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]

caracas_2.1.2.9004.tar.gz
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manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
caracas/json (API)

# 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:

Conda:

8.58 score 31 stars 1 packages 124 scripts 556 downloads 145 exports 58 dependencies

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

TargetResultTimeFilesSyslog
linux-devel-x86_64OK195
source / vignettesOK229
linux-release-x86_64OK195
macos-release-arm64OK145
macos-oldrel-arm64OK111
windows-develOK205
windows-releaseOK229
windows-oldrelOK267
wasm-releaseOK156

Exports:%*%add_prefixall_varsapartar1_sumas_characteras_character_matrixas_diagas_expras_funcas_piecewiseas_symas_vecaskbasis_colbasis_intersectbasis_leftnullbasis_nullbasis_orthcompbasis_rowbdiag_c_cancelcholcollectcolspancolSums_columnspacecrossprod_def_symdef_sym_vecdenominatorderder2detdet_determinantdiagdiag_diag<-diff_matdo_ladoitdrop_remaindereigen_eigenvaleigenveceval_to_symbolexpandexpand_funcexpand_logexpand_trigeye_symfactor_fraction_partsfree_symbolsget_basisget_pyget_sympyGramSchmidthar1_sumhas_sympyhessianinstall_sympyintintersectionspaceinvinv_blockinv_woodburyis_symis_sym_listjacobianleftnullspacelength_limlistifyls_symLUdecompositionmat_powmatrifymatrix_matrix_symmatrix_sym_diagmatrix_sym_symmetricNnullspacenumeratorones_symoptim_symorthcompspacepiecewise_condpiecewise_exprpinvprod_qrqr.Qqr.RQRdecompositionrankMatrix_re_symreciprocal_matrixrep_rowspacerowSums_rrefscale_matrixscoreseq_simplifysingular_valuessolve_linsolve_lower_triangularsolve_syssolve_upper_triangularsubssubs_exprsubs_listsum_svd_sym_classsym_inheritssymbolsymbol_classsymbol_is_matrixsympy_funcsympy_versiontaylortcrossprod_textex_aligntex_eqtex_listtexshowto_listto_matrixto_vectortoeplitz_toeplitz_sumtrace_tuplifyunbracketunscale_matrixvector_symvectorfyzeros_sym

Dependencies:backportsblockmatrixbootbroomclicolorspacecowplotcpp11DerivdoBydplyrfarverforecastfracdiffgenericsggplot2gluegtablehereisobandjsonlitelabelinglatticelifecyclelmtestmagrittrMASSMatrixmodelrnlmennetpillarpkgconfigpngpurrrR6rappdirsRColorBrewerRcppRcppArmadilloRcppTOMLreticulaterlangrprojrootS7scalesstringistringrtibbletidyrtidyselecttimeDateurcautf8vctrsviridisLitewithrzoo

16 - Mixed models with caracas
Introduction | Linear mixed model | The likelihood | Shoes data | Fitting model with caracas | Programmatic approach | Maximizing the profile likelihood | Asymptotic variance of the MLE | Maximizing the full likelihood | Comparison with gls() and lmer() | Comparison with gls() - if available | Comparison with lmer() - if available
Rendered froma16-mixed-models.Rmdusingknitr::rmarkdown

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

99 - Reference
Quick start | Sums | Products | Integrals | Limits | Derivatives | Taylor expansion | Linear algebra | Solve | Assumptions | Substitution | Subsetting | Interactively show $\LaTeX$ representation | Using SymPy directly | Output | Options
Rendered froma99-reference.Rmdusingknitr::rmarkdown

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

03 - Objects in 'caracas'
Variables, names, symbols etc. | Creating symbols | Classes | Indexing | Quick start | Linear algebra
Rendered froma03-objects.Rmdusingknitr::rmarkdown

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

05 - Extending 'caracas'
Rendered froma05-extend-caracas.Rmdusingknitr::rmarkdown

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

11 - Linear algebra in caracas
Introduction | Elementary matrix operations | Creating matrices / vectors | Matrix-matrix sum and product | Hadamard (elementwise) product | Vector operations | Reciprocal matrix | Matrix inverse; solve system of linear equations | Generalized (Penrose-Moore) inverse; solve system of linear equations [TBW] | More special linear algebra functionality | QR decomposition | Eigenvalues and eigenvectors | Inverse, Penrose-Moore pseudo inverse | Additional functionality for linear algebra | Characteristic polynomial | Rank | Cofactor | Echelon form | Cholesky factorisation | Gram Schmidt | Reduced row-echelon form (rref) | Column space, row space and null space | Singular values, svd
Rendered froma11-linear-algebra.Rmdusingknitr::rmarkdown

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

21 - Concentration and covariance matrix in an autoregressive model and in a dynamic linear model
Autoregressive model ($AR(1)$) | Dynamic linear model
Rendered froma21-ar-ssm.Rmdusingknitr::rmarkdown

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

Chunk engine for easy tex output in Rmarkdown and Quarto
Multiple lines | Check with no echo | Custom tex() | Notes
Rendered froma30-chunk-engine.Rmdusingknitr::rmarkdown

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

22 - Fastest route through the forest
Information given | Length of line segments
Rendered froma22-fastest-route.Rmdusingknitr::rmarkdown

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

91 - Using the 'SymPy' object directly
Using SymPy directly | Elaborate example | Simple example with assumptions | Another example with assumptions
Rendered froma91-sympy-object.Rmdusingknitr::rmarkdown

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

95 - Arbitrary precision arithmetic
An example | Another example
Rendered froma95-arbitrary-precision-arithmetic.Rmdusingknitr::rmarkdown

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

01 - Introduction to 'caracas'
Quick start | Linear algebra | More examples
Rendered froma01-introduction.Rmdusingknitr::rmarkdown

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

Readme and manuals

Help Manual

Help pageTopics
Extract or replace parts of an object[.caracas_symbol
Extract or replace parts of an object[<-.caracas_symbol
Add prefix to each element of matrixadd_prefix
All variablesall_vars
Partial fraction decomposition on a rational functionapart
Coerce symbol to characteras_character
Get matrix as character matrixas_character_matrix
Construct diagonal matrix from vectoras_diag
Convert caracas object to Ras.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 symbolas_sym
Stacks matrix to vectoras_vec
Convert symbol to characteras.character.caracas_symbol
Ask for a symbol's propertyask
Creates block diagonal caracas matrixbdiag_
Put rational function into standard formcancel
Collects common powers of a term in an expressioncollect
Column space (range) of a symbolic matrixcolspan
Cumulative Sumscumsum.caracas_symbol
Define (invisibly) caracas symbols in global environmentdef_sym def_sym_vec
Symbolic differentiation of an expressionder
Symbolic differentiation of second order of an expressionder2
Determinant methods for caracas_symboldeterminant,caracas_symbol,logical-method determinant,caracas_symbol,missing-method determinant-caracas
Symbolic diagonal matrixdiag_
Replace matrix diagonaldiag-set diag<-
Matrix diagonaldiag,caracas_symbol-method
Replace diagonaldiag<-.caracas_symbol
Difference matrixdiff_mat
Dimensions of a caracas symboldim.caracas_symbol
Dimensions of a caracas symboldim<-.caracas_symbol
Do linear algebra operationdo_la
Perform calculations setup previouslydoit
Remove remainder termdrop_remainder
Create a symbol from a stringeval_to_symbol
Expand a function expressionexpand_func
Expand a logarithmic expressionexpand_log
Expand a trigonometric expressionexpand_trig
Expand expressionfactor_
Get numerator and denominator of a fractiondenominator fraction_parts numerator
Get free symbol in expressionfree_symbols
Generate generic vectors and matricesgeneric-matrices matrix_sym matrix_sym_diag matrix_sym_symmetric vector_sym
Get basisget_basis
Access 'py' objectget_py
Access 'SymPy' directlyget_sympy
Check if 'SymPy' is availablehas_sympy
Head and tail for caracas matriceshead.caracas_symbol head_tail_caracas tail.caracas_symbol
Install 'SymPy'install_sympy
Integrate a functionint
Inverse of block matrixinv_block
Inverse using woodburys matrix identityinv_woodbury
Is object a caracas symbolis_sym
Is list of caracas symbolsis_sym_list
Compute Jacobianjacobian
Kronecker product of two matriceskronecker kronecker,caracas_symbol,caracas_symbol-method
Length of (caracas) objectlength_
Limit of a functionlim
Do linear algebra operationchol,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 elementslistify
List defined symbolsls_sym
Matrix powermat_pow
Math functionsMath.caracas_symbol
Creates matrix from array symbolmatrify
Symbolic matrixmatrix_
Matrix cross productcrossprod,caracas_symbol,missing-method crossprod_ matrix_cross_product tcrossprod,caracas_symbol,missing-method tcrossprod_
Matrix multiplication%*% %*%.caracas_symbol matrix-products
Numerical evaluationN
Math operatorsOps.caracas_symbol
General purpose optimization of caracas symbol.optim_sym
Create a piecewise objectas_piecewise piecewise piecewise_cond piecewise_expr [.caracas_piecewise
Print scaled matrixprint.caracas_scaled_matrix
Print solutionprint.caracas_solve_sys_sol
Print symbolprint.caracas_symbol
Product of a functionprod_
Rank of matrixrankMatrix_
Refresh as symbolre_sym
Elementwise reciprocal matrixreciprocal_matrix
Form Row and Column SumscolSums_ rowSums_ rowSums_colSums
Create list of factors as in a productscale_matrix
Score and Hessian matrixhessian score score_hessian
Simplify expressionexpand,caracas_symbol-method simplify
Solve a linear system of equationssolve_lin
Solves a system of non-linear equationssolve_sys
Solve lower or upper triangular systemsolve_lower_triangular solve_triangular solve_upper_triangular
Solve a System of Linear Equationssolve.caracas_symbol
Special matrices: zeros_sym, ones_sym, eye_symeye_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 expressionsubs
Substitute symbols (expression interface)subs_expr
Substitute symbol for valuesubs_list
Sum of a functionsum_
Summationsum.caracas_symbol
Ask type of caracas symbolsym_class
Ask if type of caracas symbol is of a requested typesym_inherits
Create a symbolsymbol
Ask type of caracas symbolsymbol_class
Check if object is a caracas matrixsymbol_is_matrix
Call a SymPy function directly on xsympy_func
Get 'SymPy' versionsympy_version
Transpose of matrixt.caracas_symbol
Taylor expansiontaylor
Export object to TeXtex
Export caracas objects to TeXtex_align tex_caracas tex_eq tex_list
Export scaled matrix to textex.caracas_scaled_matrix
Dump latex representation of sympy object.texshow
Coerce caracas objectto_list to_matrix to_something to_vector
Topelitz matrix as caracas matrix.toeplitz_
Convert object to tupletuplify
Remove inner-most dimensionunbracket
caracas version of standard R functionsc_ rep_ seq_ underscore
Extract unique elementsunique.caracas_symbol
Extract matrix from scaled matrixunscale_matrix
Create a vector alongvec_along
Creates symbol vector from list of caracas symbolsvectorfy