Some symbolic math functions for lazy boys and girls

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Documentation for package ‘lazy.symbolic’ version 1.0.0.20250731

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lazy.symbolic パッケージに含まれる主な関数のヘルプファイル一覧です。 （日本語のヘルプは所々抜けています。）
カテゴリ別のヘルプは以下の lazy.symbolic もしくは lazy.symbolic_JPH を参照してください。

A B C D E F G I J K L M N P Q R S T U V W misc

-- A --

a2l Convert array to list
a2m Convert array to supermatrix
AnalyzeExpr Decompose an Expression into Additive Terms and Multiplicative Factors
analyze_3d_val analyze three dots and values argument
analyze_expr Decompose an Expression into Additive Terms and Multiplicative Factors
analyze_expr_JPH 式の構造の表示
analyze_three_dots Analyze Three Dots and Return the Names and the Values
analyze_three_dots_JPH ThreeDots ... を解析して名前と値を返す
assign_at_expr assign new expr at path

-- B --

basis Standard Basis Vector
b_diag Makes a Block Diagonal Matrix from the Arguments
b_diag_JPH 引数からブロック対角行列を作成します

-- C --

cancel_double_expr Remove multiple consecutive t's or inv's from an expression
ceiling_n Return the Ceiling and Power of the Input using Radix (Base) of n
chkginv Check if the the second matrix is a generalized inverse of the first one, or vice versa.
chkginv_JPH 第二の行列が第一の行列の一般化逆行列であるか、またはその逆かをチェック
compose_MatProd compose MatProd
cprod Cartesian product of many vectors and matrices

-- D --

decompose_additive Decompose an expresion into additive terms
decompose_MatProd Decompose Matrix Product
demomat Set up a matrix whose elements consist of row and col numbers.
demomat_JPH 分かりやすい行列の生成
Det Determinant of a Symbolic Matrix by Sweeping
DetL Determinant of a Symbolic Matrix by Laplace Expansion
DetL_JPH ラプラス展開による記号行列の行列式
Det_JPH スウィープ演算による記号行列の行列式
Diag Diag(x) creats a diagonam matrix from its argument vector or matrix
Diag_JPH Diag(x) は、与えられたベクトルまたは行列から対角行列を生成します
diag_to_hp Convert diag(X) to I*X, the Hadamar product
distribute_t Ditstribute Transposition over Additive Terms
distribute_tr Distribute functions to each of the additive terms
dist_t Ditstribute Transposition over Multiplicative Factors
dist_t1 Ditstribute Transposition over Multiplicative Factors
drop_parens drop parens
drop_parens_JPH 不要な括弧を削除

-- E --

easy_parse Parsing text w/o writing text= and trailing [[1]]
Eval Evaluate Symbolic Matrix after Replacement
Eval_JPH 置換後の記号行列を評価する
Expand Expand Expressions by Distributing a Multiplicative Factor
expand_expr expand for expr
Expand_JPH 乗法因子を分配して式を展開する
expr2list Display the structure of input expression as recursive list
expr2list_JPH 入力式の構造を再帰リストとして表示する

-- F --

FindFactors Find multiplicative factors in a term
FindFuncs Find Function Calls in an Expression
FindTerms Find additive terms in an expression
find_a_term Find a term separated by a multiplicative operator
find_factors Decompose a Term into Multiplicative Factors separated by ' *, /, %*%, %\@%'.
find_factors_JPH 項を乗法的の因子に分解
find_terms Decompose an Expression into Additive Terms separated by '+' or '-'
find_terms_JPH 式を項（+ または - で区切られた項）に分解
find_varfunc Find Variables and Functions in an Expression
FreeQ Returns TRUE if expression is free of varname
funcinfo Returns the body of a function

-- G --

gen_random_expr Generate Random Expression
gen_random_expr_JPH ランダムな式を生成
getSM Extract a submatrix from a supermatrix
Ginv Generalized Inverse
Ginv_JPH 一般化逆行列（Generalized Inverse）
gmatch Return the captured value for each group
gradma numeric value of the analytic first derivative of a function
gradma_JPH 関数の解析的な一階導関数の数値値を計算
gradmn numerical first derivative of a function
gradmn_JPH 関数の数値的一階微分
grep_expr grep for expr
groupmatch Return the captured value for each group
gsub_expr gsub for an expression

-- I --

insertLaTex1Addin Insert toLaTeX
insert_str Insert string between substr(expr,1,from-1) and substr(expr,to+1)
insert_str_JPH 文字列に別の文字列を指定位置で挿入
interleave Interleave the columns of Two Matrices
Inv Matrix Inversion
invGE Matrix Inversion by Gaussian Elimination
invGE_JPH ガウス消去法による行列の逆行列
Inv_JPH 行列の逆行列計算
is.number Check if a string vector contains numbers only.
is.varname Check if the argument is a valid variable name
is_solo Check if the input is a single object
is_valid Check If the Input Expression is Valid
is_valid_JPH 入力式が正しいかチェックする関数

-- J --

JacobianMat Calculation of Jacobian Matrix
JacobianMat_JPH ヤコビ行列の計算

-- K --

Kmat Commutation Matrix
Kmat_JPH 交換行列（Commutation Matrix）
KP Symbolic Expression of the i-j element of the Kronecker Product
KP_JPH クロネッカー積の i-j 要素の記号式

-- L --

l2a Convert list to array
lazy.symbolic lazy.symbolic: Collection of some useful symbolic tools for lazy boys and girls
lazy.symbolic_JPH lazy.symbolic: Collection of some useful symbolic tools for lazy boys and girls　記号演算のための関数群
linear_expand Distribute functions to each of the additive terms
linear_expand_expr Lienarly Distribute Functions
linear_expand_JPH 項ごとに関数を分配する
locbalpar Return the locations of the matching parentheses in a string.
locbalpar_JPH 文字列において対応する括弧の位置を返す。
lv Retruns the Last Value
lv_JPH 最後に評価された値（最後の値）を返す

-- M --

m2a Convert supermatrix to array
make_minus_sign Add + sign before unary - sign
map Map function to each element of exp
mark_soper Mark Special Operator by Single Alpha
mat2sum Express the i-j element of an Matrix Expression using Summation Operators
mat2sum_JPH 行列式の i-j 要素を総和演算子で表現する
matindex Returns the Index to Convert vec(mat) to vec(t(mat)), etc.
matindex_JPH vec(mat) を vec(t(mat)) に変換するためのインデックスを返す関数
matKTimes Symbolic Kronecker Product
matReplace Replace the Elements of a Symbolic Matrix
matReplace_JPH 記号行列の要素置換
matSweep Symbolic Matrix Sweep Operator
matSweep_JPH 記号行列のスイープ演算子
matSwp Matrix Sweep Operator
matSwp_JPH 行列スイープ演算子
matTimes Symbolic Multiplication of Two or More Matrices
mD Derivative of a Scalar Function with respect to a Matrix
mD0 Core function for differentiation
mD_JPH スカラー関数の行列に関する微分
Mh2Mv Convert a horizontally stacked supermatrix to a vertially stacked one.
Minus Difference of Two or More Symbolic Expressions
modify_call Wrap or Repalce a Call in an Expression
modify_math_operators Modify Mathematical Operators for Symbolic Math
modify_math_operators_JPH 数値演算子の拡張
modSM<- Assign values to the submatrix of a supermatrix
move_det_out Move a multiplicative determinant factor to the left most position
Mv2Mh Convert a vertically stacked supermatrix to a horizontally stacked one.

-- N --

nFactors Calculate the Number of Factors in a Term
nterms Count the Number of Terms in an Expression
nterms2 Calculate the Number of Terms in an Expression

-- P --

P Orthogonal Projection Operators to the Column Space of the Input
Plus Sum of Two or More Symbolic Expression
pmat Generate a permutation matrix to switch row or column.
pmat_JPH 行または列を入れ替える行列の生成
Print Print multiple objects together with their names (Compact and better version of Print)
Printb Print Super Matrix ( Partitioned Matrix, Block Matrix ) with Separators.
printb Print Super Matrix ( Partitioned Matrix, Block Matrix ) with Separators.
Printb_JPH スーパー行列（分割行列、ブロック行列）を区切り付きで表示
Printm Print multiple objects together with their names (Compact and better version of Print)
printm Print multiple objects together with their names (Compact and better version of Print)
printm_JPH 複数オブジェクトを名前付きでまとめて表示 （Print の簡潔で改良版） 英語のヘルプファイルは: printm
print_tex_as_html Print the LaTex as html in RStudio Viewer pane or a RMarkdown (Quarto) document
Prod Symbolic Product of All the Elements

-- Q --

Q Projection Operators to the Orthogonal Complement of the Column Space of the Input
QRGS QR decomposition of X matrix by the Gram Schmidt orthogonalization or Finding non redundant columns of X
QRGS_JPH X 行列の QR 分解（グラム・シュミットの直交化法）または X の非冗長列の抽出

-- R --

recompose_MatProd Recompose MatProd
reduce_expr_I Remove multiplicative identity matrix I
reduce_expr_sign Remove multiple consecutive signs from an expression
reduce_sign_expr Simplify/Modify the Signs of an Expression
remove_paren Remove redundant parentheses from an expression
remove_paren0 Remove redundant parentheses around a single term from an expression
remove_paren_JPH 式から冗長な括弧を除去
replacec Replace Characters by New Ones
replacec_JPH 文字列を新しい文字列に置き換える
repmat Stack a matrix n times either horizontally or vertically.
repmat_JPH 行列を水平方向または垂直方向に n 回繰り返して積み重ねる
revchar Reverse string

-- S --

safe_deparse Deparse an expression with maximum width.cutoff
safe_deparse_JPH Deparse an expression with maximum width.cutoff
Seq Smart Sequence Generation
Seq_JPH スマートなシーケンス生成
show_ast Display the structure of input expression
show_ast_JPH 入力式の構造を表示
Simplify Simplify Symbolic Expressions (very primitive version)
simplify_power Simplify Power
ssq Returns the (doubly weighted) sum of squares of all the elements of A
ssq_JPH 行列 A の (重み付き) 二乗和を返す
Sum Symbolic Sum of All the Elements
sum2mat Express Summation Expressions in Matrix Form
sum2mat0 Express Summation Expressions in Matrix Form
sum2mat_JPH 総和記号を行列表現に変換する
sum2sum Convert s(exp,scope) to sum of exps
sumDisplay Display the Structure of Summations
sumEval Evaluate Summation:
sumEval_JPH 総和式の評価
sumExpand Expand (Distribute) summaiton
suminfo Information of Nested Summations
sumMoveIn Move summation to the right
sumSimplify Simplify an expression containing summation
supermat Declare a supermatrix with SMdim attribute
SymbolicOps Examples of Symbolic Operations
SymbolicOps_JPH 拡張された数値演算子の例

-- T --

Times Elementwise Multiplication of Two or More Symbolic Vectors/Matrices
toLaTeX Convert the input string to LaTex and display it on the RStudio viewer
to_latex Convert the input string to LaTex and display it on the RStudio viewer
to_latex_JPH 入力文字列を LaTeX に変換し、RStudio ビューアに表示
tp Transposition of a Fully Symbolic Partitioned Matrix
tr trace of the input matrix
tr2vecK Conversion of the Trace of the Product of Several Matrices using vec operator and Kronecker Product
tr2vecK_JPH 複数行列の積のトレースを vec 演算子とクロネッカー積で変換
trace_reorder Reorder the arguments of the tr and * functions
transp Transpose each matrix contained in a list/array/supermatrix..
transpose_expr Smart Transposition
tr_JPH 行列のトレース

-- U --

unary_reorder_expr Reorder unary oparators
unmark_soper Recover the Marked Special Operators

-- V --

varlist Interprete sas-like abbreviated variable list
varlist_JPH SAS風の省略変数リストの解釈
vec Vectorization of a matrix
vec2vecK Conversion of the vec of Matrix Product using vec operator and Kronecker Product
vec2vecK_JPH 行列の積の vec を vec 演算子と Kronecker 積で変換
vecdiag Returns diagonal elements of A as a vector
vech Vectorization of the lower-half or upper-half of a square matrix
vechindex Returns the index to convert vech(Mat) to Mat and vice versa.
vechindex_JPH vech(Mat) と Mat を相互変換するためのインデックスを返す
vechinv Recover the Symmetric Matrix from its lower or upper half elements stored in a vector created by vech function.
vechinv_JPH vech 関数で作成されたベクトルから対称行列を復元
vech_JPH 正方行列の下三角または上三角のベクトル化
vecvecindex Returns the index to convert vec(Mat) to vec(t(Mat)) and vice versa.
vecvecindex_JPH vec(Mat) を vec(t(Mat)) に変換するためのインデックスを返す およびその逆
vec_JPH 行列のベクトル化

-- W --

wrap_hp wrap Hadamar product with parens for apparance

-- misc --

%/.% Mathematica like postfix replacement
%m% Minus operator for Elementwise Difference
%p% Plus operator for Elementwise Sum
%T% matTimes operator for Matrix Product