R and can be integrated into other packages to help solve related tasks. The design of the package is somehow similar to the SymPy package in Python. Unlike some other computer algebra systems, it does not invent its own language or domain specific language but uses R language to manipulate the symbolic expressions.

symengine uses the S4 dispatch system extensively to differentiate between calculation over normal R objects and symengine objects. For example, the semantics of sin in expr <- Symbol("x"); sin(expr) is different from the sin used over normal R numbers.

Basic class

Basic is simply a S4 class holding a pointer representing a symbolic expression in symengine. Basic objects have the same S4 class but can have different C-level representations which can be accessed via get_type(). For example, Basic(~ 1/2) will have "Rational" type and Basic(1/2) will have "RealDouble" type.

A Basic object will also have a list of associated sub-components which can be accessed via get_args(). For example, (expr <- S("x") * 3L * S("a")) will have type "Mul", and as.list(get_args(expr)) will show the three factors of the multiplication.

A Basic object can be constructed via Basic(), S(), Symbol(), Constant() or Real().

VecBasic and DenseMatrix class

VecBasic and DenseMatrix are S4 classes representing a symbolic vector or matrix. They can be constructed with Vector(), V(), Matrix(), c(), rbind() or cbind(). For example the following code will construct a 2x3 matrix.

vec <- Vector("a", "b")
cbind(vec, vec^2L, c(S("c"), S("d")))

The following functions are expected to work naturally with VecBasic and DenseMatrix classes.

• [, [[, [<- and [[<- for subsetting and assignment.

• dim(), dim<-, length(), t(), det(), rbind(), cbind(), c(), rep()

• %*% for matrix multiplication

• solve(a, b): solve a %*% x = b where a is a square DenseMatrix and b is a VecBasic/DenseMatrix.

• solve(a): find the inverse of a where a is a square DenseMatrix.

• solve(a, b): solve system of linear equations represented by a (VecBasic) with regards to symbols in b (VecBasic).

Further, the R functions that work on Basic objects (e.g. sin) are expected work on VecBasic and DenseMatrix objects as well in a vectorized manner.

Function bindings

The following is a (incomplete) list of functions that are expected to work with symengine objects. Note that these functions can also be used inside a formula or R language objects and passed to S or Basic or Vector to construct symengine objects. For example S(~ sin(x) + 1) and S(quote(sin(x) + 1)).

• +, -, *, /, ^

• abs, sqrt, exp, expm1, log, log10, log2, log1p

• cos, cosh, sin, sinh, tan, tanh, acos, acosh, asin, asinh, atan, atanh

• cospi, sinpi, tanpi, gamma, lgamma, digamma, trigamma

• lambertw, zeta, dirichlet_eta, erf, erfc

• atan2, kronecker_delta, lowergamma, uppergamma, psigamma, beta

symengine documentation built on Oct. 23, 2022, 5:06 p.m.