# Computer Algebra ## -- A --

 add_prefix Add prefix to each element of matrix all_vars All variables apart Partial fraction decomposition on a rational function as.character.caracas_symbol Convert symbol to character ask Ask for a symbol's property as_character Coerce symbol to character as_character_matrix Get matrix as character matrix as_diag Construct diagonal matrix from vector as_expr Convert caracas object to R as_func Convert expression into function object. as_sym Convert R object to caracas symbol as_vec Stacks matrix to vector

## -- C --

 cancel Put rational function into standard form collect Collects common powers of a term in an expression colspan Column space (range) of a symbolic matrix colSums_ Form Row and Column Sums columnspace Do linear algebra operation crossprod_ Matrix cross product

## -- D --

 def_sym Define (invisibly) caracas symbols in global environment def_sym_vec Define (invisibly) caracas symbols in global environment denominator Get numerator and denominator of a fraction der Symbolic differentiation of an expression der2 Symbolic differentiation of second order of an expression det Do linear algebra operation diag Matrix diagonal diag-set Replace matrix diagonal diag.caracas_symbol Matrix diagonal diag<- Replace matrix diagonal diag<-.caracas_symbol Replace diagonal diag_ Symbolic diagonal matrix diff_mat Difference matrix dim.caracas_symbol Dimensions of a caracas symbol dim<-.caracas_symbol Dimensions of a caracas symbol doit Perform calculations setup previously do_la Do linear algebra operation drop_remainder Remove remainder term

## -- E --

 eigenval Do linear algebra operation eigenvec Do linear algebra operation eval_to_symbol Create a symbol from a string expand Expand expression expand_func Expand a function expression expand_log Expand a logarithmic expression expand_trig Expand a trigonometric expression eye_sym Special matrices: zeros_sym, ones_sym, eye_sym

## -- F --

 factor_ Expand expression fraction_parts Get numerator and denominator of a fraction free_symbols Get free symbol in expression

## -- G --

 generic-matrices Generate generic vectors and matrices get_basis Get basis get_py Access 'py' object get_sympy Access 'SymPy' directly GramSchmidt Do linear algebra operation

## -- H --

 has_sympy Check if 'SymPy' is available hessian Score and Hessian matrix

## -- I --

 install_sympy Install 'SymPy' int Integrate a function inv Do linear algebra operation is_sym Is object a caracas symbol

## -- J --

 jacobian Compute Jacobian

## -- K --

 kronecker-method Kronecker product of two matrices

## -- L --

 lim Limit of a function linalg Do linear algebra operation listify Convert object to list of elements ls_sym List defined symbols

## -- M --

 Math.caracas_symbol Math functions matrify Creates matrix from array symbol matrix-products Matrix multiplication matrix_ Symbolic matrix matrix_cross_product Matrix cross product matrix_sym Generate generic vectors and matrices matrix_sym_diag Generate generic vectors and matrices matrix_sym_symmetric Generate generic vectors and matrices mat_pow Matrix power

## -- N --

 N Numerical evaluation nullspace Do linear algebra operation numerator Get numerator and denominator of a fraction

## -- O --

 ones_sym Special matrices: zeros_sym, ones_sym, eye_sym Ops.caracas_symbol Math operators

## -- P --

 pinv Do linear algebra operation print.caracas_scaled_matrix Print scaled matrix print.caracas_solve_sys_sol Print solution print.caracas_symbol Print symbol prod_ Product of a function

## -- Q --

 QRdecomposition Do linear algebra operation

## -- R --

 rankMatrix_ Rank of matrix reciprocal_matrix Elementwise reciprocal matrix rowspace Do linear algebra operation rowSums_ Form Row and Column Sums rowSums_colSums Form Row and Column Sums rref Do linear algebra operation

## -- S --

 scale_matrix Create list of factors as in a product score Score and Hessian matrix score_hessian Score and Hessian matrix simplify Simplify expression singular_values Do linear algebra operation solve.caracas_symbol Solve a System of Linear Equations solve_lin Solve a linear system of equations solve_sys Solves a system of non-linear equations special_matrices Special matrices: zeros_sym, ones_sym, eye_sym subs Substitute symbol for value sum.caracas_symbol Summation sum_ Sum of a function symbol Create a symbol symbol_class Ask type of caracas symbol symbol_is_matrix Check if object is a caracas matrix sympy_func Call a SymPy function directly on x sympy_version Get 'SymPy' version sym_class Ask type of caracas symbol sym_inherits Ask if type of caracas symbol is of a requested type

## -- T --

 t.caracas_symbol Transpose of matrix taylor Taylor expansion tcrossprod_ Matrix cross product tex Export object to TeX tex.caracas_scaled_matrix Export scaled matrix to tex texshow Dump latex representation of sympy object. to_list Coerce caracas object to_matrix Coerce caracas object to_something Coerce caracas object to_vector Coerce caracas object trace_ Do linear algebra operation tuplify Convert object to tuple

## -- U --

 unbracket Remove inner-most dimension unscale_matrix Extract matrix from scaled matrix

## -- V --

 vectorfy Creates symbol vector from list of caracas symbols vector_sym Generate generic vectors and matrices

## -- Z --

 zeros_sym Special matrices: zeros_sym, ones_sym, eye_sym

## -- misc --

 %*% Matrix multiplication %*%.caracas_symbol Matrix multiplication %>% Pipe [.caracas_symbol Extract or replace parts of an object [<-.caracas_symbol Extract or replace parts of an object