Maxima on3lib21_test Memo
INOUE Takakatsu 更新:2022-04-18
- 言語エンジンeng_langの環境設定
- on3ライブラリー
- 2. ライブラリ on3lib の呼び出しとヘルプ-1
- 3. on3env() : on3ライブラリーのロードとlispファイルの書き出し
- 4. 関数 on3() : 区間の定義と判定
- 5. 関数 on3simp() : on3()関数の積の簡約化
- 6. 関数 on3std() : on3()関数の標準化
- 7. 関数 on3typep() : 式からon3式タイプを調べ結果を返す
- 8. 関数 on3info() : expr に含まれる変数varの関数on3(var…)の情報をリストで返す
- 9. 関数 on3decomp() : on3一般式の排他的分解処理(端点は数値のみ, 多変数対応)
- 10. 関数 on3decomp_one() : 端点は数値のみ, 1変数毎 → on3decompm に吸収予定
- 12. 関数 on3decomp21() : 変数毎の排他的区間分解(未定端点:仮定の設定,on3有理式まで対応)
- 12a. 関数 on3decompm() : 未定端点:仮定の設定,多変数on3多項式(3変数まで)の排他的区間分解
- 13. 関数 on3info() : expr に含まれる変数varの関数on3(var…)の情報をリストで返す
- 14. 関数 outLev() : on3info()の結果(リスト)の取り込み
- 14. 関数 find_key() : ツール1 キー付き引数の扱い
- 14a. 関数 ass_set(), fact_var(), fact_forget(), killvars() : ツール2 仮定の設定,表示,解除
- 15. 関数 on3ev() : on3poly の各関数部を{factor,expand,ratsimp}した表現を返す
- 16. 関数 on3diff() : on3関数式の微分
- 17. 関数 on3integ() : on3関数式の積分
- 18. 関数 on3integ19() : on3関数式の積分
- 19. 関数 on3solve() : on3 関数方程式の求解 (多変数対応版)
- 20. 関数 on3D2G() : 矩形領域 D(x,y) 変換 t=x+y, u=y のとき G(t,u) を求める
- 21. 関数 on3dim2_uni2() : 一様分布に従う独立な確率変数の和の分布
- 22. 関数 on3dim2_exp2() : 指数分布に従う独立な確率変数の和の分布
- 23. 関数 on3pw() : on3関数のカプセル化(停止中)
- 24. 関数 on3ineq_ex() : 不等式の求解
- その他のツール
言語エンジンeng_langの環境設定
HOME <- system("echo ${HOME}", intern=T)
setup_file <- paste(HOME,"/bin/eng_lang_setup.R",sep="")
source(setup_file)## === knitr, reticulate, eng_lang are go. ===1. maxima の実行例
(linel:70)$ /* 行長を指定(コメント例) */
exp1 : (x+y)^2; /* 式の定義 */
exp2 : expand(exp1); /* 式exp1を展開 */
(display2d:false)$ /* 表示形式の変更 */
factor(exp2); /* 式exp2を因数分解 */
solve(x^2-2*x-1=0,x); /* 2次方程式の求解 */
solve([a*x+b*y=e,c*x+d*y=f],[x,y]); /* 連立方程式の求解 */
/* 作図例 */
draw2d( terminal='png, file_name="test1_files/fig1",
title="Two simple plots",
xlabel="x",ylabel="y",grid=true,
color=red,key="A sinus",
explicit(sin(x),x,1,10),
color=blue,line_type=dots,key="A cosinus",
explicit(cos(x),x,1,10)
)$## ~/bin/go TMP/tmp_lang/chunk-1.mx > TMP/tmp_lang/chunk-1.out 2>&1
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-1.mx")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-1.mx
## linel:70
## exp1:(x+y)^2
## 2
## (y + x)
## exp2:expand(exp1)
## 2 2
## y + 2 x y + x
## display2d:false
## factor(exp2)
## (y+x)^2
## solve(x^2-2*x-1 = 0,x)
## [x = 1-sqrt(2),x = sqrt(2)+1]
## solve([a*x+b*y = e,c*x+d*y = f],[x,y])
## [[x = -(d*e-b*f)/(b*c-a*d),y = (c*e-a*f)/(b*c-a*d)]]
## draw2d(terminal = 'png,file_name = "test1_files/fig1",
## title = "Two simple plots",xlabel = "x",ylabel = "y",
## grid = true,color = red,key = "A sinus",
## explicit(sin(x),x,1,10),color = blue,line_type = dots,
## key = "A cosinus",explicit(cos(x),x,1,10))
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-1.mx"
test1_files/fig.pngのグラフ
on3ライブラリー
2. ライブラリ on3lib の呼び出しとヘルプ-1
batchload("/home/inoue/.maxima/max-init.mac")$
on3lib(21); /* on3ライブライリーの呼び出し */
on3help(); /* ヘルプ */
if false then (
functions /* on3ライブラリの関数一覧 */
)$
if false then (
print("--- 1. on3simp_ex ---------"), on3simp_ex(),
print("--- 2. on3std_ex ----------"), on3std_ex(),
print("--- 3. on3decomp_ex -------"), on3decomp_ex(),
print("--- 4. on3ev_ex -----------"), on3ev_ex(),
print("--- 5. on3diff_ex ---------"), on3diff_ex(),
print("--- 6. on3integ_ex --------"), on3integ_ex(),
print("--- 7. on3solve_ex --------"), on3solve_ex(),
print("--- 8. on3dim2_uni2 -------"), on3dim2_uni2('noplot,'noview),
print("--- 9. on3dim2_exp2 -------"), on3dim2_exp2('noplot,'noview),
print("---10. on3pw_ex -----------"), on3pw_ex()
)$## ~/bin/go TMP/tmp_lang/chunk-2.mx > TMP/tmp_lang/chunk-2.out 2>&1
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-2.mx")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-2.mx
## batchload("/home/inoue/.maxima/max-init.mac")
## *** INOUE's Personal Init File : ~/.maxima/max-init.mac ***
## on3lib(21)
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## "-- batchload: ~/Maxlib-20/on3lib21.mx & on3env() ---"
## on3help()
## === on3lib.mx (定義域を伴った関数の数式操作) 一覧 ===
## 0. on3help() : on3関数の機能一覧
## 1. on3(z,z0,z1,arg) : on3関数(関数定義域)の定義[変数，下限，上限，開閉]
## 2. f2l(on3funcs) : on3関数式をon3リスト形式に変換する[多変数対応版]
## 3. l2f(on3list) : on3リスト形式をon3関数形式に変換する[多変数対応版]
## 4. on3simp(on3funcs) : on3関数式の積に関する簡約化(on3decompに組み込み)
## 5. on3decomp(funcs,[args]) : [多変数対応版]
## on3関数式の和(差)において素な区間(領域)への分解表現を与える
## 6. on3std(on3func) : on3一般式の標準化
## 7. on3ev(on3func,arg) : 関数部に{factor,ratsimp,expand}を作用する
## 8. on3solve(funcs,vars) : on3関数式の求解[多変数対応版]
## 9. on3diff(func,var,p) : on3関数式の微分[多変数対応版]
## 10. on3integ(func,var,[args]) : on3関数式の積分[多変数対応版]
## on3integ(func,var) : 不定積分関数(分布関数に対応)
## on3integ(func,var,x0,x1) : 定積分値
## 11. on3chgvar2(funcs) : on3関数式f(x,y)を変換(t=x+y,u=y)した関数g(t,u)を返す
## 12. on3show(funcs) : on3関数式の表示[多変数対応版]
##
## 13. on3pw(funcs) : on3関数式のカプセル化
## ex. on3_ex(), on3simp_ex(), on3std_ex(),
## on3decomp_ex(), on3show_ex(), on3ev_ex(),
## on3diff_ex(), on3integ_ex(), on3solve_ex(),
## on3chgvar2_ex() on3pw_ex(),
## ex. on3dim2_uni2() : 一様分布に従う独立確率変数の和の分布
## on3dim2_exp2() : 指数分布に従う独立確率変数の和の分布
## ex. on3test() : on3_ex, on3list_ex, on3simp_ex, on3decomp_ex の連続実行
## ---> 関数表示 dispfun(on3,on3simp,...) または grind(on3)
##
## "--- end of on3help ---"
## if false then functions
## if false
## then (print("--- 1. on3simp_ex ---------"),on3simp_ex(),
## print("--- 2. on3std_ex ----------"),on3std_ex(),
## print("--- 3. on3decomp_ex -------"),on3decomp_ex(),
## print("--- 4. on3ev_ex -----------"),on3ev_ex(),
## print("--- 5. on3diff_ex ---------"),on3diff_ex(),
## print("--- 6. on3integ_ex --------"),on3integ_ex(),
## print("--- 7. on3solve_ex --------"),on3solve_ex(),
## print("--- 8. on3dim2_uni2 -------"),on3dim2_uni2('noplot,'noview),
## print("--- 9. on3dim2_exp2 -------"),on3dim2_exp2('noplot,'noview),
## print("---10. on3pw_ex -----------"),on3pw_ex())
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-2.mx"3. on3env() : on3ライブラリーのロードとlispファイルの書き出し
batchload("/home/inoue/Maxlib-20/on3lib21.mx")$
on3env()$
on3('ex)$
max_save()$ /* lisp ファイル /tmp/max_save.lisp に書き出す */## ~/bin/go TMP/tmp_lang/chunk-3.mx > TMP/tmp_lang/chunk-3.out 2>&1
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-3.mx")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-3.mx
## batchload("/home/inoue/Maxlib-20/on3lib21.mx")
## on3env()
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## on3('ex)
## === on3('ex) : on3 関数の使用例 ===
## ▼ 基本動作
## ★ ◎ on3(0,1,3,co) = 0
## ★ ◎ on3(1,1,3,co) = 1
## ★ ◎ on3(3,1,3,co) = 0
## ★ ◎ on3(x,1,3,co) = on3(x,1,3,co)
## ★ ◎ on3(3,1,b,co) = on3(3,1,b,co)
## ★ ◎ on3(x,minf,inf,oo) = on3(x,minf,inf,oo)
## <- ( = 1 であるが,on3decomp()の仕様のため無処理とする)
## ▼ inf/minf の取扱
## ★ ◆ 不一致 ◆ on3(inf,1,inf,co)
## = 0
## <- ans = 1
## ★ ◎ on3(inf+1,1,inf,co) = 0
## ▼ 変数式の取扱
## ★ ◎ on3(a,a-1,a+3,co) = 1
## ★ ◎ on3(a+3,a-1,a+3,co) = 0
## ★ ◎ on3(t-u,t-u,(-u)+t+3,co) = 1
## ★ ◎ on3((-u)+t+3,t-u,(-u)+t+3,co) = 0
## ▼ on3()関数のリスト変換,eval評価
## ★ ◎ on3(x^2,1,4,co,list) = [on3,x^2,1,4,co]
## ★ ◎ on3(x^2,1,4,co,eval) = on3(x,1,2,co)+on3(x,-2,-1,oc)
## ★ ◎ on3(log(x),1,2,cc,eval) = on3(x,%e,%e^2,cc)
## ★ ◎ on3(sin(x),1/2,1,cc,eval) = on3(x,%pi/6,%pi/2,cc)
## ★ ◎ on3(sin(2*x+%pi/4),1/2,1,oo,eval) = on3(x,-%pi/24,%pi/8,oo)
## max_save()
## save("/tmp/max_save.lisp", all)
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-3.mx"- 注:上記の実行結果の前に◎印があるものは,実行結果が作成者の意図した結果に一致することを示す｡一致しない場合は,作成者の意図した結果を ans = … で示す｡
4. 関数 on3() : 区間の定義と判定
on3()$
on3('ex)$## ~/bin/go TMP/tmp_lang/chunk-4.mxl > TMP/tmp_lang/chunk-4.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-4.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-4.mxl
## on3()
## --on3('help)--
## 機能: 変数zが不等式 zl <= z < zr (lc=co) のとき1を返しそのたのとき0を返す
## 文法: on3(z,zl,zr,lr,...) lrは開(o)閉(c)を表す. 追加引数としてlist,evalが可能
## 例示:
## on3(z,zl,zr,co); 変数zが不等式 zl <= z < zr のとき1を返しそのたのとき0を返す
## on3(0,1,3,co); -> 0 on3(1,1,3co) -> 1 on3(3,1,3,co) -> 0
## on3(2,1,3,co); -> 1
## on3(x,1,3,co); -> on3(x,1,3,co) 判定不能の場合は定義式を返す
## on3(a,a-1,a+3,co); -> 1
## on3(x^2,1,4,co,list); -> [on3,x^2,1,4,co] (リスト形式に変換)
## on3(log(x),1,2,cc,eval); -> on3(x,%e,%e^2,cc) (evalによる評価変換)
## メモ: findstr('on3) -> on3 を含む関数名一覧を標示する
## --end of on3('help)--
##
## on3('ex)
## === on3('ex) : on3 関数の使用例 ===
## ▼ 基本動作
## ★ ◎ on3(0,1,3,co) = 0
## ★ ◎ on3(1,1,3,co) = 1
## ★ ◎ on3(3,1,3,co) = 0
## ★ ◎ on3(x,1,3,co) = on3(x,1,3,co)
## ★ ◎ on3(3,1,b,co) = on3(3,1,b,co)
## ★ ◎ on3(x,minf,inf,oo) = on3(x,minf,inf,oo)
## <- ( = 1 であるが,on3decomp()の仕様のため無処理とする)
## ▼ inf/minf の取扱
## ★ ◆ 不一致 ◆ on3(inf,1,inf,co)
## = 0
## <- ans = 1
## ★ ◎ on3(inf+1,1,inf,co) = 0
## ▼ 変数式の取扱
## ★ ◎ on3(a,a-1,a+3,co) = 1
## ★ ◎ on3(a+3,a-1,a+3,co) = 0
## ★ ◎ on3(t-u,t-u,(-u)+t+3,co) = 1
## ★ ◎ on3((-u)+t+3,t-u,(-u)+t+3,co) = 0
## ▼ on3()関数のリスト変換,eval評価
## ★ ◎ on3(x^2,1,4,co,list) = [on3,x^2,1,4,co]
## ★ ◎ on3(x^2,1,4,co,eval) = on3(x,1,2,co)+on3(x,-2,-1,oc)
## ★ ◎ on3(log(x),1,2,cc,eval) = on3(x,%e,%e^2,cc)
## ★ ◎ on3(sin(x),1/2,1,cc,eval) = on3(x,%pi/6,%pi/2,cc)
## ★ ◎ on3(sin(2*x+%pi/4),1/2,1,oo,eval) = on3(x,-%pi/24,%pi/8,oo)
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-4.mxl"5. 関数 on3simp() : on3()関数の積の簡約化
on3simp()$
on3simp('ex)$## ~/bin/go TMP/tmp_lang/chunk-5.mxl > TMP/tmp_lang/chunk-5.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-5.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-5.mxl
## on3simp()
## --begin of on3simp('help)--
## 機能: on3(z,zl,zr,lr) 関数の積に関する簡約化(簡約化規則 on3rule2 を使用する)
## 文法: on3simp(on3()の積)
## 例示: on3simp(x * on3(x,0,3,co) * on3(x,0,3,co)) -> x*on3(x,0,3,co)
## on3simp(x* on3(x,minf,3,co) * x^2 * on3(x,2,4,co)) -> x^3*on3(x,2,3,co)
## on3simp(x^3 * on3(x,0,3,co) / (x*on3(x,1,5,co))) -> x^2*on3(x,1,3,co)
## on3simp(1/(f1*on3(x,1,5,co) + f2*on3(x,2,8,co)) * on3(x,3,10,co))
## -> on3(x,3,10,co)/(f2*on3(x,2,8,co)+f1*on3(x,1,5,co))
## --end of on3simp('help')--
##
## on3simp('ex)
## --begin of on3simp('ex)--
## 例．on3関数の積/商の簡約化
## ★ ◎ on3simp(x * on3(x,0,3,co) * on3(x,0,3,co)) = x*on3(x,0,3,co)
## ★ ◎ on3simp(x^3 * on3(x,0,3,co) / (x * on3(x,0,3,co)))
## = x^2*on3(x,0,3,co)
## ★ ◎ on3simp(x* on3(x,minf,3,co) * x^2 * on3(x,2,4,co))
## = x^3*on3(x,2,3,co)
## ★ ◎ on3simp(x^3 * on3(x,0,3,co) / (x*on3(x,1,5,co)))
## = x^2*on3(x,1,3,co)
## ★ ◎ on3simp(x* on3(x,1,3,co) * x^3 * on3(x,2,4,co) * x * on3(x,2,5,co))
## = x^5*on3(x,2,3,co)
## ★ ◎ on3simp((f1*on3(x,1,5,co) + f2*on3(x,2,8,co)) * on3(x,3,10,co))
## = f2*on3(x,3,8,co)+f1*on3(x,3,5,co)
## ★ ◎ on3simp(1/(f1*on3(x,1,5,co) + f2*on3(x,2,8,co)) * on3(x,3,10,co))
## = on3(x,3,10,co)/(f2*on3(x,2,8,co)+f1*on3(x,1,5,co))
## on3(x, 3, 10, co)
## out = -----------------------------------------
## f2 on3(x, 2, 8, co) + f1 on3(x, 1, 5, co)
## ★ ◎ on3simp((f1*on3(x,1,5,co) + f2*on3(x,2,8,co))*on3(x,minf,inf,oo))
## = f2*on3(x,2,8,co)+f1*on3(x,1,5,co)
## 例0．on3関数の積(評価不能の場合と置数後の評価)
## CS: a = a , ex0 = x^3 * on3(x,0,3,co) / (x*on3(x,a,3,co)) , ex0f =
## on3simp(x^3 * on3(x,0,3,co) / (x*on3(x,a,3,co)))
## ++ 仮定: assume : a <= 3 を追加し,処理を続行する ++
## (%t3) out = x^2*on3(x,0,3,co)*on3(x,a,3,co)
## CS: a = 2
## (%t4) a = 2
## (%t5) out2 = x^2*on3(x,2,3,co)
## --end of on3simp('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-5.mxl"6. 関数 on3std() : on3()関数の標準化
on3std()$
on3std('ex)$## ~/bin/go TMP/tmp_lang/chunk-6.mxl > TMP/tmp_lang/chunk-6.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-6.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-6.mxl
## on3std()
## --begin of on3std('help)--
## 機能: 式から指定変数に関するon3標準型(微分･積分可能な多項式)表現を返す
## R1: 非on3式(on3none) → 無処理
## R2: on3単項式(on3monoone,on3mono) → 無処理
## R3: on3多項式(on3poly) → 定数項 f0 があれば f0*on3(x,minf,inf,oo) とする
## R4: on3有理式(on3inv,on3polyinv) → on3排他的区分分解形(on3多項式になる)を返す
## 文法: on3std(expr,var,...)
## 例示: on3std(expr) (1変数の場合) on3std(expr,var) (2変数以上の場合)
## --end of on3std('help')--
##
## on3std('ex)
## --begin of on3std('ex)--
## == on3std_ex : 標準型(変数毎,on3有理式はon3decomp21()が必要) ===
## ◆ 例1
## ex = f0
## on3vars(ex) -> [] var -> var on3typep(ex) -> on3none
## ◎ out = f0
## ◆ 例2
## ex = on3(x,1,2,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3monoone
## ◎ out = on3(x,1,2,co)
## ◆ 例3
## ex = -on3(x,1,2,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3mono
## ◎ out = -on3(x,1,2,co)
## ◆ 例4
## ex = on3(x,1,2,co)+f0
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f0*on3(x,minf,inf,oo)+on3(x,1,2,co)
## ◆ 例5
## ex = f1*f2*on3(x,1,2,co)+f0
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f0*on3(x,minf,inf,oo)+f1*f2*on3(x,1,2,co)
## ◆ 例6
## ex = f1*log(x)*on3(x,1,2,co)+f0
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## ◆ 例7
## ex = f1*on3(x,5,7,co)+f1*on3(x,3,5,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f1*on3(x,5,7,co)+f1*on3(x,3,5,co)
## ◆ 例8
## ex = f2*on3(x,2,5,co)+f1*on3(x,1,3,co)+f3*on3(x,0,inf,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f2*on3(x,2,5,co)+f1*on3(x,1,3,co)+f3*on3(x,0,inf,co)
## ◆ 例9
## ex = 1/(f2*on3(x,3,7,co)+f1*on3(x,1,5,co))+f0*on3(x,3,5,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3polyinv
## ◎ out = on3(x,5,7,co)/f2+((f0*(f2+f1)+1)*on3(x,3,5,co))/(f2+f1)+on3(x,1,3,co)/f1
## ◆ 例10
## ex = 1/((f2*on3(x,3,7,co))/(f22*on3(x,3,5,co)+f21*on3(x,1,3,co))+f1*on3(x,1,5,co))+f0
##
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3polyinv
## ◎ out =
## f0*on3(x,5,7,co)+(((f0*f1+1)*f22+f0*f2)*on3(x,3,5,co))/(f1*f22+f2)
## +((f0*f1+1)*on3(x,1,3,co))/f1
## ◆ 例11
## ex = x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)+((1-x^2)*on3(x,0,1,oo))/2+sin(x)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out =
## sin(x)*on3(x,minf,inf,oo)+x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)
## -((x^2-1)*on3(x,0,1,oo))/2
## ◆ 例12
## ex = x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)+((1-x^2)*on3(x,0,1,oo))/2+myfunc(x)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out =
## myfunc(x)*on3(x,minf,inf,oo)+x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)
## -((x^2-1)*on3(x,0,1,oo))/2
## ◆ 例13
## ex = %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co)
## ◆ 例14
## ex = f2*on3(x,c,d,co)+f1*on3(x,a,b,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f2*on3(x,c,d,co)+f1*on3(x,a,b,co)
## ◆ 例15
## ex = f2(x)*on3(x,2,4,co)+f1(x)*on3(x,1,3,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f2(x)*on3(x,2,4,co)+f1(x)*on3(x,1,3,co)
## ◆ 例16
## ex = f2(x)*on3(x,c,d,co)+f1(x)*on3(x,a,b,co)
## on3vars(ex) -> [x] var -> x on3typep(ex) -> on3poly
## ◎ out = f2(x)*on3(x,c,d,co)+f1(x)*on3(x,a,b,co)
## ◆ 例17
## ex = f1*log(x)*on3(x,1,2,co)*on3(y,3,4,co)+f0
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = f1*log(x)*on3(x,1,2,co)*on3(y,3,4,co)+f0*on3(x,minf,inf,oo)
## ◆ 例18
## ex = f1*on3(x,1,2,co)*on3(y,3,4,co)+f2+f0
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = f1*on3(x,1,2,co)*on3(y,3,4,co)+(f2+f0)*on3(x,minf,inf,oo)
## ◆ 例19
## ex = f0*on3(y,5,6,co)+f1*on3(x,1,2,co)*on3(y,3,4,co)
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = f0*on3(x,minf,inf,oo)*on3(y,5,6,co)+f1*on3(x,1,2,co)*on3(y,3,4,co)
## ◆ 例20
## ex = f1*on3(x,3,7,co)*on3(y,4,8,co)+f2*on3(x,1,5,co)*on3(y,2,6,co)
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = f1*on3(x,3,7,co)*on3(y,4,8,co)+f2*on3(x,1,5,co)*on3(y,2,6,co)
## ◆ 例21
## ex =
## (y+x+5)*(on3(x,2,3,co)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-3,-2,co)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-2,2,co)*on3(y,-sqrt(9-x^2),-sqrt(4-x^2),cc)
## +on3(x,-2,2,co)*on3(y,sqrt(4-x^2),sqrt(9-x^2),cc))
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out =
## on3(x,2,3,co)*(y+x+5)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-3,-2,co)*(y+x+5)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-2,2,co)*((y+x+5)*on3(y,-sqrt(9-x^2),-sqrt(4-x^2),cc)
## +(y+x+5)*on3(y,sqrt(4-x^2),sqrt(9-x^2),cc))
## ◆ 例22
## ex = r*on3(r,2,3,cc)*(r*sin(t)+r*cos(t)+5)*on3(t,0,2*%pi,cc)
## on3vars(ex) -> [r,t] var -> r on3typep(ex) -> on3poly
## ◎ out = on3(r,2,3,cc)*(r^2*sin(t)+r^2*cos(t)+5*r)*on3(t,0,2*%pi,cc)
## ◆ 例23
## ex = f2*on3(x,1,2,co)*on3(y,3,4,co)+f1*on3(x,1,2,co)*on3(y,3,4,co)
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = (f2+f1)*on3(x,1,2,co)*on3(y,3,4,co)
## ◆ 例24
## ex = f2*on3(x,1,2,co)*on3(y,4,6,co)+f1*on3(x,1,2,co)*on3(y,3,5,co)
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3poly
## ◎ out = on3(x,1,2,co)*(f2*on3(y,4,6,co)+f1*on3(y,3,5,co))
## ◆ 例25
## ex = 1/(f2*on3(x,1,2,co)*on3(y,4,6,co)+f1*on3(x,1,2,co)*on3(y,3,5,co))
## on3vars(ex) -> [x,y] var -> x on3typep(ex) -> on3inv
## ◎ out = on3(x,1,2,co)/(f2*on3(y,4,6,co)+f1*on3(y,3,5,co))
## ◆ 例26
## ex = on3(x,1,2,co)*on3(y,3,4,co)*on3(z,5,6,co)
## on3vars(ex) -> [x,y,z] var -> x on3typep(ex) -> on3mono
## ◎ out = on3(x,1,2,co)*on3(y,3,4,co)*on3(z,5,6,co)
## ◆ 例27
## ex = f1*on3(x,1,2,co)*on3(y,3,4,co)*on3(z,5,6,co)+f2*on3(y,3,4,co)*on3(z,5,6,co)
## on3vars(ex) -> [x,y,z] var -> x on3typep(ex) -> on3poly
## ◎ out =
## f2*on3(x,minf,inf,oo)*on3(y,3,4,co)*on3(z,5,6,co)
## +f1*on3(x,1,2,co)*on3(y,3,4,co)*on3(z,5,6,co)
## --end of on3std('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-6.mxl"7. 関数 on3typep() : 式からon3式タイプを調べ結果を返す
on3typep()$
on3typep('ex)$## ~/bin/go TMP/tmp_lang/chunk-7.mxl > TMP/tmp_lang/chunk-7.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-7.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-7.mxl
## on3typep()
## --begin of on3typep('help)--
## 機能: 式からon3式タイプを調べ結果を返す
## on3noe(非on3式), on3monoone(on3単項式,関数部1), on3mono(on3単項式),
## on3inv(on3分数式), on3poly(on3多項式), on3polyinv(on3有理式),
## on3unknown(その他のon3式),
## 文法: on3typep(expr,...)
## 例示:
## --end of on3typep('help')--
##
## on3typep('ex)
## --begin of on3typep('ex)--
## ---<on3タイプ情報>---
## ex = f0
## out:on3typep(ex) = on3none
## ---<on3タイプ情報>---
## ex = on3(x,1,2,co)
## out:on3typep(ex) = on3monoone
## ---<on3タイプ情報>---
## ex = -on3(x,1,2,co)
## out:on3typep(ex) = on3mono
## ---<on3タイプ情報>---
## ex = on3(x,1,2,co)+f0
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f0-f1*on3(x,1,2,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1*f2*on3(x,1,2,co)+f0
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1*log(x)*on3(x,1,2,co)+f0
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1*on3(x,5,7,co)+f1*on3(x,3,5,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f2*on3(x,2,5,co)+f1*on3(x,1,3,co)+f3*on3(x,0,inf,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = 1/(f2*on3(x,3,7,co)+f1*on3(x,1,5,co))+f0*on3(x,3,5,co)
## out:on3typep(ex) = on3polyinv
## ---<on3タイプ情報>---
## ex = 1/((f2*on3(x,3,7,co))/(f22*on3(x,3,5,co)+f21*on3(x,1,3,co))+f1*on3(x,1,5,co))+f0
##
## out:on3typep(ex) = on3polyinv
## ---<on3タイプ情報>---
## ex = x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)+((1-x^2)*on3(x,0,1,oo))/2+sin(x)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)+((1-x^2)*on3(x,0,1,oo))/2+myfunc(x)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1*on3(x,a,b,co)
## out:on3typep(ex) = on3mono
## ---<on3タイプ情報>---
## ex = f2*on3(x,c,d,co)+f1*on3(x,a,b,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1(x)*on3(x,1,2,co)
## out:on3typep(ex) = on3mono
## ---<on3タイプ情報>---
## ex = f2(x)*on3(x,2,4,co)+f1(x)*on3(x,1,3,co)
## out:on3typep(ex) = on3poly
## ---<on3タイプ情報>---
## ex = f1(x)*on3(x,a,b,co)
## out:on3typep(ex) = on3mono
## ---<on3タイプ情報>---
## ex = f2(x)*on3(x,c,d,co)+f1(x)*on3(x,a,b,co)
## out:on3typep(ex) = on3poly
## --end of on3typep('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-7.mxl"8. 関数 on3info() : expr に含まれる変数varの関数on3(var…)の情報をリストで返す
on3info()$
on3info('ex)$## ~/bin/go TMP/tmp_lang/chunk-8.mxl > TMP/tmp_lang/chunk-8.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-8.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-8.mxl
## on3info()
## --begin of on3info('help)--
## 機能: expr に含まれる変数varの関数on3(var...)の情報をリストで返す
## 結果のリストはoutLev()で取り出せる.
## on3多項式を前提とするため,定数項が存在する合も考慮されている(変数毎のon3stdの機能を有する)
## 引数に'std がある場合は指定された変数に関する標準化の結果を返す
## expr が on3有理式の場合は on3decomp21(expr,x,[仮定1,...]) によりon3多項式化を得る.
## 文法: on3info(expr,x,...) or on3info(expr)
## on3info(expr,x,'factor), on3info(expr,x,'std)
## 例示: on3info(f1*log(x)*on3(x,1,2,co)+f0, x,'std)
## -> f0*on3(x,minf,1,oo) + (f0+f1)*on3(x,1,2,co) + f0*on3(x,2,inf,co) (標準化)
## --end of on3info('help')--
##
## on3info('ex)
## --begin of on3info('ex)--
## ---begin of on3info_ex---
## ◆ 例0 ex0 = f1*log(x)*on3(x,1,2,co)+f0 <- on3std未処理の場合
## on3info(ex0,x) =
## [expr = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co),var = x,
## Lon3 = [[on3,x,1,2,co],[on3,x,minf,inf,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)],Lon3coef = [f1*log(x),f0],
## Lon3lr0 = [minf,1,2,inf],Lon3lr = [1,2],undefpnts = [],
## outf = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)]
## ◆ on3info(ex0,x,'std) = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- 'std 指定の場合
## ◆ 例1 ex1 = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- on3std処理済みの場合
## on3info(ex1,x) =
## [expr = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co),var = x,
## Lon3 = [[on3,x,1,2,co],[on3,x,minf,inf,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)],Lon3coef = [f1*log(x),f0],
## Lon3lr0 = [minf,1,2,inf],Lon3lr = [1,2],undefpnts = [],
## outf = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)]
## ◆ 例1-2 ex1 = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- 結果リストの一括取り込みと一括削除の例
## ★ (outLev(on3info(ex1,x),"test_"), /* 結果リストをtest_*で取り込む */
## c0show(test_Lon3f), c0show(test_Lon3coef), /* 取り込みリストの表示 */
## killvars(["test_"]) /* 取り込みリストの一括削除 */ , values)
## test_Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)]
## test_Lon3coef = [f1*log(x),f0]
## out =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,std,expr,
## var,wL,ic,Lon3,Lon3lr0,Lon3lr,on3v,on3f,on3coef,Lon3v,Lon3f,Lon3coef,
## undefpnts,outL,outf,ex0,ex1,ex2,ex22,ex3,ex4,ex,cmds,L,out,chk,ans,hlp,hlpL,
## cmdsansL,cmdsL,w_out,chkm,k]
## ◆ 例2-1 ex2 = (f*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## <- 有理式の分母に適用した場合
## ratdenom(ex2) = on3(x,a,b,co)*f1+f2*on3(x,c,d,co)
## on3info(ratdenom(ex2),x) =
## [expr = f2*on3(x,c,d,co)+f1*on3(x,a,b,co),var = x,
## Lon3 = [[on3,x,a,b,co],[on3,x,c,d,co]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,a,b,co),on3(x,c,d,co)],Lon3coef = [f1,f2],Lon3lr0 = [a,b,c,d],
## Lon3lr = [a,b,c,d],undefpnts = [false,false,false,false],
## outf = f2*on3(x,c,d,co)+f1*on3(x,a,b,co)]
## ◆ 例2-2 ex22 =
## (f4*on3(x,2,4,co)+f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## <- 有理式に適用した場合
## ex22 = (f4*on3(x,2,4,co)+f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## on3info(ex22,x,'std) =
## (f4*on3(x,2,4,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## +(f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
##
## ■ on3decomp21(ex22,x,[1<a,a<2,2<c,c<3,3<b,b<4,4<d]) を実行しon3多項式(排他的分解済)を得る
##
## on3decomp21(ex22,x,[1 < a,a < 2,2 < c,c < 3,3 < b,b < 4,4 < d]) =
## ((f4+f3)*on3(x,c,3,co))/(f2+f1)+(f4*on3(x,b,4,co))/f2+(f3*on3(x,a,2,co))/f1
## +(f4*on3(x,3,b,co))/(f2+f1)+((f4+f3)*on3(x,2,c,co))/f1
## ◆ 例3 ex3 = ex3 第1引数が単変数でない場合
## ex3 = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co)
## on3info(ex3,t) =
## [expr = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co),var = t,
## Lon3 = [[on3,t-u,1,3,co],[on3,t-u,u,inf,co]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(t-u,1,3,co),on3(t-u,u,inf,co)],Lon3coef = [f1,f2],Lon3lr0 = [1,3,inf,u],
## Lon3lr = [1,3,u],undefpnts = [false],outf = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co)]
## ◆ 例4 ex4 = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc)
## 2変数関数の場合
## on3info(ex4,y) =
## [expr = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc),var = y,
## Lon3 = [[on3,y,2,5,cc],[on3,y,minf,3,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(y,2,5,cc),on3(y,minf,3,oo)],Lon3coef = [f2(x,y),on3(x,1,8,co)*f1(x,y)],
## Lon3lr0 = [minf,2,3,5],Lon3lr = [2,3,5],undefpnts = [],
## outf = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc)]
## --end of on3info('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-8.mxl"9. 関数 on3decomp() : on3一般式の排他的分解処理(端点は数値のみ, 多変数対応)
on3decomp()$
on3decomp('ex)$## ~/bin/go TMP/tmp_lang/chunk-9.mxl > TMP/tmp_lang/chunk-9.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-9.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-9.mxl
## on3decomp()
## --begin of on3decomp('help)--
## 機能: on3一般式の排他的分解処理全般
## 文法: on3decomp(expr,...)
## 例示: on3decomp(on3(x,1,2,co)+f0) =
## f0*on3(x,minf,1,oo)+f0*on3(x,2,inf,co)+(f0+1)*on3(x,1,2,co)
## on3decomp(1/(on3(x,1,2,co)+f0)) =
## on3(x,minf,1,oo)/f0+on3(x,2,inf,co)/f0+on3(x,1,2,co)/(f0+1)
## --end of on3decomp('help')--
##
## on3decomp('ex)
## --begin of on3decomp('ex)--
## == on3decomp_ex : 排他的領域分解 ==
## ★ ◎ on3decomp(on3(x,1,2,co)+f0) =
## f0*on3(x,minf,1,oo)+f0*on3(x,2,inf,co)+(f0+1)*on3(x,1,2,co)
## ★ ◎ on3decomp(1/(on3(x,1,2,co)+f0)) =
## on3(x,minf,1,oo)/f0+on3(x,2,inf,co)/f0+on3(x,1,2,co)/(f0+1)
## [ 1 ]
## [ ------ (1 <= x < 2) ]
## [ f0 + 1 ]
## [ ]
## [ 1 ]
## [ -- (2 <= x < inf) ]
## out = [ f0 ]
## [ ]
## [ 1 ]
## [ -- (minf < x < 1) ]
## [ f0 ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎ on3decomp(f1*on3(x,5,7,co)+f1*on3(x,3,5,co)) = f1*on3(x,3,7,co) 領域結合
## ★ ◎ on3decomp(f2*on3(x,2,5,co)+f1*on3(x,1,3,co)+f3*on3(x,0,inf,co))
## =
## f3*on3(x,5,inf,co)+(f3+f2)*on3(x,3,5,co)+(f3+f2+f1)*on3(x,2,3,co)
## +(f3+f1)*on3(x,1,2,co)+f3*on3(x,0,1,co)
## ★ ◎ on3decomp(on3(x,3,10,co)/(f2*on3(x,2,8,co)+f1*on3(x,1,5,co)))
## = on3(x,5,8,co)/f2+on3(x,3,5,co)/(f2+f1)
## [ 1 ]
## [ ------- (3 <= x < 5) ]
## [ f2 + f1 ]
## [ ]
## out = [ 1 ]
## [ -- (5 <= x < 8) ]
## [ f2 ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎ on3decomp(f2*on3(x,2,8,co)+f1*on3(x,1,5,co)) =
## f2*on3(x,5,8,co)+(f2+f1)*on3(x,2,5,co)+f1*on3(x,1,2,co)
## [ f1 (1 <= x < 2) ]
## [ ]
## [ f2 + f1 (2 <= x < 5) ]
## out = [ ]
## [ f2 (5 <= x < 8) ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎ on3decomp(1/(f2*on3(x,3,7,co)+f1*on3(x,1,5,co))+f0*on3(x,3,5,co))
## = on3(x,5,7,co)/f2+((f0*f2+f0*f1+1)*on3(x,3,5,co))/(f2+f1)+on3(x,1,3,co)/f1
## [ 1 ]
## [ -- (1 <= x < 3) ]
## [ f1 ]
## [ ]
## [ f0 f2 + f0 f1 + 1 ]
## [ ----------------- (3 <= x < 5) ]
## out = [ f2 + f1 ]
## [ ]
## [ 1 ]
## [ -- (5 <= x < 7) ]
## [ f2 ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎
## on3decomp(1/((f2*on3(x,3,7,co))/(f22*on3(x,3,5,co)+f21*on3(x,1,3,co))+f1*on3(x,1,5,co))+f0)
##
## =
## f0*on3(x,minf,1,oo)+f0*on3(x,5,inf,co)
## +((f0*f1*f22+f22+f0*f2)*on3(x,3,5,co))/(f1*f22+f2)
## +((f0*f1+1)*on3(x,1,3,co))/f1
## [ f0 f1 + 1 ]
## [ --------- (1 <= x < 3) ]
## [ f1 ]
## [ ]
## [ f0 f1 f22 + f22 + f0 f2 ]
## [ ----------------------- (3 <= x < 5) ]
## out = [ f1 f22 + f2 ]
## [ ]
## [ f0 (5 <= x < inf) ]
## [ ]
## [ f0 (minf < x < 1) ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎ on3decomp(f0*on3(y,5,6,co)+f1*on3(x,1,2,co)*on3(y,3,4,co))
## =
## f0*on3(x,minf,1,oo)*on3(y,5,6,co)+f0*on3(x,1,inf,co)*on3(y,5,6,co)
## +f1*on3(x,1,2,co)*on3(y,3,4,co)
## [ f1 (1 <= x < 2) & (3 <= y < 4) ]
## [ ]
## [ f0 (1 <= x < inf) & (5 <= y < 6) ]
## out = [ ]
## [ f0 (minf < x < 1) & (5 <= y < 6) ]
## [ ]
## [ 0 ( otherwise ) ]
## --end of on3decomp('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-9.mxl"10. 関数 on3decomp_one() : 端点は数値のみ, 1変数毎 → on3decompm に吸収予定
on3decomp_one()$
on3decomp_one('ex)$## ~/bin/go TMP/tmp_lang/chunk-10.mxl > TMP/tmp_lang/chunk-10.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-10.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-10.mxl
## on3decomp_one()
## --begin of on3decomp_one('help)--
## 機能: 変数毎の逐次排他的領域分解:特定変数に着目したon3()関数の排他的領域分解を行う.
## 引数に'invが指定されると結果の逆数が返される.
## 条件: 指定した特定変数に関する端点はすべて数値で大小関係は既知とする.
## on3info(expr,var,'std)処理済み
## 文法: on3decomp_one(on3func,var,...)
## 例示:
## ex : f1(x)*on3(x,1,3,co) + f2(x)*on3(x,2,5,co)
## -> f(x,xf) : f1(x)*on3(xf,1,3,co) + f2(x)*on3(xf,2,5,co)
## 端点 minf---1---2---3---5---inf
## -> f1(x)*on3(xf,1,2,co) + (f1(x)+f2(x))*on3(xf,2,3,co) + f2(x)*on3(xf,3,5,co)
## -> 1/f1(x)*on3(xf,1,2,co) + 1/(f1(x)+f2(x))*on3(xf,2,3,co) + 1/f2(x)*on3(xf,3,5,co)
## ('inv が指定された場合)
## 端点の開閉
## ev(f(x,xf),xf=1)=f1(x), ev(f(x,xf,xf=1.5)=f1(x), ev(f(x,xf),xf=2)=f1(x)+f2(x)
## -> on3(xf,1,2,co)
## ev(f(x,xf),xf=2)=f1(x)+f2(x), ev(f(x,xf,xf=2.5)=f1(x)+f2(x), ev(f(x,xf),xf=3)=f2(x)
## -> on3(xf,2,3,co)
## ev(f(x,xf),xf=3)=f2(x), ev(f(x,xf,xf=4)=f2(x), ev(f(x,xf),xf=5)=0
## -> on3(xf,3,5,co)
## --end of on3decomp_one('help')--
##
## on3decomp_one('ex)
## --begin of on3decomp_one('ex)--
## ★ (/* 例1. 排他的区分分解 */
## ex : f1(x)*on3(x,minf,3,co) + f2(x)*on3(x,2,5,cc),
## f : on3decomp_one(ex,x)
## )
## ◎ out = f1(x)*on3(x,minf,2,oo)+f2(x)*on3(x,3,5,cc)+(f2(x)+f1(x))*on3(x,2,3,co)
## ★ (/* 例2-1. 2変量関数を変数yで分解 */
## f20 : f1(x,y)*on3(x,1,8,co)*on3(y,minf,3,oo) + f2(x,y)*on3(y,2,5,cc),
## fy : on3decomp_one(f20,y)
## )
## ◎ out =
## on3(x,1,8,co)*f1(x,y)*on3(y,minf,2,oo)+f2(x,y)*on3(y,3,5,cc)
## +(f2(x,y)+on3(x,1,8,co)*f1(x,y))*on3(y,2,3,co)
##
## ★ (/* 例2-2. fy を変数xで分解 */
## fy : ratexpand(fy), fyx : on3decomp_one(fy,x)
## )
## ◎ out =
## on3(x,1,8,co)*(f1(x,y)*on3(y,minf,2,oo)+f2(x,y)*on3(y,3,5,cc)+f2(x,y)*on3(y,2,3,co)
## +f1(x,y)*on3(y,2,3,co))
## +on3(x,minf,1,oo)*(f2(x,y)*on3(y,3,5,cc)+f2(x,y)*on3(y,2,3,co))
## +on3(x,8,inf,co)*(f2(x,y)*on3(y,3,5,cc)+f2(x,y)*on3(y,2,3,co))
## ● ev(fy,y = 2) = f2(x,2)+on3(x,1,8,co)*f1(x,2)
## --end of on3decomp_one('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-10.mxl"12. 関数 on3decomp21() : 変数毎の排他的区間分解(未定端点:仮定の設定,on3有理式まで対応)
on3decomp21()$
on3decomp21('ex)$## ~/bin/go TMP/tmp_lang/chunk-12.mxl > TMP/tmp_lang/chunk-12.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-12.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-12.mxl
## on3decomp21()
## --begin of on3decomp21('help)--
## 機能: 指定変数varに関するon3(var,,,,)関数式の排他的区分分解を変数var毎に試みる
## on3有理式,未定端点に対応する, 特異点(分母が零になる点), 特異区間に対応
## 比較 : on3decomp()は未定端点無しの場合に多変数領域の排他的領域分解を与える
## 文法: on3decomp21(on3func,var,...)
## 例示:
## on3decomp21(1/(x-3),x) -> 1/(x-3)*on3(x,minf,3,oo) + 1/(x-3)*on3(x,3,inf,oo) (特異点)
## ex : f0 + f1*on3(x,a,b,co),
## on3decomp21(ex,x),
## -> f0*on3(x,minf,a,oo) + (f0+f1)*on3(x,a,b,co) + f0*on3(x,b,inf,co)
## on3decomp21(1/(f0 + f1*on3(x,1,3,co)), x),
## -> 1/f0*on3(x,minf,1,oo) + 1/(f0+f1)*on3(x,1,3,co) + 1/f0*on3(x,3,inf,co)
## on3decomp21(1/(f0 + f1*on3(x,a,b,co)), x),
## -> 1/f0*on3(x,minf,a,oo) + 1/(f0+f1)*on3(x,a,b,co) + 1/f0*on3(x,b,inf,co)
## --end of on3decomp21('help')--
##
## on3decomp21('ex)
## --begin of on3decomp21('ex)--
## ★ (/* 例1, on3多項式(未定端点を含む) 明示仮定 */
## ex : f0 + f1*on3(x,a,b,co),
## out : on3decomp21(ex,x,[a<b],debug0))
## ◎ out = f0*on3(x,b,inf,co)+(f1+f0)*on3(x,a,b,co)+f0*on3(x,minf,a,oo)
## ★
## (/* 例2 on3多項式(係数部にxの関数), 未定端点, 明示仮定 ---a---c---b---d--- */
##
## ex3 : f0(x) + f1(x)*on3(x,a,b,co) + f2(x)*on3(x,c,d,co),
## out : on3decomp21(1/ex3,x,[a<c,c<b,b<d],debug0))
## ◎ out =
## on3(x,d,inf,co)/f0(x)+on3(x,c,b,co)/(f2(x)+f1(x)+f0(x))+on3(x,b,d,co)/(f2(x)+f0(x))
## +on3(x,a,c,co)/(f1(x)+f0(x))+on3(x,minf,a,oo)/f0(x)
## ★
## (/* 例3 on3多項式,未定端点を含む, 明示仮定 ---1---a---2---b---3---4--- */
##
## ex : f1*on3(x,1,3,co) + f2*on3(x,2,4,co) + f3*on3(x,a,b,co),
## out : on3decomp21(ex,x,[1<a, a<2, 2<b, b<3],debug0))
## ◎ out =
## (f2+f1)*on3(x,b,3,co)+(f3+f1)*on3(x,a,2,co)+f2*on3(x,3,4,co)
## +(f3+f2+f1)*on3(x,2,b,co)+f1*on3(x,1,a,co)
## ★
## (/* 例4-1. on3有理式:分母が0となる区間が存在しない場合, 未定端点なし */
##
## ex : f0*on3(x,2,6,co)/(f1*on3(x,1,5,co) + f2*on3(x,3,7,co)),
## out : on3decomp21(ex,x,debug0))
## ◎ out = (f0*on3(x,5,6,co))/f2+(f0*on3(x,3,5,co))/(f2+f1)+(f0*on3(x,2,3,co))/f1
## 注:特異区間を明示した解 ansd ->
## None*on3(x,7,8,oo)+(f0*on3(x,5,7,co))/f2+(f0*on3(x,3,5,co))/(f2+f1)
## +(f0*on3(x,1,3,co))/f1+None*on3(x,0,1,oo)
##
## --> ev(ansd,None=0) で特異区間項(None*で始まる項)を除いた表現を得る
##
## ★
## (/* 例4-2. on3有理式:分母が0となる区間が存在する場合の対応, 未定端点なし */
##
## ex : f0*on3(x,0,8,co)/(f1*on3(x,1,5,co) + f2*on3(x,3,7,co)),
## out : on3decomp21(ex,x,debug0))
## ◎ out = (f0*on3(x,5,7,co))/f2+(f0*on3(x,3,5,co))/(f2+f1)+(f0*on3(x,1,3,co))/f1
## ★ (/* 例5-1 on3有理式:分母が0となる区間が存在しない場合 */
## /* 未定端点を含む, 明示仮定 ---a---1---c---b---5---d--- */
## ex : (f2*on3(x,1,5,co)+f3*on3(x,c,d,co))/(f0 + f1*on3(x,a,b,co)),
## out : on3decomp21(ex,x,[a<1,1<c,c<b,b<5,5<d],debug0))
## ◎ out =
## ((f3+f2)*on3(x,c,b,co))/(f1+f0)+((f3+f2)*on3(x,b,5,co))/f0+(f3*on3(x,5,d,co))/f0
## +(f2*on3(x,1,c,co))/(f1+f0)
## ★ (/* 例5-2 on3有理式:分母が0となる区間が存在する場合の対応, */
##
## /* 未定端点を含む, 明示仮定 ---a---c---b---d--- */
## ex : f0/(f1*on3(x,a,b,co) + f2*on3(x,c,d,co)),
## out : on3decomp21(ex,x,[a<c,c<b,b<d],debug0))
## ◎ out = (f0*on3(x,c,b,co))/(f2+f1)+(f0*on3(x,b,d,co))/f2+(f0*on3(x,a,c,co))/f1
## 特異区間項(None*で始まる項)を含めた結果 ansd ->
## None*on3(x,d,inf,oo)+(f0*on3(x,c,b,co))/(f2+f1)+(f0*on3(x,b,d,co))/f2
## +(f0*on3(x,a,c,co))/f1+None*on3(x,minf,a,oo)
##
## --> ev(ansd,None=0) で特異区間項(None*で始まる項)を除いた表現を得る
##
## ★ (/* 例5-3 on3有理式:分母が0となる区間が存在する場合の対応, */
##
##
## /* 未定端点を含む, 特異点[e,c], 明示仮定 ---a--(e)--(c)---b---d--- */
##
## f0 : 1/((x-e)*(x-c)),
## ex : f0/(on3(x,a,b,co) + on3(x,c,d,co)),
## out : on3decomp21(ex,x,[a<e,e<c,c<b,b<d],debug0))
## ◎ out =
## on3(x,e,c,oo)/((x-c)*(x-e))+on3(x,c,b,oo)/(2*(x-c)*(x-e))
## +on3(x,b,d,co)/((x-c)*(x-e))+on3(x,a,e,co)/((x-c)*(x-e))
## ★ (/* 例6-1. 2変量関数を変数 y で分解 */
## f20 : f1(x,y)*on3(x,1,8,co)*on3(y,minf,3,oo) + f2(x,y)*on3(y,2,5,cc),
## fy : on3decomp21(f20,y,debug0))
## ◎ out =
## on3(x,1,8,co)*f1(x,y)*on3(y,minf,2,oo)+f2(x,y)*on3(y,3,5,cc)
## +(f2(x,y)+on3(x,1,8,co)*f1(x,y))*on3(y,2,3,co)
##
## ★ (/* 例6-2. 2変量関数を変数 x で分解 */
## fy : ratexpand(fy), fyx : on3decomp21(fy,x,debug0), c0show(ev(fy,y = 2)), fyx)
## ev(fy,y = 2) = f2(x,2)+on3(x,1,8,co)*f1(x,2)
## ◎ out =
## on3(x,1,8,co)*(f1(x,y)*(on3(y,minf,2,oo)+on3(y,2,3,co))
## +f2(x,y)*(on3(y,3,5,cc)+on3(y,2,3,co)))
## +on3(x,minf,1,oo)*f2(x,y)*(on3(y,3,5,cc)+on3(y,2,3,co))
## +on3(x,8,inf,co)*f2(x,y)*(on3(y,3,5,cc)+on3(y,2,3,co))
## ★ (/* 例7-1 on3多項式 + on3有理式 の排他的分解-1(共通分母), */
## ex : on3(x,1,5,co) + on3(x,1,5,co)/(on3(x,1,3,co)+on3(x,2,4,co)),
## out : on3decomp21(ex,x,debug0))
## ◎ out = 2*on3(x,3,4,co)+(3*on3(x,2,3,co))/2+2*on3(x,1,2,co)
## ★
## (/* 例7-2 on3多項式 + on3有理式 の排他的分解-2(有理式部分の分解), */
##
## ex : on3decomp21(on3(x,1,5,co)/(on3(x,1,3,co)+on3(x,2,4,co)),x) ,
## cashow(ex),
## out : on3decomp21(on3(x,1,5,co) + ex, x,debug0))
## ex -> on3(x,3,4,co)+on3(x,2,3,co)/2+on3(x,1,2,co)
## ◎ out = on3(x,4,5,co)+2*on3(x,3,4,co)+(3*on3(x,2,3,co))/2+2*on3(x,1,2,co)
## --end of on3decomp21('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-12.mxl"12a. 関数 on3decompm() : 未定端点:仮定の設定,多変数on3多項式(3変数まで)の排他的区間分解
on3decomp21() を内部使用する｡
on3decompm()$
on3decompm('ex)$## ~/bin/go TMP/tmp_lang/chunk-13.mxl > TMP/tmp_lang/chunk-13.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-13.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-13.mxl
## on3decompm()
## --begin of on3decompm('help)--
## 機能: 区間関数 on3(x,...) の多項式を排他的区間に分解する処理を変数リスト'varsL=[x,y,z] の順序で行なう｡
## 制限:3変数までのon3多項式｡適切な仮定の設定があれば,区間の端点は未定定数を許す｡以下の手順に従う｡
## 第1分解 expr : sum_{i=1}^iend v1_Lon3f[i]*v1_Lon3coef[i] = v1_outf
## 第2分解 v1_Lon3coef[i] : sum_{j=1}^jend v2_Lon3f[j]*v2_Lon3coef[j] = v2_outf
## 第3分解 v2_Lon3coef[j] : sum_{k=1}^kend v3_Lon3f[k]*v3_Lon3coef[k] = v3_outf
## 文法: on3decompm(expr, ’varsL=[x,y], 'assume=[...])
## 例示:
## ex11 : f1(x)*on3(x,1,5,co) + f2(x)*on3(x,3,7,co),
## on3decompm(ex11,'vars=[x]);
## ---> f1(x)*on3(x,1,3,co) + (f1(x)+f2(x))*on3(x,3,5,co) + f2(x)*on3(x,5,7,co)
## ex12 : f1(x)*on3(x,1,5,co) + f2(x)*on3(x,a,b,co), /* 1--a--5--b */
## assw1 : [1<a,a<5,5<b], /* 仮定の設定 */
## on3decompm(ex12,'vars=[x], 'assume=assw1);
## ---> f1(x)*on3(x,1,a,co) + (f1(x)+f2(x))*on3(x,a,5,co) + f2(x)*on3(x,5,b,co),
## ex22 : f2(x,y)*on3(x,3,7,co)*on3(y,b,d,co)
## + f1(x,y)*on3(x,1,5,co)*on3(y,2,6,co), /* --2--b--6--d-- */
## assw2 : [2<b, b<6, 6<d], /* 仮定の設定 */
## on3decompm(ex22,'vars=[x,y], 'assume=assw2),
## ---> on3(x,3,5,co)*((f1(x,y)+f2(x,y))*on3(y,b,6,co)+f2(x,y)*on3(y,6,d,co)
## +f1(x,y)*on3(y,2,b,co))
## +on3(x,5,7,co)*f2(x,y)*on3(y,b,d,co)
## +on3(x,1,3,co)*f1(x,y)*on3(y,2,6,co),
## --end of on3decompm('help')--
##
## on3decompm('ex)
## --begin of on3decompm('ex)--
## ★ ( /* 例.1 on3decompm() の結果 */
## c0show(expr, varsL, assw),
## out : on3decompm(expr,'vars=varsL, 'assume=assw, debug)
## )
## expr = f2(x)*on3(x,3,7,co)+f1(x)*on3(x,1,5,co) varsL = [x] assw = []
## ◎ out = f2(x)*on3(x,5,7,co)+(f2(x)+f1(x))*on3(x,3,5,co)+f1(x)*on3(x,1,3,co)
## ★ ( /* 例.2 on3decompm() の結果 */
## c0show(expr, varsL, assw),
## out : on3decompm(expr,'vars=varsL, 'assume=assw, debug)
## )
## expr = f2(x)*on3(x,a,b,co)+f1(x)*on3(x,1,5,co) varsL = [x] assw =
## [1 < a,a < 5,5 < b]
## ◎ out = (f2(x)+f1(x))*on3(x,a,5,co)+f2(x)*on3(x,5,b,co)+f1(x)*on3(x,1,a,co)
## ★ ( /* 例.3 on3decompm() の結果 */
## c0show(expr, varsL, assw),
## out : on3decompm(expr,'vars=varsL, 'assume=assw, debug)
## )
## expr = on3(x,3,7,co)*f2(x,y)*on3(y,4,8,co)+on3(x,1,5,co)*f1(x,y)*on3(y,2,6,co) varsL
## = [x,y] assw = []
## ◎ out =
## on3(x,3,5,co)*(f2(x,y)*on3(y,6,8,co)+(f2(x,y)+f1(x,y))*on3(y,4,6,co)
## +f1(x,y)*on3(y,2,4,co))
## +on3(x,5,7,co)*f2(x,y)*on3(y,4,8,co)+on3(x,1,3,co)*f1(x,y)*on3(y,2,6,co)
## ★ ( /* 例.4 on3decompm() の結果 */
## c0show(expr, varsL, assw),
## out : on3decompm(expr,'vars=varsL, 'assume=assw, debug)
## )
## expr = on3(x,3,7,co)*f2(x,y)*on3(y,b,d,co)+on3(x,1,5,co)*f1(x,y)*on3(y,2,6,co) varsL
## = [x,y] assw = [2 < b,b < 6,6 < d]
## ◎ out =
## on3(x,5,7,co)*f2(x,y)*on3(y,b,d,co)+on3(x,3,5,co)
## *((f2(x,y)+f1(x,y))*on3(y,b,6,co)
## +f2(x,y)*on3(y,6,d,co)+f1(x,y)*on3(y,2,b,co))
## +on3(x,1,3,co)*f1(x,y)*on3(y,2,6,co)
## ★ ( /* 例.5 on3decompm() の結果 */
## c0show(expr, varsL, assw),
## out : on3decompm(expr,'vars=varsL, 'assume=assw, debug)
## )
## expr =
## f1*on3(x,1,5,co)*on3(y,2,6,co)*on3(z,5,10,co)
## +f2*on3(x,3,7,co)*on3(y,4,8,co)*on3(z,0,10,co) varsL = [x,y,z] assw = []
## ◎ out =
## on3(x,3,5,co)*(on3(y,4,6,co)*((f2+f1)*on3(z,5,10,co)+f2*on3(z,0,5,co))
## +f1*on3(y,2,4,co)*on3(z,5,10,co)+f2*on3(y,6,8,co)*on3(z,0,10,co))
## +f1*on3(x,1,3,co)*on3(y,2,6,co)*on3(z,5,10,co)
## +f2*on3(x,5,7,co)*on3(y,4,8,co)*on3(z,0,10,co)
## --end of on3decompm('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-13.mxl"13. 関数 on3info() : expr に含まれる変数varの関数on3(var…)の情報をリストで返す
on3info()$
on3info('ex)$## ~/bin/go TMP/tmp_lang/chunk-14.mxl > TMP/tmp_lang/chunk-14.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-14.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-14.mxl
## on3info()
## --begin of on3info('help)--
## 機能: expr に含まれる変数varの関数on3(var...)の情報をリストで返す
## 結果のリストはoutLev()で取り出せる.
## on3多項式を前提とするため,定数項が存在する合も考慮されている(変数毎のon3stdの機能を有する)
## 引数に'std がある場合は指定された変数に関する標準化の結果を返す
## expr が on3有理式の場合は on3decomp21(expr,x,[仮定1,...]) によりon3多項式化を得る.
## 文法: on3info(expr,x,...) or on3info(expr)
## on3info(expr,x,'factor), on3info(expr,x,'std)
## 例示: on3info(f1*log(x)*on3(x,1,2,co)+f0, x,'std)
## -> f0*on3(x,minf,1,oo) + (f0+f1)*on3(x,1,2,co) + f0*on3(x,2,inf,co) (標準化)
## --end of on3info('help')--
##
## on3info('ex)
## --begin of on3info('ex)--
## ---begin of on3info_ex---
## ◆ 例0 ex0 = f1*log(x)*on3(x,1,2,co)+f0 <- on3std未処理の場合
## on3info(ex0,x) =
## [expr = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co),var = x,
## Lon3 = [[on3,x,1,2,co],[on3,x,minf,inf,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)],Lon3coef = [f1*log(x),f0],
## Lon3lr0 = [minf,1,2,inf],Lon3lr = [1,2],undefpnts = [],
## outf = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)]
## ◆ on3info(ex0,x,'std) = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- 'std 指定の場合
## ◆ 例1 ex1 = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- on3std処理済みの場合
## on3info(ex1,x) =
## [expr = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co),var = x,
## Lon3 = [[on3,x,1,2,co],[on3,x,minf,inf,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)],Lon3coef = [f1*log(x),f0],
## Lon3lr0 = [minf,1,2,inf],Lon3lr = [1,2],undefpnts = [],
## outf = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)]
## ◆ 例1-2 ex1 = f0*on3(x,minf,inf,oo)+f1*log(x)*on3(x,1,2,co)
## <- 結果リストの一括取り込みと一括削除の例
## ★ (outLev(on3info(ex1,x),"test_"), /* 結果リストをtest_*で取り込む */
## c0show(test_Lon3f), c0show(test_Lon3coef), /* 取り込みリストの表示 */
## killvars(["test_"]) /* 取り込みリストの一括削除 */ , values)
## test_Lon3f = [on3(x,1,2,co),on3(x,minf,inf,oo)]
## test_Lon3coef = [f1*log(x),f0]
## out =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,std,expr,
## var,wL,ic,Lon3,Lon3lr0,Lon3lr,on3v,on3f,on3coef,Lon3v,Lon3f,Lon3coef,
## undefpnts,outL,outf,ex0,ex1,ex2,ex22,ex3,ex4,ex,cmds,L,out,chk,ans,hlp,hlpL,
## cmdsansL,cmdsL,w_out,chkm,k]
## ◆ 例2-1 ex2 = (f*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## <- 有理式の分母に適用した場合
## ratdenom(ex2) = on3(x,a,b,co)*f1+f2*on3(x,c,d,co)
## on3info(ratdenom(ex2),x) =
## [expr = f2*on3(x,c,d,co)+f1*on3(x,a,b,co),var = x,
## Lon3 = [[on3,x,a,b,co],[on3,x,c,d,co]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,a,b,co),on3(x,c,d,co)],Lon3coef = [f1,f2],Lon3lr0 = [a,b,c,d],
## Lon3lr = [a,b,c,d],undefpnts = [false,false,false,false],
## outf = f2*on3(x,c,d,co)+f1*on3(x,a,b,co)]
## ◆ 例2-2 ex22 =
## (f4*on3(x,2,4,co)+f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## <- 有理式に適用した場合
## ex22 = (f4*on3(x,2,4,co)+f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## on3info(ex22,x,'std) =
## (f4*on3(x,2,4,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
## +(f3*on3(x,1,3,co))/(f2*on3(x,c,d,co)+f1*on3(x,a,b,co))
##
## ■ on3decomp21(ex22,x,[1<a,a<2,2<c,c<3,3<b,b<4,4<d]) を実行しon3多項式(排他的分解済)を得る
##
## on3decomp21(ex22,x,[1 < a,a < 2,2 < c,c < 3,3 < b,b < 4,4 < d]) =
## ((f4+f3)*on3(x,c,3,co))/(f2+f1)+(f4*on3(x,b,4,co))/f2+(f3*on3(x,a,2,co))/f1
## +(f4*on3(x,3,b,co))/(f2+f1)+((f4+f3)*on3(x,2,c,co))/f1
## ◆ 例3 ex3 = ex3 第1引数が単変数でない場合
## ex3 = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co)
## on3info(ex3,t) =
## [expr = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co),var = t,
## Lon3 = [[on3,t-u,1,3,co],[on3,t-u,u,inf,co]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(t-u,1,3,co),on3(t-u,u,inf,co)],Lon3coef = [f1,f2],Lon3lr0 = [1,3,inf,u],
## Lon3lr = [1,3,u],undefpnts = [false],outf = f2*on3(t-u,u,inf,co)+f1*on3(t-u,1,3,co)]
## ◆ 例4 ex4 = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc)
## 2変数関数の場合
## on3info(ex4,y) =
## [expr = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc),var = y,
## Lon3 = [[on3,y,2,5,cc],[on3,y,minf,3,oo]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(y,2,5,cc),on3(y,minf,3,oo)],Lon3coef = [f2(x,y),on3(x,1,8,co)*f1(x,y)],
## Lon3lr0 = [minf,2,3,5],Lon3lr = [2,3,5],undefpnts = [],
## outf = on3(x,1,8,co)*f1(x,y)*on3(y,minf,3,oo)+f2(x,y)*on3(y,2,5,cc)]
## --end of on3info('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-14.mxl"14. 関数 outLev() : on3info()の結果(リスト)の取り込み
outLev()$
outLev('ex)$## ~/bin/go TMP/tmp_lang/chunk-15.mxl > TMP/tmp_lang/chunk-15.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-15.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-15.mxl
## outLev()
## --begin of outLev('help)--
## 機能: 名前付きリストを展開する
## 文法: outLev(outL,"test_")
## 例示: outL : [L1=[l11,l12],L2=[l21]]
## outLev(outL,"test_") -> test_L1=[l11,l12], test_L2=[l21]
## --end of outLev('help')--
##
## outLev('ex)
## --begin of outLev('ex)--
## ★ (/* outLev() の実行例 */
## ex : on3(x,a,b,co)*on3(y,yl,yr,oo) + x*on3(x,c,d,cc),
## outL : on3info(ex,x), /* on3info()の結果(名前付きリスト)を得る */
## c0show(outL), /* outL の内容確認 */
## outLev(outL,"test_"), /* 変数test_* の形で展開 */
## cshow(values) /* 変数一覧で確認する */
## )
## outL =
## [expr = on3(x,a,b,co)*on3(y,yl,yr,oo)+x*on3(x,c,d,cc),var = x,
## Lon3 = [[on3,x,a,b,co],[on3,x,c,d,cc]],Lon3v = [on3v_1,on3v_2],
## Lon3f = [on3(x,a,b,co),on3(x,c,d,cc)],Lon3coef = [on3(y,yl,yr,oo),x],
## Lon3lr0 = [a,b,c,d],Lon3lr = [a,b,c,d],undefpnts = [false,false,false,false],
## outf = on3(x,a,b,co)*on3(y,yl,yr,oo)+x*on3(x,c,d,cc)]
## CS: values =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,L,Ll,Lr,prestr,str,
## ex,x,outL,cmds,ans,hlp,hlpL,cmdsansL,cmdsL,w_out,chk,chkm,k,test_expr,test_var,
## test_Lon3,test_Lon3v,test_Lon3f,test_Lon3coef,test_Lon3lr0,test_Lon3lr,
## test_undefpnts,test_outf]
## out =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,L,Ll,Lr,
## prestr,str,ex,x,outL,cmds,ans,hlp,hlpL,cmdsansL,cmdsL,w_out,chk,chkm,k,
## test_expr,test_var,test_Lon3,test_Lon3v,test_Lon3f,test_Lon3coef,test_Lon3lr0,
## test_Lon3lr,test_undefpnts,test_outf]
## --end of outLev('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-15.mxl"14. 関数 find_key() : ツール1 キー付き引数の扱い
find_key()$
find_key('ex)$
find_key_no()$
find_key_no('ex)$## ~/bin/go TMP/tmp_lang/chunk-16.mxl > TMP/tmp_lang/chunk-16.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-16.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-16.mxl
## find_key()
## --begin of find_key('help)--
## 機能: キー付きリストからキー名を含む最初の要素を取り出す. キー名がない場合はFALSEを返す.
## 文法: find_key(list,key,...)
## 例示: find_key([key1=a,key2=b,key3=c],key2) -> key2=b
## --end of find_key('help')--
##
## find_key('ex)
## --begin of find_key('ex)--
## --begin of find_key_ex
## dlist =
## [terminal = png,file_name = "figs/find_key-1",columns = 2,dimensions = [1000,400]]
## find_key(dlist,'columns) = columns = 2
## find_key(dlist,'file_name) = file_name = "figs/find_key-1"
## find_key(dlist,'not_key_name) = false
## --end of find_key('ex)--
## find_key_no()
## --begin of find_key_no('help)--
## 機能: キー付きリストからキー名を含む要素の位置を取り出す
## 文法: find_key_no(list,key,...)
## 例示: find_key_no([key1=a,key2=b,key3=c],key2); -> 2
## find_key_no([key1=a,key2=b,key3=c],key4); -> 0
## --end of find_key_no('help')--
##
## find_key_no('ex)
## --begin of find_key_no('ex)--
## --begin of find_key_no_ex
## dlist =
## [terminal = png,file_name = "figs/find_key_no-1",columns = 2,dimensions = [1000,400]]
## find_key_no(dlist,'columns) = 3
## find_key_no(dlist,'file_name) = 2
## --end of find_key_no('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-16.mxl"14a. 関数 ass_set(), fact_var(), fact_forget(), killvars() : ツール2 仮定の設定,表示,解除
ass_set()$
ass_set('ex)$
fact_var()$
fact_var('ex)$
fact_forget()$
fact_forget('ex)$
killvars()$
killvars('ex)$## ~/bin/go TMP/tmp_lang/chunk-17.mxl > TMP/tmp_lang/chunk-17.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-17.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-17.mxl
## ass_set()
## --begin of ass_set('help)--
## 機能: 仮定の設定
## 文法: ass_set([a<c,c<b,b<d])
## 例示: ass_set([a<c,c<b,b<d])
## var_fact([a,b,c,d]) facts()出力から変数リストに関連する事実を表示する
## fact_var([a<c,c<b,b<d]) 引数で指定された事実(facts)に現れる変数をリストで返す
## fact_forget([a,b,c,d]) 変数リスト/事実リストで指定された事実を消去する
## on3byon3([[on3,x,1,3,co],[on3,x,2,4,co]],debug1) -> on3(x,2,3,co)
## --end of ass_set('help')--
##
## ass_set('ex)
## --begin of ass_set('ex)--
## ★ /* 仮定の設定: */ ass_set([a<c,c<b,b<d])
## ◎ out = [c > a,b > c,d > b]
## ★ /* 事実の表示: */ var_fact([a,b,c,d])
## ◎ out = [b > c,c > a,d > b]
## ★ /* 事実の変数: */ fact_var([c > a,b > c,d > b])
## ◎ out = [a,b,c,d]
## ★ /* 仮定の本での on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## ◎ out = on3(x,c,b,co)
## ★ /* 事実の消去: */ fact_forget([a,b,c,d])
## ◎ out = []
## ★ /*事実消去の確認: */ var_fact([a,b,c,d])
## ◎ out = []
## ★ /* 無仮定の場合の on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## progn = <on3byon3> wout = unknown ← 積の結果
## ◎ out = unknown
## fact_var()
## --begin of fact_var('help)--
## 機能: facts()出力から変数リストに関連する事実を表示する
## 文法: fact_var([a,b,c,d])
## 例示: fact_var([a<c,c<b,b<d]) -> [a,b,c,d]
## fact_var('facts) -> facts()出力から変数リストに関連する事実を表示する
## --end of fact_var('help)--
##
## fact_var('ex)
## --begin of ass_set('ex)--
## --begin of ass_set('ex)--
## ★ /* 仮定の設定: */ ass_set([a<c,c<b,b<d])
## ◎ out = [c > a,b > c,d > b]
## ★ /* 事実の表示: */ var_fact([a,b,c,d])
## ◎ out = [b > c,c > a,d > b]
## ★ /* 事実の変数: */ fact_var([c > a,b > c,d > b])
## ◎ out = [a,b,c,d]
## ★ /* 仮定の本での on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## ◎ out = on3(x,c,b,co)
## ★ /* 事実の消去: */ fact_forget([a,b,c,d])
## ◎ out = []
## ★ /*事実消去の確認: */ var_fact([a,b,c,d])
## ◎ out = []
## ★ /* 無仮定の場合の on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## progn = <on3byon3> wout = unknown ← 積の結果
## ◎ out = unknown
## fact_forget()
## --begin of fact_forget('help)--
## 機能: 変数リスト/事実リストで指定された事実を消去する
## 文法: fact_forget([a,b,c,d])
## 例示: fact_forget([a,b,c,d]) -> [a,b,c,d] で指定された事実を消去する
## --end of fact_forget('help)--
##
## fact_forget('ex)
## --begin of ass_set('ex)--
## --begin of ass_set('ex)--
## ★ /* 仮定の設定: */ ass_set([a<c,c<b,b<d])
## ◎ out = [c > a,b > c,d > b]
## ★ /* 事実の表示: */ var_fact([a,b,c,d])
## ◎ out = [b > c,c > a,d > b]
## ★ /* 事実の変数: */ fact_var([c > a,b > c,d > b])
## ◎ out = [a,b,c,d]
## ★ /* 仮定の本での on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## ◎ out = on3(x,c,b,co)
## ★ /* 事実の消去: */ fact_forget([a,b,c,d])
## ◎ out = []
## ★ /*事実消去の確認: */ var_fact([a,b,c,d])
## ◎ out = []
## ★ /* 無仮定の場合の on3()関数の積 */
## on3byon3(on3(x,a,b,co)*on3(x,c,d,co))
## progn = <on3byon3> wout = unknown ← 積の結果
## ◎ out = unknown
## killvars()
## --begin of killvars('help)--
## 機能: values; で表示される変数リストからkeysで指定された変数を(一括)削除する
## 文法: killvars(["denom_","numer_","w_","out_"],...)
## 例示:
## values;
## killvars(["denom_","numer_","w_","out_"]);
## values;
## --end of killvars('help')--
##
## killvars('ex)
## --begin of killvars('ex)--
## 現在の変数リスト: values =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,keys,key,str,svL]
## killvars(["denom_","numer_","w_","out_"]) =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,keys,key,str,svL]
## 上記処理後の変数リスト: values =
## [ass_hist,chkerrsum,icerror,USER,HOME,ENV,cmd,tmpdirsL,tmp_dir,tmp_maxima_dir,
## tmp_user_dir,tmp_lang_dir,figs_dir,args,max_save_file,progn,debug,keys,key,str,svL]
## --end of killvars('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-17.mxl"15. 関数 on3ev() : on3poly の各関数部を{factor,expand,ratsimp}した表現を返す
on3ev()$
on3ev('ex)$## ~/bin/go TMP/tmp_lang/chunk-18.mxl > TMP/tmp_lang/chunk-18.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-18.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-18.mxl
## on3ev()
## --begin of on3ev('help)--
## 機能: on3poly の各関数部を{factor,expand,ratsimp}した表現を返す
## 文法: on3ev(expr,...)
## 例示: ex : x*on3(x,3,4,co)+(x^2-2*x+1)*on3(x,1,2,co)
## on3ev(ex,factor) = x*on3(x,3,4,co)+(x-1)^2*on3(x,1,2,co)
## ex1e : %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co)
## out : on3integ(ex1e,x)
## = (%e^-x*(4*%e^x-3*%e)*on3(x,1,inf,co))/3+(x^3*on3(x,0,1,co))/3
## on3ev(out,expand) = (4/3-%e^(1-x))*on3(x,1,inf,co)+(x^3*on3(x,0,1,co))/3
## --end of on3ev('help')--
##
## on3ev('ex)
## --begin of on3ev('ex)--
## --- on3ev_ex ---
## ★ ( /* 例1. on3 多項式の関数部の因数分解 */
## ex1 : (x^2-2*x+1)*on3(x,1,2,co) + x*on3(x,3,4,co),
## out : on3ev(ex1,factor) )
## ◎ out = x*on3(x,3,4,co)+(x-1)^2*on3(x,1,2,co)
## ★ ( /* 例2. on3 多項式の展開 */
## ex2 : %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co),
## out0 : on3integ(ex2,x), print(" out0 = ",out0),
## out : on3ev(out0,expand) )
## out0 = (1-%e^(1-x))*on3(x,1,inf,co)+on3(x,1,inf,co)/3+(x^3*on3(x,0,1,co))/3
## ◎ out = (4/3-%e^(1-x))*on3(x,1,inf,co)+(x^3*on3(x,0,1,co))/3
## --end of on3ev('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-18.mxl"16. 関数 on3diff() : on3関数式の微分
on3diff()$
on3diff('ex)$## ~/bin/go TMP/tmp_lang/chunk-19.mxl > TMP/tmp_lang/chunk-19.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-19.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-19.mxl
## on3diff()
## --begin of on3diff('help)--
## 機能: on3 関数の微分(多変数関数の1変数に関するp階偏微分)を求める
## 文法: on3diff(expr,var,p,...)
## 例示: on3diff(expr,var) <- p=1 として1階偏微分を返す
## ★ ◎ on3diff(sin(x),x) = cos(x)
## ★ ◎ on3diff(x^2*on3(x,0,1,co) + %e^(1-x)*on3(x,1,inf,co), x, 1)
## = 2*x*on3(x,0,1,co)-%e^(1-x)*on3(x,1,inf,oo)
## --end of on3diff('help')--
##
## on3diff('ex)
## --begin of on3diff('ex)--
## == on3diff : 微分 ==
## ▼ 微分
## ★ ◎ on3diff(sin(x),x) = cos(x)
## ★ ◎ on3diff(x^2*on3(x,0,1,co) + %e^(1-x)*on3(x,1,inf,co), x, 1)
## = 2*x*on3(x,0,1,co)-%e^(1-x)*on3(x,1,inf,oo)
## [ 2 x (0 <= x < 1) ]
## [ ]
## out = [ 1 - x ]
## [ - %e (1 < x < inf) ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎
## on3diff(x^2*on3(x,minf,0,oo)+1/2*(1-x^2)*on3(x,0,1,oo)+(1-x)*on3(x,1,inf,oo), x, 1)
## = 2*x*on3(x,minf,0,oo)-on3(x,1,inf,co)-x*on3(x,0,1,oo)
## [ - x (0 < x < 1) ]
## [ ]
## [ - 1 (1 <= x < inf) ]
## out = [ ]
## [ 2 x (minf < x < 0) ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ◎
## on3diff(x^2 * on3(x,minf,0,oo) + 1/2*(1-x^2)*on3(x,0,1,oo) + (1-x)*on3(x,1,inf,oo) + sin(x)*on3(x,minf,inf,oo), x, 1)
##
## = (cos(x)+2*x)*on3(x,minf,0,oo)+(cos(x)-1)*on3(x,1,inf,co)+(cos(x)-x)*on3(x,0,1,oo)
##
## [ cos(x) - x (0 < x < 1) ]
## [ ]
## [ cos(x) - 1 (1 <= x < inf) ]
## out = [ ]
## [ cos(x) + 2 x (minf < x < 0) ]
## [ ]
## [ 0 ( otherwise ) ]
## --end of on3diff('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-19.mxl"17. 関数 on3integ() : on3関数式の積分
on3integ()$
on3integ('ex)$## ~/bin/go TMP/tmp_lang/chunk-20.mxl > TMP/tmp_lang/chunk-20.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-20.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-20.mxl
## on3integ()
## --begin of on3integ('help)--
## 機能: on3()関数を含む式の不定積分,定積分を返す.未定端点,on3有理式に対応(on3decomp21()を使用)
## 文法: on3integ(on3func,var,{vl,vr},...)
## F_i(x) = (F_i(x)-F_i(xl))*on3(x,xl,xr,lr)
## +(F_i(xr)-F_i(xl))*on3(x,xr,inf,lr1),
## where if xl=minf then F_i(xl)=0 (積分定数の定義),
## lr=cc or oc then lr1=oo, lr=co or oo then lr1=co
## 例示: on3integ(on3func,x) 変数xに関する不定積分
## on3integ(2*x, x) -> x^2
## on3integ(2*x + on3(x,1,3,co), x)$
## -> x^2 + (x-1)*on3(x,1,3,co) + (3-1)*on3(x,3,inf,co)
## f2 : 2*on3(x,0,%pi/2,cc)*sin(2*x)+cos(x)*on3(x,0,%pi/2,cc)$
## on3integ(f2,x) ->
## (-on3(x,0,%pi/2,cc)*cos(2*x))+3*on3(x,%pi/2,inf,oo)
## +(sin(x)+1)*on3(x,0,%pi/2,cc)
## f4 : 2*on3(x,0,%pi/4,cc)*sin(2*x)+cos(x)*on3(x,0,%pi/2,cc)
## on3integ(f4,x) ->
## (on3(x,0,%pi/4,cc)*(1-cos(2*x))+on3(x,%pi/4,inf,oo)
## +sin(x)*on3(x,0,%pi/2,cc)+on3(x,%pi/2,inf,oo)
## on3integ(on3func,x,xl,xr) 変数xに関する区間[xl,xr]の定積分
## on3integ(f4,x,minf,inf) -> 2
## ev(out4,x = inf) -> 2
## on3integ(expr(-x)*on3(x,0,inf,co),x,0,inf); -> 1
## --end of on3integ('help')--
##
## on3integ('ex)
## --begin of on3integ('ex)--
## ★ ( /* 例1. 不定積分 */
## ex : on3(x,1,3,co) + on3(x,5,7,oc),
## F : on3integ(ex,x)
## )
## ◎ out = 2*on3(x,7,inf,oo)+(x-5)*on3(x,5,7,oc)+2*on3(x,3,inf,co)+(x-1)*on3(x,1,3,co)
## 注: 不定積分関数 F の微分: on3diff(F,x) = on3(x,5,7,oo)+on3(x,1,3,oo)
## <- 端点の開閉に注意
## ★ ( /* 例2-1. 不定積分(on3多項式:非排他分解) */
## ex : on3(x,1,5,co) + on3(x,3,7,oc),
## F : on3integ(ex,x)
## )
## ◎ out = 4*on3(x,7,inf,oo)+4*on3(x,5,inf,co)+(x-3)*on3(x,3,7,oc)+(x-1)*on3(x,1,5,co)
## 注: 不定積分関数 F の排他的分解: on3decomp21(F,x) =
## 8*on3(x,7,inf,oo)+(x+1)*on3(x,5,7,cc)+(2*x-4)*on3(x,3,5,oo)+(x-1)*on3(x,1,3,cc)
## ★
## ( /* 例2-2. 不定積分(on3多項式:非排他分解->排他的分解,不定積分,排他的分解) */
##
## ex : on3(x,1,5,co) + on3(x,3,7,oc),
## ex1 : on3decomp21(ex,x), c0show("on3排他分解:",ex1),
## F : on3integ(ex1,x)
## )
## on3排他分解: ex1 = on3(x,5,7,cc)+2*on3(x,3,5,oo)+on3(x,1,3,cc)
## ◎ out =
## 2*on3(x,7,inf,oo)+4*on3(x,5,inf,co)+(x-5)*on3(x,5,7,cc)+2*on3(x,3,inf,oo)
## +(2*x-6)*on3(x,3,5,oo)+(x-1)*on3(x,1,3,cc)
## 注: 不定積分関数 F の排他的分解: on3decomp21(F,x) =
## 8*on3(x,7,inf,oo)+(x+1)*on3(x,5,7,cc)+(2*(x-3)+2)*on3(x,3,5,oo)+(x-1)*on3(x,1,3,cc)
## 注: 不定積分関数 F の微分: on3diff(F,x) =
## on3(x,5,7,oo)+2*on3(x,3,5,oo)+on3(x,1,3,oo)
## ★ ( /* 例3. 不定積分 */
## ex : %e^(1-x)*on3(x,1,inf,co)+x^2*on3(x,0,1,co),
## F : on3integ(ex,x)
## )
## ◎ out = (1-%e^(1-x))*on3(x,1,inf,co)+on3(x,1,inf,co)/3+(x^3*on3(x,0,1,co))/3
## [ 3 ]
## [ x ]
## [ -- (0 <= x < 1) ]
## [ 3 ]
## F = [ ]
## [ 4 1 - x ]
## [ - - %e (1 <= x < inf) ]
## [ 3 ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ( /* 例4. 不定積分 */
## ex : %e^x*on3(x,minf,0,oo)+%e^(-x)*on3(x,0,inf,co),
## F : on3integ(ex,x), F : on3decomp21(F,x)
## )
## ◎ out = %e^x*on3(x,minf,0,oo)+%e^-x*(2*%e^x-1)*on3(x,0,inf,co)
## [ - x x ]
## [ %e (2 %e - 1) (0 <= x < inf) ]
## [ ]
## F = [ x ]
## [ %e (minf < x < 0) ]
## [ ]
## [ 0 ( otherwise ) ]
## ★ ( /* 例5. 不定積分 */
## ex : 3*x^2*on3(x,3,4,co)*on3(y,6,8,co)+2*x*on3(x,1,4,co)*y*on3(y,2,4,co),
## F : on3integ(ex,x), F : on3decomp21(F,x)
## )
## ◎ out =
## on3(x,3,4,co)*((x-3)*(x^2+3*x+9)*on3(y,6,8,co)+(x-1)*(x+1)*y*on3(y,2,4,co))
## +on3(x,4,inf,co)*(37*on3(y,6,8,co)+15*y*on3(y,2,4,co))
## +(x-1)*(x+1)*on3(x,1,3,co)*y*on3(y,2,4,co)
## ★ ( /* 例6. 不定積分 */
## ex : f1*on3(x,a,b,co)+f2*on3(x,c,d,co),
## F : on3integ(ex,x)
## )
## ◎ out =
## (d*f2-c*f2)*on3(x,d,inf,co)+(f2*x-c*f2)*on3(x,c,d,co)+(b*f1-a*f1)*on3(x,b,inf,co)
## +(f1*x-a*f1)*on3(x,a,b,co)
## ★ ( /* 例7. 不定積分 */
## ex : f1*on3(x,a,b,co)+f2*on3(x,c,d,co),
## F : on3integ(ex,x)
## )
## ◎ out =
## (d*f2-c*f2)*on3(x,d,inf,co)+(f2*x-c*f2)*on3(x,c,d,co)+(b*f1-a*f1)*on3(x,b,inf,co)
## +(f1*x-a*f1)*on3(x,a,b,co)
## ★ ( /* 例8. 不定積分 */
## ex : f0+1/(f1*on3(x,a,b,co)+f2*on3(x,c,d,co)),
## ex : on3decomp21(ex,x,[a<c,c<b,b<d],debug0), c0show(ex),
## F : on3integ(ex,x)
## )
## ex =
## ((f0*f2+f0*f1+1)*on3(x,c,b,co))/(f2+f1)+((f0*f2+1)*on3(x,b,d,co))/f2
## +((f0*f1+1)*on3(x,a,c,co))/f1
## ◎ out =
## ((d*(f0*f2+1))/f2-(b*(f0*f2+1))/f2)*on3(x,d,inf,co)
## +(((f0*f2+f0*f1+1)*x)/(f2+f1)-(c*(f0*f2+f0*f1+1))/(f2+f1))*on3(x,c,b,co)
## +((c*(f0*f1+1))/f1-(a*(f0*f1+1))/f1)*on3(x,c,inf,co)
## +(((f0*f2+1)*x)/f2-(b*(f0*f2+1))/f2)*on3(x,b,d,co)
## +((b*(f0*f2+f0*f1+1))/(f2+f1)-(c*(f0*f2+f0*f1+1))/(f2+f1))*on3(x,b,inf,co)
## +(((f0*f1+1)*x)/f1-(a*(f0*f1+1))/f1)*on3(x,a,c,co)
## ★ ( /* 例9. 不定積分関数 (y に関して) */
## ex : f2*on3(x,0,1,co)*on3(y,x,2,co)+f1*on3(x,0,1,co)*on3(y,x,1,co),
## F : on3integ(ex,y), F : ev(F, ratexpand, ratsimp)
## )
## ◎ out =
## on3(x,0,1,co)*(y*(f2*on3(y,x,2,co)+f1*on3(y,x,1,co))
## +2*f2*on3(y,2,inf,co)+f1*on3(y,1,inf,co))
## +x*on3(x,0,1,co)
## *(f2*((-on3(y,x,2,co))-on3(y,2,inf,co))+f1*((-on3(y,x,1,co))-on3(y,1,inf,co)))
## ★ ( /* 例10. 不定積分関数 (y に関して) */
## ex : f1*on3(x,1,2,co)*on3(y,y1(x),y2(x),co),
## F : on3integ(ex,y)
## )
## ◎ out =
## (f1*y2(x)*on3(x,1,2,co)-f1*y1(x)*on3(x,1,2,co))*on3(y,y2(x),inf,co)
## +(f1*on3(x,1,2,co)*y-f1*y1(x)*on3(x,1,2,co))*on3(y,y1(x),y2(x),co)
## ★ ( /* 例11. 2重定積分 */
## ex : (y+x+5)*(on3(x,2,3,co)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-3,-2,co)*on3(y,-sqrt(9-x^2),sqrt(9-x^2),cc)
## +on3(x,-2,2,co)*on3(y,-sqrt(9-x^2),-sqrt(4-x^2),cc)
## +on3(x,-2,2,co)*on3(y,sqrt(4-x^2),sqrt(9-x^2),cc)),
## Fx : on3integ(ex,y,minf,inf), print(" Fx = ",Fx),
## F : on3integ(Fx,x,minf,inf) )
## Fx =
## 2*(x+5)*sqrt(9-x^2)*on3(x,2,3,co)+2*(x+5)*sqrt(9-x^2)*on3(x,-2,2,co)
## -2*(x+5)*sqrt(4-x^2)*on3(x,-2,2,co)
## +2*(x+5)*sqrt(9-x^2)*on3(x,-3,-2,co)
## ◎ out = 25*%pi
## --end of on3integ('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-20.mxl"18. 関数 on3integ19() : on3関数式の積分
on3integ19()$
on3integ19('ex)$## ~/bin/go TMP/tmp_lang/chunk-21.mxl > TMP/tmp_lang/chunk-21.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-21.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-21.mxl
## on3integ19()
## --begin of on3integ19('help)--
## 機能: on3()関数を含む式の不定積分,定積分を返す.(on3decomp()を必要としない)
## 文法: on3integ19(on3func,var,{vl,vr},...)
## F_i(x) = (F_i(x)-F_i(xl))*on3(x,xl,xr,lr)
## +(F_i(xr)-F_i(xl))*on3(x,xr,inf,lr1),
## where if xl=minf then F_i(xl)=0 (積分定数の定義),
## lr=cc or oc then lr1=oo, lr=co or oo then lr1=co
## 例示: on3integ19(on3func,x) 変数xに関する不定積分
## on3integ19(2*x, x) -> x^2
## on3integ19(2*x + on3(x,1,3,co), x)$
## -> x^2 + (x-1)*on3(x,1,3,co) + (3-1)*on3(x,3,inf,co)
## f2 : 2*on3(x,0,%pi/2,cc)*sin(2*x)+cos(x)*on3(x,0,%pi/2,cc)$
## on3integ19(f2,x) ->
## (-on3(x,0,%pi/2,cc)*cos(2*x))+3*on3(x,%pi/2,inf,oo)
## +(sin(x)+1)*on3(x,0,%pi/2,cc)
## f4 : 2*on3(x,0,%pi/4,cc)*sin(2*x)+cos(x)*on3(x,0,%pi/2,cc)
## on3integ19(f4,x) ->
## (on3(x,0,%pi/4,cc)*(1-cos(2*x))+on3(x,%pi/4,inf,oo)
## +sin(x)*on3(x,0,%pi/2,cc)+on3(x,%pi/2,inf,oo)
## on3integ19(on3func,x,xl,xr) 変数xに関する区間[xl,xr]の定積分
## on3integ19(f4,x,minf,inf) -> 2
## ev(out4,x = inf) -> 2
## on3integ19(exp(-x)*on3(x,0,inf,co),x,0,inf); -> 1
## --end of on3integ19('help')--
##
## on3integ19('ex)
## --begin of on3integ19('ex)--
## ★ ( /* 例1. 不定積分 */
## f : f0, cashow(on3typep(f)),
## F : on3integ19(f,x) )
## on3typep(f) -> on3none
## ◎ out = f0*x
## ★ ( /* 例2. 不定積分 */
## f : f1*on3(x,1,3,co) + f2*on3(x,4,6,co),
## F : on3integ19(f,x), F : on3decomp(F) )
## ◎ out =
## 2*(f2+f1)*on3(x,6,inf,co)+(f2*x-4*f2+2*f1)*on3(x,4,6,co)+2*f1*on3(x,3,4,co)
## +f1*(x-1)*on3(x,1,3,co)
## ★ ( /* 例3. 不定積分 */
## f : 2*sin(2*x)*on3(x,0,%pi/2,cc) + 3*cos(3*x)*on3(x,0,%pi/3,cc),
## F : on3integ19(f,x) )
## ◎ out =
## on3(x,0,%pi/3,cc)*sin(3*x)+on3(x,0,%pi/2,cc)*(1-cos(2*x))+2*on3(x,%pi/2,inf,oo)
## on3ev(F,factor) ->
## on3(x,0,%pi/3,cc)*sin(3*x)-on3(x,0,%pi/2,cc)*(cos(2*x)-1)+2*on3(x,%pi/2,inf,oo)
## 例4a: 微分関数の積分
## f = %e^(x-1)*on3(x,minf,1,oo)+%e^(1-x)*on3(x,1,inf,co)
## df:on3diff(f,x) -> df = %e^(x-1)*on3(x,minf,1,oo)-%e^(1-x)*on3(x,1,inf,oo)
## out : on3integ19(df,x) -> out =
## %e^((-x)-1)*(%e^(2*x)*on3(x,minf,1,oo)-%e^(x+1)*on3(x,1,inf,oo)+%e^2*on3(x,1,inf,oo)
## +%e^(x+1)*on3(x,1,inf,co))
## out1 : on3ev(out,expand) -> out1 =
## %e^(x-1)*on3(x,minf,1,oo)+(%e^(1-x)-1)*on3(x,1,inf,oo)+on3(x,1,inf,co)
## is(equal(out1,f)) = unknown
## on3ev(chk1,expand) = (-on3(x,1,inf,oo))+on3(x,1,inf,co)-on3(x,1,1,cc)
## 例4b: 積分関数の微分
## f = %e^(x-1)*on3(x,minf,1,oo)+%e^(1-x)*on3(x,1,inf,co)
## F : on3integ19(f,x) -> F =
## %e^((-x)-1)*(%e^(2*x)*on3(x,minf,1,oo)+(2*%e^(x+1)-%e^2)*on3(x,1,inf,co))
## F : on3ev(F,expand) -> F = %e^(x-1)*on3(x,minf,1,oo)+(2-%e^(1-x))*on3(x,1,inf,co)
## dF : on3diff(F,x) -> dF = %e^(x-1)*on3(x,minf,1,oo)+%e^(1-x)*on3(x,1,inf,co)
## is(equal(dF,f)) = true
## ★
## ( /* F (直前の結果) の微分 on3diff(F,x) と f の比較(端点を除いて一致する)*/
##
## dF : on3diff(F,x)
## )
## ◎ out = %e^(x-1)*on3(x,minf,1,oo)+%e^(1-x)*on3(x,1,inf,co)
## --end of on3integ19('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-21.mxl"19. 関数 on3solve() : on3 関数方程式の求解 (多変数対応版)
on3solve()$
on3solve('ex)$## ~/bin/go TMP/tmp_lang/chunk-22.mxl > TMP/tmp_lang/chunk-22.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-22.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-22.mxl
## on3solve()
## --begin of on3solve('help)--
## 機能: on3 関数方程式の求解 (多変数対応版)
## 文法: on3solve(funcs,vars,...)
## 例示:
## 例1. 不等式の求解
## eq1 : x^2 * on3(x,minf,0,oo) + (1-x^2)/2 * on3(x,0,1,co)
## + (1-x) * on3(x,1,inf,co) - 1/8$
## out : on3solve(eq1, x);
## -> [x = -1/2^(3/2),x = sqrt(3)/2]
## 例2. 連立不等式の求解
## eq21 : (x^2+y^2-2)*on3(y,0,inf,co) + (x^2+y^2-9)*on3(y,minf,0,oo)$
## eq22 : (x-y)*on3(x,1,inf,co) + (3*x-2*y)*on3(x,0,1,co)
## + (2*x-y)*on3(x,minf,0,oo)$
## out : on3solve([eq21,eq22],[x,y]);
## -> [[x = -3/sqrt(5),y = -6/sqrt(5)],
## [x = 2^(3/2)/sqrt(13),y = (3*sqrt(2))/sqrt(13)],
## [x = 1,y = 1]]
## --end of on3solve('help')--
##
## on3solve('ex)
## --begin of on3solve('ex)--
## --begin of on3solve_ex--
## ★ ( /* 例1. 不等式の求解 */
##
## eq1 : x^2 * on3(x,minf,0,oo) + (1-x^2)/2 * on3(x,0,1,co) + (1-x) * on3(x,1,inf,co) -1/8,
##
## out : on3solve(eq1, x) )
## ◎ out = [x = -1/2^(3/2),x = sqrt(3)/2]
## ★ ( /* 例2. 連立不等式の求解 */
## eq21 : (x^2+y^2-2)*on3(y,0,inf,co) + (x^2+y^2-9)*on3(y,minf,0,oo),
## eq22 : (x-y)*on3(x,1,inf,co) + (3*x-2*y)*on3(x,0,1,co) + (2*x-y)*on3(x,minf,0,oo),
## out : on3solve([eq21,eq22],[x,y]) )
## ◎ out =
## [[x = -3/sqrt(5),y = -6/sqrt(5)],[x = 2^(3/2)/sqrt(13),y = (3*sqrt(2))/sqrt(13)],
## [x = 1,y = 1]]
## --end of on3solve('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-22.mxl"20. 関数 on3D2G() : 矩形領域 D(x,y) 変換 t=x+y, u=y のとき G(t,u) を求める
on3D2G()$
on3D2G('ex)$
on3D2G('test)$## ~/bin/go TMP/tmp_lang/chunk-23.mxl > TMP/tmp_lang/chunk-23.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-23.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-23.mxl
## on3D2G()
## --begin of on3D2G('help)--
## 機能: on3D2G : 矩形領域 D(x,y) 変換 t=x+y, u=y のとき G(t,u) を求める
## 文法: on3D2G(on3(x,xl,xr,xlr)*on3(y,yl,yr,ylr),'typeA|'typeB|'typeE)
## or on3D2G([on3,x,xl,xr,xlr],[on3,y,yl,yr,ylr],'typeA|'typeB|'typeE)
## on3D2G('ex|'test)
## 例示: on3D2G([on3,x,xl,xr,cc],[on3,y,yl,yr,oc],'typeA)
## -> on3(t,tl,tr,tlr)*on3(u,ul,ur,ulr) + ...
## --end of on3D2G('help')--
##
## on3D2G('ex)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,co)*on3(y,yl,yr,cc)
## xL = [on3,x,xl,xr,co] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = by Case facts(yr) = []
## G(t,u) =
## if xr-xl <= yr-yl
## then 'on3(t,yr+xl,yl+xr,oc)*on3(u,yl,yr,cc)
## +'on3(t,yl+xl,yr+xl,cc)*on3(u,yl,t-xl,cc)+'on3(t,yl+xr,yr+xr,oc)*on3(u,t-xr,yr,cc)
## else 'on3(t,yl+xl,yl+xr,cc)*on3(u,yl,t-xl,cc)
## +'on3(t,yr+xl,yr+xr,oc)*on3(u,t-xr,yr,cc)
## +'on3(t,yl+xr,yr+xl,oc)*on3(u,t-xr,t-xl,cc)
## on3D2G(ex) =
## if xr-xl <= yr-yl
## then 'on3(t,yr+xl,yl+xr,oc)*on3(u,yl,yr,cc)
## +'on3(t,yl+xl,yr+xl,cc)*on3(u,yl,t-xl,cc)+'on3(t,yl+xr,yr+xr,oc)*on3(u,t-xr,yr,cc)
## else 'on3(t,yl+xl,yl+xr,cc)*on3(u,yl,t-xl,cc)
## +'on3(t,yr+xl,yr+xr,oc)*on3(u,t-xr,yr,cc)
## +'on3(t,yl+xr,yr+xl,oc)*on3(u,t-xr,t-xl,cc)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,co)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type A (xrng > yrng) を仮定する
## xL = [on3,x,xl,xr,co] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = A facts(yr) = [(-yr)+yl+xr-xl > 0]
## x_l = c x_r = o y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yr+xl,yl+xr] tr = [yr+xl,yl+xr,yr+xr] tlr = [cc,oo,oo]
## ul = [yl,yl,t-xr] ur = [t-xl,yr,yr] ulr = [cc,cc,oc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yr+xl,cc),on3(t,yr+xl,yl+xr,oo),on3(t,yl+xr,yr+xr,oo)]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,yr,cc),on3(u,t-xr,yr,oc)]
## on3D2G(ex,'typeA) =
## on3(t,yr+xl,yl+xr,oo)*on3(u,yl,yr,cc)+on3(t,yl+xl,yr+xl,cc)*on3(u,yl,t-xl,cc)
## +on3(t,yl+xr,yr+xr,oo)*on3(u,t-xr,yr,oc)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,co)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type B (xrng < yrng) を仮定する
## xL = [on3,x,xl,xr,co] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = B facts(yr) = [yr-yl-xr+xl > 0]
## x_l = c x_r = o y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yl+xr,yr+xl] tr = [yl+xr,yr+xl,yr+xr] tlr = [co,oc,oo]
## ul = [yl,t-xr,t-xr] ur = [t-xl,t-xl,yr] ulr = [cc,oc,oc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yl+xr,co),on3(t,yl+xr,yr+xl,oc),on3(t,yr+xl,yr+xr,oo)]
## uL = [on3(u,yl,t-xl,cc),on3(u,t-xr,t-xl,oc),on3(u,t-xr,yr,oc)]
## on3D2G(ex,'typeB) =
## on3(t,yl+xl,yl+xr,co)*on3(u,yl,t-xl,cc)+on3(t,yr+xl,yr+xr,oo)*on3(u,t-xr,yr,oc)
## +on3(t,yl+xr,yr+xl,oc)*on3(u,t-xr,t-xl,oc)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,co)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type E (xrng = yrng) を仮定する
## xL = [on3,x,xl,xr,co] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = E facts(yr) = [equal((-yr)+yl+xr-xl,0)]
## x_l = c x_r = o y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yr+xl,yl+xr] tr = [yr+xl,yl+xr,yr+xr] tlr = [cc,oo,oo]
## ul = [yl,yl,t-xr] ur = [t-xl,yr,yr] ulr = [cc,cc,oc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yr+xl,cc),0,on3(t,yl+xr,yr+xr,oo)]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,yr,cc),on3(u,t-xr,yr,oc)]
## on3D2G(ex,'typeE) =
## on3(t,yl+xl,yr+xl,cc)*on3(u,yl,t-xl,cc)+on3(t,yl+xr,yr+xr,oo)*on3(u,t-xr,yr,oc)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,inf,co)
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,inf,co]
## xrng = xr-xl yrng = inf type = B facts(yr) = []
## x_l = c x_r = c y_l = c y_r = o
## before join & reduce ->
## tl = [yl+xl,yl+xr,inf] tr = [yl+xr,inf,inf] tlr = [cc,oo,oo]
## ul = [yl,t-xr,t-xr] ur = [t-xl,t-xl,inf] ulr = [cc,cc,co]
## after join & reduce ->
## tL = [on3(t,yl+xl,yl+xr,cc),on3(t,yl+xr,inf,oo),0]
## uL = [on3(u,yl,t-xl,cc),on3(u,t-xr,t-xl,cc),on3(u,t-xr,inf,co)]
## on3D2G(ex) =
## on3(t,yl+xl,yl+xr,cc)*on3(u,yl,t-xl,cc)+on3(t,yl+xr,inf,oo)*on3(u,t-xr,t-xl,cc)
## on3D2G('test)
## CS: progn = <on3D2G_ex> , is go.
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,yr,cc)
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = by Case facts(yr) = []
## G(t,u) =
## if xr-xl <= yr-yl
## then 'on3(t,yr+xl,yl+xr,oc)*on3(u,yl,yr,cc)
## +'on3(t,yl+xl,yr+xl,cc)*on3(u,yl,t-xl,cc)+'on3(t,yl+xr,yr+xr,oc)*on3(u,t-xr,yr,cc)
## else 'on3(t,yl+xl,yl+xr,cc)*on3(u,yl,t-xl,cc)
## +'on3(t,yr+xl,yr+xr,oc)*on3(u,t-xr,yr,cc)
## +'on3(t,yl+xr,yr+xl,oc)*on3(u,t-xr,t-xl,cc)
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type A (xrng > yrng) を仮定する
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = A facts(yr) = [(-yr)+yl+xr-xl > 0]
## x_l = c x_r = c y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yr+xl,yl+xr] tr = [yr+xl,yl+xr,yr+xr] tlr = [cc,oc,oc]
## ul = [yl,yl,t-xr] ur = [t-xl,yr,yr] ulr = [cc,cc,cc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yr+xl,cc),on3(t,yr+xl,yl+xr,oc),on3(t,yl+xr,yr+xr,oc)]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,yr,cc),on3(u,t-xr,yr,cc)]
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type B (xrng < yrng) を仮定する
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = B facts(yr) = [yr-yl-xr+xl > 0]
## x_l = c x_r = c y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yl+xr,yr+xl] tr = [yl+xr,yr+xl,yr+xr] tlr = [cc,oc,oc]
## ul = [yl,t-xr,t-xr] ur = [t-xl,t-xl,yr] ulr = [cc,cc,cc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yl+xr,cc),on3(t,yl+xr,yr+xl,oc),on3(t,yr+xl,yr+xr,oc)]
## uL = [on3(u,yl,t-xl,cc),on3(u,t-xr,t-xl,cc),on3(u,t-xr,yr,cc)]
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,yr,cc)
## 判定結果: by Case -> type E (xrng = yrng) を仮定する
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,yr,cc]
## xrng = xr-xl yrng = yr-yl type = E facts(yr) = [equal((-yr)+yl+xr-xl,0)]
## x_l = c x_r = c y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yr+xl,yl+xr] tr = [yr+xl,yl+xr,yr+xr] tlr = [cc,oc,oc]
## ul = [yl,yl,t-xr] ur = [t-xl,yr,yr] ulr = [cc,cc,cc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yr+xl,cc),0,on3(t,yl+xr,yr+xr,oc)]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,yr,cc),on3(u,t-xr,yr,cc)]
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,yl,inf,co)
## xL = [on3,x,xl,xr,cc] yL = [on3,y,yl,inf,co]
## xrng = xr-xl yrng = inf type = B facts(yr) = []
## x_l = c x_r = c y_l = c y_r = o
## before join & reduce ->
## tl = [yl+xl,yl+xr,inf] tr = [yl+xr,inf,inf] tlr = [cc,oo,oo]
## ul = [yl,t-xr,t-xr] ur = [t-xl,t-xl,inf] ulr = [cc,cc,co]
## after join & reduce ->
## tL = [on3(t,yl+xl,yl+xr,cc),on3(t,yl+xr,inf,oo),0]
## uL = [on3(u,yl,t-xl,cc),on3(u,t-xr,t-xl,cc),on3(u,t-xr,inf,co)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,minf,yr,oc)
## xL = [on3,x,xl,xr,cc] yL = [on3,y,minf,yr,oc]
## xrng = xr-xl yrng = inf type = B facts(yr) = []
## x_l = c x_r = c y_l = o y_r = c
## before join & reduce ->
## tl = [minf,minf,yr+xl] tr = [minf,yr+xl,yr+xr] tlr = [oo,oc,oc]
## ul = [minf,t-xr,t-xr] ur = [t-xl,t-xl,yr] ulr = [oc,cc,cc]
## after join & reduce ->
## tL = [0,on3(t,minf,yr+xl,oc),on3(t,yr+xl,yr+xr,oc)]
## uL = [on3(u,minf,t-xl,oc),on3(u,t-xr,t-xl,cc),on3(u,t-xr,yr,cc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,xr,cc)*on3(y,minf,inf,oo)
## xL = [on3,x,xl,xr,cc] yL = [on3,y,minf,inf,oo]
## xrng = xr-xl yrng = inf type = B facts(yr) = []
## x_l = c x_r = c y_l = o y_r = o
## before join & reduce ->
## tl = [minf,minf,inf] tr = [minf,inf,inf] tlr = [oo,oo,oo]
## ul = [minf,t-xr,t-xr] ur = [t-xl,t-xl,inf] ulr = [oc,cc,co]
## after join & reduce ->
## tL = [0,on3(t,minf,inf,oo),0]
## uL = [on3(u,minf,t-xl,oc),on3(u,t-xr,t-xl,cc),on3(u,t-xr,inf,co)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,inf,co)*on3(y,yl,yr,cc)
## xL = [on3,x,xl,inf,co] yL = [on3,y,yl,yr,cc]
## xrng = inf yrng = yr-yl type = A facts(yr) = []
## x_l = c x_r = o y_l = c y_r = c
## before join & reduce ->
## tl = [yl+xl,yr+xl,inf] tr = [yr+xl,inf,inf] tlr = [cc,oo,oo]
## ul = [yl,yl,minf] ur = [t-xl,yr,yr] ulr = [cc,cc,oc]
## after join & reduce ->
## tL = [on3(t,yl+xl,yr+xl,cc),on3(t,yr+xl,inf,oo),0]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,yr,cc),on3(u,minf,yr,oc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,inf,co)*on3(y,yl,inf,co)
## xL = [on3,x,xl,inf,co] yL = [on3,y,yl,inf,co]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = c x_r = o y_l = c y_r = o
## before join & reduce ->
## tl = [yl+xl,inf,inf] tr = [inf,inf,inf] tlr = [co,oo,oo]
## ul = [yl,yl,minf] ur = [t-xl,inf,inf] ulr = [cc,co,oo]
## after join & reduce ->
## tL = [on3(t,yl+xl,inf,co),0,0]
## uL = [on3(u,yl,t-xl,cc),on3(u,yl,inf,co),on3(u,minf,inf,oo)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,inf,co)*on3(y,minf,yr,oc)
## xL = [on3,x,xl,inf,co] yL = [on3,y,minf,yr,oc]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = c x_r = o y_l = o y_r = c
## before join & reduce ->
## tl = [minf,yr+xl,minf+inf] tr = [yr+xl,minf+inf,inf] tlr = [oc,oo,oo]
## ul = [minf,minf,minf] ur = [t-xl,yr,yr] ulr = [oc,oc,oc]
## after join & reduce ->
## tL = [on3(t,minf,yr+xl,oc),on3(t,yr+xl,inf,oo),0]
## uL = [on3(u,minf,t-xl,oc),on3(u,minf,yr,oc),on3(u,minf,yr,oc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,xl,inf,co)*on3(y,minf,inf,oo)
## xL = [on3,x,xl,inf,co] yL = [on3,y,minf,inf,oo]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = c x_r = o y_l = o y_r = o
## before join & reduce ->
## tl = [minf,inf,minf+inf] tr = [inf,minf+inf,inf] tlr = [oo,oo,oo]
## ul = [minf,minf,minf] ur = [t-xl,inf,inf] ulr = [oc,oo,oo]
## after join & reduce ->
## tL = [on3(t,minf,inf,oo),0,0]
## uL = [on3(u,minf,t-xl,oc),on3(u,minf,inf,oo),on3(u,minf,inf,oo)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,xr,oc)*on3(y,yl,yr,cc)
## xL = [on3,x,minf,xr,oc] yL = [on3,y,yl,yr,cc]
## xrng = inf yrng = yr-yl type = A facts(yr) = []
## x_l = o x_r = c y_l = c y_r = c
## before join & reduce ->
## tl = [minf,minf,yl+xr] tr = [minf,yl+xr,yr+xr] tlr = [oo,oc,oc]
## ul = [yl,yl,t-xr] ur = [inf,yr,yr] ulr = [co,cc,cc]
## after join & reduce ->
## tL = [0,on3(t,minf,yl+xr,oc),on3(t,yl+xr,yr+xr,oc)]
## uL = [on3(u,yl,inf,co),on3(u,yl,yr,cc),on3(u,t-xr,yr,cc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,xr,oc)*on3(y,yl,inf,co)
## xL = [on3,x,minf,xr,oc] yL = [on3,y,yl,inf,co]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = c y_l = c y_r = o
## before join & reduce ->
## tl = [minf,minf+inf,yl+xr] tr = [minf+inf,yl+xr,inf] tlr = [oo,oc,oo]
## ul = [yl,yl,t-xr] ur = [inf,inf,inf] ulr = [co,co,co]
## after join & reduce ->
## tL = [on3(t,minf,yl+xr,oc),0,on3(t,yl+xr,inf,oo)]
## uL = [on3(u,yl,inf,co),on3(u,yl,inf,co),on3(u,t-xr,inf,co)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,xr,oc)*on3(y,minf,yr,oc)
## xL = [on3,x,minf,xr,oc] yL = [on3,y,minf,yr,oc]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = c y_l = o y_r = c
## before join & reduce ->
## tl = [minf,minf,minf] tr = [minf,minf,yr+xr] tlr = [oo,oo,oc]
## ul = [minf,minf,t-xr] ur = [inf,yr,yr] ulr = [oo,oc,cc]
## after join & reduce ->
## tL = [0,0,on3(t,minf,yr+xr,oc)]
## uL = [on3(u,minf,inf,oo),on3(u,minf,yr,oc),on3(u,t-xr,yr,cc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,xr,oc)*on3(y,minf,inf,oo)
## xL = [on3,x,minf,xr,oc] yL = [on3,y,minf,inf,oo]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = c y_l = o y_r = o
## before join & reduce ->
## tl = [minf,minf+inf,minf] tr = [minf+inf,minf,inf] tlr = [oo,oo,oo]
## ul = [minf,minf,t-xr] ur = [inf,inf,inf] ulr = [oo,oo,co]
## after join & reduce ->
## tL = [0,0,on3(t,minf,inf,oo)]
## uL = [on3(u,minf,inf,oo),on3(u,minf,inf,oo),on3(u,t-xr,inf,co)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,inf,oo)*on3(y,yl,yr,cc)
## xL = [on3,x,minf,inf,oo] yL = [on3,y,yl,yr,cc]
## xrng = inf yrng = yr-yl type = A facts(yr) = []
## x_l = o x_r = o y_l = c y_r = c
## before join & reduce ->
## tl = [minf,minf,inf] tr = [minf,inf,inf] tlr = [oo,oo,oo]
## ul = [yl,yl,minf] ur = [inf,yr,yr] ulr = [co,cc,oc]
## after join & reduce ->
## tL = [0,on3(t,minf,inf,oo),0]
## uL = [on3(u,yl,inf,co),on3(u,yl,yr,cc),on3(u,minf,yr,oc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,inf,oo)*on3(y,yl,inf,co)
## xL = [on3,x,minf,inf,oo] yL = [on3,y,yl,inf,co]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = o y_l = c y_r = o
## before join & reduce ->
## tl = [minf,minf+inf,inf] tr = [minf+inf,inf,inf] tlr = [oo,oo,oo]
## ul = [yl,yl,minf] ur = [inf,inf,inf] ulr = [co,co,oo]
## after join & reduce ->
## tL = [on3(t,minf,inf,oo),0,0]
## uL = [on3(u,yl,inf,co),on3(u,yl,inf,co),on3(u,minf,inf,oo)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,inf,oo)*on3(y,minf,yr,oc)
## xL = [on3,x,minf,inf,oo] yL = [on3,y,minf,yr,oc]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = o y_l = o y_r = c
## before join & reduce ->
## tl = [minf,minf,minf+inf] tr = [minf,minf+inf,inf] tlr = [oo,oo,oo]
## ul = [minf,minf,minf] ur = [inf,yr,yr] ulr = [oo,oc,oc]
## after join & reduce ->
## tL = [0,on3(t,minf,inf,oo),0]
## uL = [on3(u,minf,inf,oo),on3(u,minf,yr,oc),on3(u,minf,yr,oc)]
## -- end of progn = <on3D2G_ex> ---
## -- D:xl<x<xr, yl<y<yr --(t=x+y,u=y)--> G:G(t,u) --
## ◇ ex = on3(x,minf,inf,oo)*on3(y,minf,inf,oo)
## xL = [on3,x,minf,inf,oo] yL = [on3,y,minf,inf,oo]
## xrng = inf yrng = inf type = E facts(yr) = []
## x_l = o x_r = o y_l = o y_r = o
## before join & reduce ->
## tl = [minf,minf+inf,minf+inf] tr = [minf+inf,minf+inf,inf] tlr = [oo,oo,oo]
## ul = [minf,minf,minf] ur = [inf,inf,inf] ulr = [oo,oo,oo]
## after join & reduce ->
## tL = [on3(t,minf,inf,oo),0,0]
## uL = [on3(u,minf,inf,oo),on3(u,minf,inf,oo),on3(u,minf,inf,oo)]
## -- end of progn = <on3D2G_ex> ---
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-23.mxl"21. 関数 on3dim2_uni2() : 一様分布に従う独立な確率変数の和の分布
figs_dir : "test1_files"$
on3dim2_uni2('plot,'noview)$## ~/bin/go TMP/tmp_lang/chunk-24.mxl > TMP/tmp_lang/chunk-24.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-24.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-24.mxl
## figs_dir:"test1_files"
## on3dim2_uni2('plot,'noview)
## ---Run with NoView Mode---
## 一様分布 U[0,1]に従う独立確率変数の和の分布(密度関数)を求める
## ◆ 1個の和の分布
## ★ ( f[1](t) )
## ◎ out = on3(t, 0, 1, cc)
## f (t) = on3(t, 0, 1, cc)
## 1
## ◆ 2個の和の分布
## CS: h (t, u) = on3(t, 1, 2, co) on3(u, t - 1, 1, cc) + on3(t, 0, 1, co) on3(u, 0, t, cc)
## 2
## ★ ( f[2](t) )
## ◎ out = t on3(t, 0, 1, co) - (t - 2) on3(t, 1, 2, co)
## [ t (0 <= t < 1) ]
## [ ]
## f (t) = [ 2 - t (1 <= t < 2) ]
## 2 [ ]
## [ 0 ( otherwise ) ]
## ◆ 3個の和の分布
## ★ ( f[3](t) )
## ◎ out =
## ((t-3)^2*on3(t,2,3,co))/2-((2*t^2-6*t+3)*on3(t,1,2,co))/2+(t^2*on3(t,0,1,co))/2
## [ 2 ]
## [ t ]
## [ -- (0 <= t < 1) ]
## [ 2 ]
## [ ]
## [ 2 ]
## [ 2 t - 6 t + 3 ]
## f (t) = [ - -------------- (1 <= t < 2) ]
## 3 [ 2 ]
## [ ]
## [ 2 ]
## [ (t - 3) ]
## [ -------- (2 <= t < 3) ]
## [ 2 ]
## [ ]
## [ 0 ( otherwise ) ]
## ◆ 4個の和の分布
## ★ ( f[4](t) )
## ◎ out =
## (-((t-4)^3*on3(t,3,4,co))/6)+((3*t^3-24*t^2+60*t-44)*on3(t,2,3,co))/6
## -((3*t^3-12*t^2+12*t-4)*on3(t,1,2,co))/6
## +(t^3*on3(t,0,1,co))/6
## [ 3 ]
## [ t ]
## [ -- (0 <= t < 1) ]
## [ 6 ]
## [ ]
## [ 3 2 ]
## [ 3 t - 12 t + 12 t - 4 ]
## [ - ----------------------- (1 <= t < 2) ]
## [ 6 ]
## [ ]
## f (t) = [ 3 2 ]
## 4 [ 3 t - 24 t + 60 t - 44 ]
## [ ------------------------ (2 <= t < 3) ]
## [ 6 ]
## [ ]
## [ 3 ]
## [ (t - 4) ]
## [ - -------- (3 <= t < 4) ]
## [ 6 ]
## [ ]
## [ 0 ( otherwise ) ]
## ◆ 5個の和の分布
## ★ ( f[5](t) )
## ◎ out =
## ((t-5)^4*on3(t,4,5,co))/24-((4*t^4-60*t^3+330*t^2-780*t+655)*on3(t,3,4,co))/24
## +((6*t^4-60*t^3+210*t^2-300*t+155)*on3(t,2,3,co))/24
## -((4*t^4-20*t^3+30*t^2-20*t+5)*on3(t,1,2,co))/24
## +(t^4*on3(t,0,1,co))/24
## [ 4 ]
## [ t ]
## [ -- (0 <= t < 1) ]
## [ 24 ]
## [ ]
## [ 4 3 2 ]
## [ 4 t - 20 t + 30 t - 20 t + 5 ]
## [ - ------------------------------- (1 <= t < 2) ]
## [ 24 ]
## [ ]
## [ 4 3 2 ]
## [ 6 t - 60 t + 210 t - 300 t + 155 ]
## f (t) = [ ----------------------------------- (2 <= t < 3) ]
## 5 [ 24 ]
## [ ]
## [ 4 3 2 ]
## [ 4 t - 60 t + 330 t - 780 t + 655 ]
## [ - ----------------------------------- (3 <= t < 4) ]
## [ 24 ]
## [ ]
## [ 4 ]
## [ (t - 5) ]
## [ -------- (4 <= t < 5) ]
## [ 24 ]
## [ ]
## [ 0 ( otherwise ) ]
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-24.mxl"
test1_files/on3dim2_uni2-sum.pngのグラフ
test1_files/on3dim2_uni2-av.pngのグラフ
22. 関数 on3dim2_exp2() : 指数分布に従う独立な確率変数の和の分布
figs_dir : "test1_files"$
on3dim2_exp2('plot,'noview)$## ~/bin/go TMP/tmp_lang/chunk-25.mxl > TMP/tmp_lang/chunk-25.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-25.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-25.mxl
## figs_dir:"test1_files"
## on3dim2_exp2('plot,'noview)
## ---Run with NoView Mode---
## 指数分布 Ex(1)に従う独立確率変数の和の分布(密度関数)を求める
## ◆ 1個の和の分布
## ★ ( f[1](t) )
## - t
## ◎ out = %e on3(t, 0, inf, co)
## - t
## f (t) = %e on3(t, 0, inf, co)
## 1
## ◆ 2個の和の分布
## ★ ( f[2](t) )
## - t
## ◎ out = t %e on3(t, 0, inf, co)
## - t
## f (t) = t %e on3(t, 0, inf, co)
## 2
## ◆ 3個の和の分布
## ★ ( f[3](t) )
## ◎ out = (t^2*%e^-t*on3(t,0,inf,co))/2
## 2 - t
## t %e on3(t, 0, inf, co)
## f (t) = ---------------------------
## 3 2
## ◆ 4個の和の分布
## ★ ( f[4](t) )
## ◎ out = (t^3*%e^-t*on3(t,0,inf,co))/6
## 3 - t
## t %e on3(t, 0, inf, co)
## f (t) = ---------------------------
## 4 6
## ◆ 5個の和の分布
## ★ ( f[5](t) )
## ◎ out = (t^4*%e^-t*on3(t,0,inf,co))/24
## 4 - t
## t %e on3(t, 0, inf, co)
## f (t) = ---------------------------
## 5 24
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-25.mxl"
test1_files/on3dim2_exp2-sum.pngのグラフ
test1_files/on3dim2_exp2-av.pngのグラフ
23. 関数 on3pw() : on3関数のカプセル化(停止中)
on3pw_ex()$## ~/bin/go TMP/tmp_lang/chunk-26.mxl > TMP/tmp_lang/chunk-26.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-26.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-26.mxl
## on3pw_ex()
## --- begin of on3pw_ex ---
## ◆ 準備:関数 F1(x),f0(x)の作成
## ★ (
## f0(x) := sin(x),
## f1(x) := x^2*on3(x,minf,0,oo) + (1-x^2)/2 *on3(x,0,1,oo)
## + (1-x)*on3(x,1,inf,oo),
## ldisplay(f0(x)), ldisplay(f1(x))
## )
## (%t2) f0(x) = sin(x)
## (%t3) f1(x) = x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)+((1-x^2)*on3(x,0,1,oo))/2
## ◆ 使用例1:on3pw()を用いない場合
## ★ (
## define(df_direct(x), on3diff(f1(x),x,1) + diff(f0(x),x,1)),
## ldisplay(df_direct(x)),
## ldisplay(df_direct(1)),
## define(F_direct(x), on3integ(f1(x),x) + integrate(f0(x),x)),
## ldisplay(F_direct(x)),
## mshow(F_direct(2) - F_direct(-1))
## )
## (%t4) df_direct(x) = 2*x*on3(x,minf,0,oo)-on3(x,1,inf,co)-x*on3(x,0,1,oo)+cos(x)
## (%t5) df_direct(1) = cos(1)-1
## (%t6) F_direct(x) = (x^3*on3(x,minf,0,oo))/3+((-x^2/2)+x-1/2)*on3(x,1,inf,oo)
## +on3(x,1,inf,co)/3
## +((x-x^3/3)*on3(x,0,1,oo))/2-cos(x)
## ◆ 使用例2:on3pw()を用いる場合
## ★ (
## f(x) := on3pw(f1(x))+f0(x), /* on3関数f1(x)のカプセル化 */
## define(df(x), diff(f(x),x)), /* 関数f(x)の微分関数 df(x)の定義 */
## ldisplay(df(x)),
## ldisplay(df(1)),
## define(F(x), integrate(f(x),x)), /* 関数f(x)の不定積分 F(x)の定義 */
## ldisplay(F(x)),
## mshow(F(2) - F(-1))
## )
## (%t7) df(x) = 'diff(on3pw(x^2*on3(x,minf,0,oo)+(1-x)*on3(x,1,inf,oo)
## +((1-x^2)*on3(x,0,1,oo))/2),x,1)
## +cos(x)
## diff: variable must not be a number; found: 1
## #0: df(x=1)
## #1: logshow(args=["( @f(x) := on3pw(f1(x))+f0(x), /* on3関数f1(x)のカプセル化 */ @define(df(x), diff(f(x),x...)
## #2: on3pw_ex()
## -- an error. To debug this try: debugmode(true);
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-26.mxl"24. 関数 on3ineq_ex() : 不等式の求解
figs_dir : "test1_files"$
on3ineq_ex(C2, 'file_name="test1_files/on3ineq-C2", 'noview)$## ~/bin/go TMP/tmp_lang/chunk-27.mxl > TMP/tmp_lang/chunk-27.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-27.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-27.mxl
## figs_dir:"test1_files"
## ineqex(C2,'file_name = "test1_files/on3ineq-C2",'noview)
## CS: === ■ ■ ■ progn = <on3ineq_ex> , ■ ■ ■ ===
## CS: excase = C2
## CS: ev(excase) = [[[y^3+2*x*y+x^2,1,9,co]],xrange = [-5,5],yrange = [-5,5]]
## --[Result display]--
## varl = [x,y]
## LL =
## [[['V[1][5],'V[1][1],oc],['V[2][4],'V[2][1],co]],
## [['V[1][1],'V[1][2],oc],['V[2][4],'V[2][2],co]],
## [['V[1][1],'V[1][2],oc],['V[2][3],'V[2][1],oo]],
## [['V[1][2],'V[1][3],oc],['V[2][4],'V[2][1],co]],
## [['V[1][3],'V[1][4],oc],['V[2][5],'V[2][6],cc]],
## [['V[1][3],'V[1][4],oc],['V[2][4],'V[2][1],co]],
## [['V[1][4],'V[1][6],oo],['V[2][4],'V[2][1],co]]]
## , where
## V[ 1 ]= [-4.3414023,-2.2876237,-2.0459579,-0.65266742,minf,inf]
## V[ 2 ]=
## [-(Expt*Sum(3)-Product(4))/(144*x^2),
## ((Product(4)+Negterm)*x^2*Sum(3)^(1/3)+Sum(3)^(2/3)
## *(Product(2)+Product(2)+Negterm+Negterm))
## /(288*x^2),-(Sum(2)*Expt*Expt+Expt*Sum(4))/(288*x^2),
## -(Expt*Sum(3)-Product(4))/(144*x^2),
## ((Product(4)+Negterm)*x^2*Sum(3)^(1/3)+Sum(3)^(2/3)
## *(Product(2)+Product(2)+Negterm+Negterm))
## /(288*x^2),-(Sum(2)*Expt*Expt+Expt*Sum(4))/(288*x^2),minf,inf]
## ---end---
## CS: 参照可能変数: varl,V,LL,vsing,on3f,fL,on3floatnump,acnode
## CS: progn = <on3regionview> , ==2変数関数==
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-27.mxl"
test1_files/on3ineq-C2.pngのグラフ
その他のツール
25. funcs ライブラリー一覧と検索ツール
funcs()$
funcs('ex)$
findstr()$
findstr('ex)$## ~/bin/go TMP/tmp_lang/chunk-28.mxl > TMP/tmp_lang/chunk-28.out 2>&1
## -- <on3env> logbegin --
## maxima_tempdir = TMP/tmp_maxima figs_dir = figs
## batch("/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-28.mxl")
## read and interpret /home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-28.mxl
## funcs()
## ==ユーザ定義の関数名,マクロ名一覧: functions , sortmode= true ==
## ["ON3on3([args])","acnode_join(LWT0,[args])","args_flat([args])","ass_set([args])",
## "chk1g([args])","chk1show([args])","chk2D([args])","chk2g([args])","chk2show([args])",
## "chk3g([args])","debug_ex(x,[args])","debug_sub(y,[args])","ecsort([args])",
## "elimalg1([args])","elimalg1_ex([args])","exchk(on3func_name,exansL,[args])",
## "exchk_ex([args])","exmk(ex,[args])","exmk_ex([args])","exp2l([args])","extry([args])",
## "f2l([args])","f2l_full([args])","f2l_one([args])","fact_forget([args])",
## "fact_var([args])","find_key([args])","find_key_ex([args])","find_key_no([args])",
## "find_key_no_ex([args])","findstr([args])","findstr_ex([args])","floatfix([args])",
## "floatfix_ex([args])","flrlimit([args])","flrlimit_ex([args])","fna([args])",
## "funcs([args])","funcxy([args])","funcxy_ex([args])","gcd2l([args])",
## "globalvar([args])","gr2v([args])","gr2v_ex([args])","gr2vf([args])","gr3v([args])",
## "gr3v_ex([args])","grv([args])","grv_ex([args])","ineqex([args])","jumppoints([args])",
## "killvars([args])","l2f([args])","l2f_one([args])","list2str([args])",
## "list2str_ex([args])","ll2on3(varl,va,LL,[args])","loffuncs([args])","logshow([args])",
## "lpup([args])","mergeL([args])","mergeL_ex([args])","mk_draw([args])",
## "mk_draw_ex([args])","mk_fullname([args])","mk_yrange([args])","mkfloat([args])",
## "mkfloat_ex([args])","msort([args])","msort_ex()","nor2d([args])","on3([args])",
## "on3D2G([args])","on3D2G_ex([args])","on3_same_var([args])","on3asdecomp([args])",
## "on3asdecomp_ex([args])","on3byon3([args])","on3chgv([args])","on3chgvar2([args])",
## "on3chgvar2_ex([args])","on3chgvar2_test()","on3chgvar3([args])",
## "on3cspline(tab,[select])","on3cspline_ex([args])","on3decomp([args])",
## "on3decomp21([args])","on3decomp_decomp(expr,[args])","on3decomp_ex([args])",
## "on3decomp_inv(u,[args])","on3decomp_one([args])","on3decomp_reduce(LWT0,[args])",
## "on3decompm([args])","on3diff([args])","on3diff_ex([args])","on3dim2_exp2([args])",
## "on3dim2_uni2([args])","on3dplot2([args])","on3edge([args])","on3edge_ex([args])",
## "on3ev([args])","on3evdef([args])","on3ex([args])","on3factor([args])",
## "on3find([args])","on3find_ex([args])","on3ftrue([args])","on3funcdraw([args])",
## "on3gr([args])","on3gr2([args])","on3gr_ex([args])","on3help()","on3iftrue([args])",
## "on3ineq([args])","on3ineq_acnode(LF,[args])","on3ineq_backsolve(LF,[args])",
## "on3ineq_fwd(varl,va,vlist,vsing,[args])","on3ineq_jex([args])",
## "on3ineq_shrink([args])","on3info([args])","on3integ([args])","on3integ10([args])",
## "on3integ19([args])","on3integ19_ex([args])","on3integ20([args])",
## "on3integ20_ex([args])","on3integ_ex([args])","on3lrl([args])",
## "on3lspline(tab,[select])","on3lspline_ex([args])","on3pw_ex()","on3regionview([args])",
## "on3rngm([args])","on3rngm_ex1([args])","on3rngm_ex2([args])","on3rngone(rng1,rng2)",
## "on3romberg([args])","on3show_ex([args])","on3show_sub(funcs,[args])","on3simp([args])",
## "on3solve([args])","on3solve_ex([args])","on3std([args])","on3std_ex([args])",
## "on3termsep([args])","on3test([args])","on3typep([args])","on3varfix([args])",
## "on3vars([args])","on3x([args])","outLev([args])","p2surface([args])","polydeg([args])",
## "q3([args])","q4([args])","realp([args])","salgall([args])","salgall_ex([args])",
## "shrink10(LYLR,[args])","slit([args])","sqrt2d([args])","sqrt2d_ex([args])","t(x)",
## "ush([args])","va_unique([args])","var_fact([args])","wt(atom)"]
##
## ==ユーザ定義の関数名,マクロ名一覧: macros , sortmode= true ==
## ["c0show([lis])","c1show([lis])","c2show([lis])","c3show([lis])","cashow([lis])",
## "cshow([lis])","d1show([lis])","d2show([lis])","d3show([lis])","ifargd()",
## "max_restore([args])","max_save([args])","on3env([args])","on3lib([args])",
## "on3rules([args])","on3show([args])"]
##
## funcs('ex)
## --begin of funcs('ex)--
## ev(str) = funcs('show)
## --end of funcs('ex)--
## findstr()
## --begin of findstr('help)--
## 機能: ユーザ定義の関数,マクロから指定文字列を含む関数(マクロ)名を検索する
## 文法: findstr(str)
## 例示: findstr('solve)
## --end of findstr('help')--
##
## findstr('ex)
## --begin of func1('ex)--
## ★
## ( findstr('solve), /* 文字列solve を含む関数名,マクロ名を標示する */
##
##
## findstr('decomp), /* 文字列decomp を含む関数名,マクロ名を標示する */
##
## findstr('show) /* 文字列show を含む関数名,マクロ名を標示する */
## )
## <findstr> search string = solve
## <findstr> functions -->
## ["on3solve([args])","on3solve_ex([args])","on3ineq_backsolve(LF,[args])"]
## <findstr> macros --> []
## <findstr> search string = decomp
## <findstr> functions -->
## ["on3decomp_reduce(LWT0,[args])","on3decomp_decomp(expr,[args])",
## "on3decomp_inv(u,[args])","on3decomp_one([args])","on3asdecomp([args])",
## "on3asdecomp_ex([args])","on3decompm([args])","on3decomp21([args])",
## "on3decomp([args])","on3decomp_ex([args])"]
## <findstr> macros --> []
## <findstr> search string = show
## <findstr> functions -->
## ["chk2show([args])","on3show_sub(funcs,[args])","on3show_ex([args])",
## "logshow([args])","chk1show([args])"]
## <findstr> macros -->
## ["on3show([args])","cashow([lis])","c0show([lis])","cshow([lis])",
## "c1show([lis])","c2show([lis])","c3show([lis])","d1show([lis])",
## "d2show([lis])","d3show([lis])"]
## out = --- end of findstr ---
## --end of findstr('ex)--
## "/home/inoue/Maxlib-20/LANG/TMP/tmp_lang/chunk-28.mxl"