Package: caracas 2.1.2.9004

Mikkel Meyer Andersen

caracas: Computer Algebra

Computer algebra via the 'SymPy' library (<https://www.sympy.org/>). This makes it possible to solve equations symbolically, find symbolic integrals, symbolic sums and other important quantities.

Authors:Mikkel Meyer Andersen [aut, cre, cph], Søren Højsgaard [aut, cph]

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manual.pdf |manual.html✨
card.svg |card.png
caracas/json (API)
NEWS

# Install 'caracas' in R:

install.packages('caracas', repos = c('https://r-cas.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/r-cas/caracas/issues

Pkgdown/docs site:https://r-cas.github.io

On CRAN:

8.74 score 31 stars 1 packages 108 scripts 574 downloads 145 exports 59 dependencies

Last updated from:5adbca4cd6. Checks:9 OK. Indexed: yes.

Target	Result	Time
linux-devel-x86_64	OK	180
source / vignettes	OK	222
linux-release-x86_64	OK	184
macos-release-arm64	OK	153
macos-oldrel-arm64	OK	237
windows-devel	OK	187
windows-release	OK	219
windows-oldrel	OK	276
wasm-release	OK	126

Exports:%*%add_prefix all_vars apart ar1_sum as_character as_character_matrix as_diag as_expr as_func as_piecewise as_sym as_vec ask basis_col basis_intersect basis_leftnull basis_null basis_orthcomp basis_row bdiag_c_cancel chol collect colspan colSums_columnspace crossprod_def_sym def_sym_vec denominator der der2 det det_determinant diag diag_diag<-diff_mat do_la doit drop_remainder eigen_eigenval eigenvec eval_to_symbol expand expand_func expand_log expand_trig eye_sym factor_fraction_parts free_symbols get_basis get_py get_sympy GramSchmidt har1_sum has_sympy hessian install_sympy int intersectionspace inv inv_block inv_woodbury is_sym is_sym_list jacobian leftnullspace length_lim listify ls_sym LUdecomposition mat_pow matrify matrix_matrix_sym matrix_sym_diag matrix_sym_symmetric N nullspace numerator ones_sym optim_sym orthcompspace piecewise_cond piecewise_expr pinv prod_qr qr.Q qr.R QRdecomposition rankMatrix_re_sym reciprocal_matrix rep_rowspace rowSums_rref scale_matrix score seq_simplify singular_values solve_lin solve_lower_triangular solve_sys solve_upper_triangular subs subs_expr subs_list sum_svd_sym_class sym_inherits symbol symbol_class symbol_is_matrix sympy_func sympy_version taylor tcrossprod_tex tex_align tex_eq tex_list texshow to_list to_matrix to_vector toeplitz_toeplitz_sum trace_tuplify unbracket unscale_matrix vector_sym vectorfy zeros_sym

Dependencies:backports blockmatrix boot broom cli colorspace cowplot cpp11 Deriv doBy dplyr farver forecast fracdiff generics ggplot2 glue gtable here isoband jsonlite labeling lattice lifecycle lmtest magrittr MASS Matrix microbenchmark modelr nlme nnet pillar pkgconfig png purrr R6 rappdirs RColorBrewer Rcpp RcppArmadillo RcppTOML reticulate rlang rprojroot S7 scales stringi stringr tibble tidyr tidyselect timeDate urca utf8 vctrs viridisLite withr zoo

01 - Introduction to 'caracas'

Rendered froma01-introduction.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2022-06-29
Started: 2022-06-29

03 - Objects in 'caracas'

Rendered froma03-objects.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2025-01-09
Started: 2022-08-31

05 - Extending 'caracas'

Rendered froma05-extend-caracas.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2025-01-09
Started: 2022-06-30

11 - Linear algebra in caracas

Mikkel Meyer Andersen and Søren Højsgaard

Rendered froma11-linear-algebra.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2025-01-09
Started: 2022-06-30

16 - Mixed models with caracas

Rendered froma16-mixed-models.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2026-01-27
Started: 2025-01-06

21 - Concentration and covariance matrix in an autoregressive model and in a dynamic linear model

Mikkel Meyer Andersen and Søren Højsgaard

Rendered froma21-ar-ssm.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2023-10-10
Started: 2022-06-29

22 - Fastest route through the forest

Rendered froma22-fastest-route.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2023-08-11
Started: 2022-06-29

91 - Using the 'SymPy' object directly

Rendered froma91-sympy-object.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2022-06-30
Started: 2022-06-30

95 - Arbitrary precision arithmetic

Rendered froma95-arbitrary-precision-arithmetic.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2022-06-30
Started: 2022-06-29

99 - Reference

Rendered froma99-reference.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2025-05-05
Started: 2022-06-29

Chunk engine for easy tex output in Rmarkdown and Quarto

Rendered froma30-chunk-engine.Rmdusingknitr::rmarkdownon May 27 2026.

Last update: 2023-08-16
Started: 2023-08-14

Citation

Development and contributors

Readme and manuals

Help Manual

Help page	Topics
Extract or replace parts of an object	[.caracas_symbol
Extract or replace parts of an object	[<-.caracas_symbol
Add prefix to each element of matrix	add_prefix
All variables	all_vars
Partial fraction decomposition on a rational function	apart
Coerce symbol to character	as_character
Get matrix as character matrix	as_character_matrix
Construct diagonal matrix from vector	as_diag
Convert caracas object to R	as.expression.caracas_solve_sys_sol as.expression.caracas_symbol as_expr
Convert expression into function object.	as.function.caracas_symbol as_func
Convert R object to caracas symbol	as_sym
Stacks matrix to vector	as_vec
Convert symbol to character	as.character.caracas_symbol
Ask for a symbol's property	ask
Creates block diagonal caracas matrix	bdiag_
Put rational function into standard form	cancel
Collects common powers of a term in an expression	collect
Column space (range) of a symbolic matrix	colspan
Cumulative Sums	cumsum.caracas_symbol
Define (invisibly) caracas symbols in global environment	def_sym def_sym_vec
Symbolic differentiation of an expression	der
Symbolic differentiation of second order of an expression	der2
Determinant methods for caracas_symbol	determinant,caracas_symbol,logical-method determinant,caracas_symbol,missing-method determinant-caracas
Symbolic diagonal matrix	diag_
Replace matrix diagonal	diag-set diag<-
Matrix diagonal	diag,caracas_symbol-method
Replace diagonal	diag<-.caracas_symbol
Difference matrix	diff_mat
Dimensions of a caracas symbol	dim.caracas_symbol
Dimensions of a caracas symbol	dim<-.caracas_symbol
Do linear algebra operation	do_la
Perform calculations setup previously	doit
Remove remainder term	drop_remainder
Create a symbol from a string	eval_to_symbol
Expand a function expression	expand_func
Expand a logarithmic expression	expand_log
Expand a trigonometric expression	expand_trig
Expand expression	factor_
Get numerator and denominator of a fraction	denominator fraction_parts numerator
Get free symbol in expression	free_symbols
Generate generic vectors and matrices	generic-matrices matrix_sym matrix_sym_diag matrix_sym_symmetric vector_sym
Get basis	get_basis
Access 'py' object	get_py
Access 'SymPy' directly	get_sympy
Check if 'SymPy' is available	has_sympy
Head and tail for caracas matrices	head.caracas_symbol head_tail_caracas tail.caracas_symbol
Install 'SymPy'	install_sympy
Integrate a function	int
Inverse of block matrix	inv_block
Inverse using woodburys matrix identity	inv_woodbury
Is object a caracas symbol	is_sym
Is list of caracas symbols	is_sym_list
Compute Jacobian	jacobian
Kronecker product of two matrices	kronecker kronecker,caracas_symbol,caracas_symbol-method
Length of (caracas) object	length_
Limit of a function	lim
Do linear algebra operation	chol,caracas_symbol-method columnspace det det_ eigenval eigenvec eigen_ GramSchmidt intersectionspace inv leftnullspace linalg LUdecomposition nullspace orthcompspace pinv qr,caracas_symbol-method qr.Q,QRdecomposition-method qr.R,QRdecomposition-method QRdecomposition rowspace singular_values svd_ trace_
Finds the basis of the (right) null space.	basis_col basis_intersect basis_leftnull basis_null basis_orthcomp basis_row is_caracas_matrix linear_algebra rref
Convert object to list of elements	listify
List defined symbols	ls_sym
Matrix power	mat_pow
Math functions	Math.caracas_symbol
Creates matrix from array symbol	matrify
Symbolic matrix	matrix_
Matrix cross product	crossprod,caracas_symbol,missing-method crossprod_ matrix_cross_product tcrossprod,caracas_symbol,missing-method tcrossprod_
Matrix multiplication	%% %%.caracas_symbol matrix-products
Numerical evaluation	N
Math operators	Ops.caracas_symbol
General purpose optimization of caracas symbol.	optim_sym
Create a piecewise object	as_piecewise piecewise piecewise_cond piecewise_expr [.caracas_piecewise
Print scaled matrix	print.caracas_scaled_matrix
Print solution	print.caracas_solve_sys_sol
Print symbol	print.caracas_symbol
Product of a function	prod_
Rank of matrix	rankMatrix_
Refresh as symbol	re_sym
Elementwise reciprocal matrix	reciprocal_matrix
Form Row and Column Sums	colSums_ rowSums_ rowSums_colSums
Create list of factors as in a product	scale_matrix
Score and Hessian matrix	hessian score score_hessian
Simplify expression	expand,caracas_symbol-method simplify
Solve a linear system of equations	solve_lin
Solves a system of non-linear equations	solve_sys
Solve lower or upper triangular system	solve_lower_triangular solve_triangular solve_upper_triangular
Solve a System of Linear Equations	solve.caracas_symbol
Special matrices: zeros_sym, ones_sym, eye_sym	eye_sym ones_sym special_matrices zeros_sym
Structured sums for Toeplitz, AR(1), and heterogeneous AR(1) matrices.	ar1_sum har1_sum structured_sums toeplitz_sum
Substitute symbols in an expression	subs
Substitute symbols (expression interface)	subs_expr
Substitute symbol for value	subs_list
Sum of a function	sum_
Summation	sum.caracas_symbol
Ask type of caracas symbol	sym_class
Ask if type of caracas symbol is of a requested type	sym_inherits
Create a symbol	symbol
Ask type of caracas symbol	symbol_class
Check if object is a caracas matrix	symbol_is_matrix
Call a SymPy function directly on x	sympy_func
Get 'SymPy' version	sympy_version
Transpose of matrix	t.caracas_symbol
Taylor expansion	taylor
Export object to TeX	tex
Export caracas objects to TeX	tex_align tex_caracas tex_eq tex_list
Export scaled matrix to tex	tex.caracas_scaled_matrix
Dump latex representation of sympy object.	texshow
Coerce caracas object	to_list to_matrix to_something to_vector
Topelitz matrix as caracas matrix.	toeplitz_
Convert object to tuple	tuplify
Remove inner-most dimension	unbracket
caracas version of standard R functions	c_ rep_ seq_ underscore
Extract unique elements	unique.caracas_symbol
Extract matrix from scaled matrix	unscale_matrix
Create a vector along	vec_along
Creates symbol vector from list of caracas symbols	vectorfy