ターミナル立ち上げてすぐに数式を入力できる
数値計算・代数計算にとって強力な助っ人SymPyをもっと簡単に
Pythonは素晴らしい言語です
SymPyライブラリは数学の強力助っ人
でも使うためにはいくつものお膳立てが必要
ターミナルにコマンドpcを打ち込むだけでPython一行コードを即入力・即出力を可能にします
Pythonを立ち上げる必要なし
Pythonのコーディングも必要なし
SymPyライブラリのインポートはじめお膳立ても必要なし
シェルスクリプトは1つpc.shだけだから設置が容易
3ステップで高度な数学計算ができる
1.ターミナルを立ち上げる
2.コマンドpcを打ち込む
3.数式 expand((x+y+z)**3)を入力
【更新】
20240626
・マニュアルを拡充
SymPyに加え-math — 数学関数-を追加
・オプションに
[math]Open Math module Web
を追加
python標準モジュールmath
math module Doc Web表示
20230908
・インストールするファイルを1つだけにした
・モードを9つにした
・出力を7つにした
・カラー表示にした
・複数行コード入力メニュー[2c]Codeを追加
【動作確認環境】
【macOS14.5】
M3Mac
Python 3.11.9
zsh
【macOS12.6.5】
Python 3.11.4
Bash、zsh
【Ubuntu22.04.2LTS】
Python 3.11.1
Bash
【必須Pythonライブラリ】
SymPyライブラリ
mpmathライブラリ
【インストール】
HOMEにディレクトリmyscript/pcをつくる
HOME/myscript/pcに
py.sh
を配置
もし設置するディレクトリを変更する場合
変数PCDIRを変更
# pc.sh
# pc.shの設置ディレクトリ
PCDIR=$HOME/myscript/pc
MacOS .zshrcに以下を追記
# .zshrc
source $HOME/myscript/pc/pc.sh
ubuntu .bashrcに以下を追記
# .bashrc
alias open=xdg-open
source $HOME/myscript/pc/pc.sh
【OPTION】
[n] set precision n digits (default:16 digits)
[c] Enter multiple Code TAB OK Press ‘##’ to Stop inputting
[f] 2/3 -> Fraction(“2/3”).limit_denominator()
[mpf] 3.14 -> mpf(“3.14”) mp(multiple-precision)f(Real float)
[r] verify Rumps example
[m] less manual This manual page Press ‘q’ to stop
[M] open manual
[h] open history open $PCDIR/pchistory.txt
[s] open SymPy Web Site
[math] Open Math module Web
[qq] quit pc
【OUTPUT】
[1]pprint(eq,use_unicode=False)
[2]pprint(eq,use_unicode=True)
[3]pprint(eval(eq))
[4]print(eval(eq))
[5]N(eq, precision)
[6]latex(eval(eq))
[7]latex(N(eq,precision))
シェルスクリプト pc.sh
#!/usr/bin/env bash
# pc
# -- One Line Python(SymPy) Code Calculator --
pcversion='20240626'
# Select Color Set
# Terminal Back Color : Black (Font Color : White)
blue='\033[94m';violet='\033[95m';green='\033[92m';mizu='\033[96m';red='\033[91m';yellow='\033[93m'
# Terminal Back Color : White (Font Color : Black)
# blue='\033[1;30m';violet='\033[1;30m';green='\033[1;30m';mizu='\033[1;30m'
# pc.shの設置ディレクトリ
PCDIR=$HOME/myscript/pc
# コマンド pce
# pc.sh 編集
function pce(){
open $PCDIR/pc.sh
}
# コマンド pcl
# 入力履歴表示
function pcl(){
open $PCDIR/pchistory.txt
}
# コマンド pcd
# SymPy Doc Web表示
function pcd(){
open 'https://docs.sympy.org/latest/tutorials/intro-tutorial/features.html'
}
# コマンド pcmath
# math module Doc Web表示
function pcmath(){
open 'https://docs.python.org/ja/3/library/math.html'
}
# コマンド help
function helppc(){
echo -e "$helptxt" | less -R -X
}
# コマンド helpe Manual外部エディターに表示
function helpe(){
echo -e "$helptxt" | sed -e 's%[[]9[2-6]m%%g' -e 's%[[]1;30m%%g' -e 's%[[]0m%%g' -e 's%[[]m%%g'>$PCDIR/help.txt
open $PCDIR/help.txt
}
# Manual TEXT
helptxt=$(cat << EOF
General Commands Manual
NAME
pc - One Line Python(SymPy) Code Calculator
SYNTAX
pc
VERSION
This man page documents pc version ${pcversion}
Copyright 2023 sakurAi Science Factory, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
Recommended Terminal Font
Ubuntu Mono
DESCRIPTION
Enter One Line Code > \$eq [n]16digits [c][f][mpf][r][m][M][h][s][qq]
One Line Python(SymPy) Code
you can use '^' instead of '**'
IMPORT LIBRARY･MODULE
import math
from fractions import Fraction as Frac
from mpmath import *
from pprint import pprint
mp.pretty = True
from sympy import *
from spb import * # SymPy Plotting Backends (SPB)
import japanize_matplotlib
import matplotlib.pyplot as plt
init_printing() #降べきの順
# init_printing(order='rev-lex') #昇べきの順
var('a:z')
f = Function('f')
OPTION
[n] set precision n digits (default:16 digits)
[c] Enter multiple Code TAB OK Press '##' to Stop inputting
[f] 2/3 -> Fraction("2/3").limit_denominator()
[mpf] 3.14 -> mpf("3.14") mp(multiple-precision)f(Real float)
[r] verify Rumps example
[m] less manual This manual page Press 'q' to stop
[M] open manual
[h] open history open \$PCDIR/pchistory.txt
[s] open SymPy Web Site
[math] Open Math module Web
[qq] quit pc
OUTPUT One Line Python(SymPy) Code [f]Frac [mpf]mpf
[1]pprint(eq,use_unicode=False)
[2]pprint(eq,use_unicode=True)
[3]pprint(eval(eq))
[4]print(eval(eq))
[5]N(eq, precision)
[6]latex(eval(eq))
[7]latex(N(eq,precision))
OUTPUT [c]multiple Code
[8]exec('eq')
[EXPRESSION] All SymPy Code OK
${blue}────────────────────────────────────────────────────────────────────
${violet}Math\033[0m
SymPy Code
${green}OUTPUT\033[0m
${mizu}-BASIC-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}algebra symbolic variable\033[0m
from a to z
${blue}────────────────────────────────────────────────────────────────────
${violet}algebra symbolic function\033[0m
default only f
x, y = symbols('x y', positive=True)
a, b = symbols('a b', real=True)
${blue}────────────────────────────────────────────────────────────────────
${violet}Natural Representation\033[0m
print(expand((x+y)**2))
${green}x**2 + 2*x*y + y**2\033[0m
pprint(expand((x+y)**2))
${green} 2 2
${green}x + 2⋅x⋅y + y \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}substitution\033[0m
(x^2+x+1).subs(x, 1)
${green}3\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}quotient\033[0m
13 // 5
${green}2\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}remainder\033[0m
13 % 5
${green}3\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}quotient and remainder\033[0m
divmod(25, 3)
${green}(8, 1)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}fraction\033[0m
2/3
${green}0.6666666666666666\033[m
Frac(2,3)
${green}2/3\033[m
Frac("2/3")
${green}6004799503160661/9007199254740992\033[m
Frac("2/3").limit_denominator()
${green}2/3\033[m
[c]Code
pprint(Frac("2/3")+Frac("1/7"))
${green}17
${green}──
${green}21\033[m
[f]Frac
2/3+1/7
${green}17
${green}──
${green}21\033[0m
${mizu}-NUMBER-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Pi\033[0m
pi
${green}3.141592653589793 (default 16digits)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Napier Constant\033[0m
E
${green}2.718281828459045 (default 16digits)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}imaginary unit\033[0m
(2+3j)*(5-7j)
${green}(31+1j)
${green}31.0 + 1.0⋅ⅈ\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}imaginary unit(SymPy)\033[0m
exp(cos(E**I)+sin(E*pi))
${green} ⎛ ⅈ⎞
${green} cos⎝ℯ ⎠ + sin(ℯ⋅π)
${green}ℯ
${green}6.237024243670621 - 3.292937458733587⋅ⅈ\033[0m
I**I
${green} ⅈ
${green}ⅈ
${green}0.2078795763507619\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Degree\033[0m
mp.degree
${green}0.0174532925199433\033[0m
pi/180
${green}0.01745329251994330\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Golden Ratio\033[0m
phi
${green}1.618033988749895\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Euler's constant Gamma\033[0m
mp.euler
${green}0.5772156649015329\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Catalan’s constant\033[0m
mp.catalan
${green}0.915965594177219\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Khinchin’s constant\033[0m
mp.khinchin
${green}2.685452001065306\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Glaisher’s constant\033[0m
mp.glaisher
${green}1.282427129100623\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Mertens constant\033[0m
mp.mertens
${green}0.2614972128476428\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Twin prime constant\033[0m
mp.twinprime
${green}0.6601618158468696\033[0m
${mizu}-FUNCTION-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}square root\033[0m
sqrt(2)
${green}1.414213562373095 (default 16digits)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}LCM (Least Common Multiple)\033[0m
lcm(120, 99)
${green}3960\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}GCD (Greatest Common Divisor)\033[0m
gcd(12, 18)
${green}6\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}trigonometry\033[0m
sin(pi/3)
${green} ___
${green}\/ 3
${green}-----
${green} 2 \033[0m
sin(radians(60))
${green}0.8660254037844387\033[0m
degrees(pi/3).evalf()
${green}60.0000000000000\033[0m
asin()
sinh()
asinh()
${blue}────────────────────────────────────────────────────────────────────
${violet}exponential\033[0m
exp(1)
${green}e
${green}ℯ
${green}E
${green}2.718281828459045\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}natural logarithm\033[0m
log(E**2)
${green}2\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}common lagarithm\033[0m
log(2,10) log(x, base)
${green}log(2)/log(10)
${green}0.3010299956639812\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}gamma function\033[0m
gamma(4)
${green}6\033[0m
gamma(sqrt(2))
${green}0.8865814287192591\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}binomial\033[0m
binomial(5,2)
${green}10\033[0m
binomial(n,3)
${green}⎛n⎞
${green}⎜ ⎟
${green}⎝3⎠\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}permutation\033[0m
math.perm(5,2)
${green}20\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}combination\033[0m
math.comb(5,2)
${green}10\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}absolute value\033[0m
abs(-3)
${green}3\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}prime factorization\033[0m
factorint(60)
${green}{2: 2, 3: 1, 5: 1}\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}factorial\033[0m
factorial(10)
${green}3628800\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}KroneckerDelta\033[0m
KroneckerDelta(1, 2)
${green}0\033[0m
KroneckerDelta(i, j)
${green}δ
${green} i,j\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}besseli\033[0m
besselj(n, z).diff(z)
${green}besselj(n - 1, z) besselj(n + 1, z)
${green}───────────────── - ─────────────────
${green} 2 2 \033[0m
besselj(n, z).rewrite(jn)
${green}√2⋅√z⋅jn(n - 1/2, z)
${green}────────────────────
${green} √π \033[0m
${mizu}-SIMPILIFICATION-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}simplify\033[0m
simplify(cos(x)**2+sin(x)**2)
${green}1\033[0m
(x**2 + 2*x + 1)/(x**2 + x)
${green} 2
${green}x + 2⋅x + 1
${green}────────────
${green} 2
${green} x + x \033[0m
simplify((x**2 + 2*x + 1)/(x**2 + x))
${green}x + 1
${green}─────
${green} x \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand\033[0m
expand((x+y+z)**3)
${green} 3 2 2 2 2 3 2 2 3
${green}x + 3⋅x ⋅y + 3⋅x ⋅z + 3⋅x⋅y + 6⋅x⋅y⋅z + 3⋅x⋅z + y + 3⋅y ⋅z + 3⋅y⋅z + z \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}factor\033[0m
factor(a^8-b^8)
${green} ⎛ 2 2⎞ ⎛ 4 4⎞
${green}(a - b)⋅(a + b)⋅⎝a + b ⎠⋅⎝a + b ⎠\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}collec\033[0m
x*y^2+3*x^3*y+5*x*y-7*x^3*y^2
${green} 3 2 3 2
${green}- 7⋅x ⋅y + 3⋅x ⋅y + x⋅y + 5⋅x⋅y\033[0m
collect(x*y^2+3*x^3*y+5*x*y-7*x^3*y^2, x)
${green} 3 ⎛ 2 ⎞ ⎛ 2 ⎞
${green}x ⋅⎝- 7⋅y + 3⋅y⎠ + x⋅⎝y + 5⋅y⎠\033[0m
collect(x*y^2+3*x^3*y+5*x*y-7*x^3*y^2, y)
${green} 2 ⎛ 3 ⎞ ⎛ 3 ⎞
${green}y ⋅⎝- 7⋅x + x⎠ + y⋅⎝3⋅x + 5⋅x⎠\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}cancel\033[0m
(x**2 + 2*x + 1)/(x**2 + x)
${green} 2
${green}x + 2⋅x + 1
${green}────────────
${green} 2
${green} x + x \033[0m
cancel((x**2 + 2*x + 1)/(x**2 + x))
${green}x + 1
${green}─────
${green} x \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}apart\033[0m
1/((x-1)*(x+1))
${green} 1
${green}───────────────
${green}(x - 1)⋅(x + 1)\033[0m
apart(1/((x-1)*(x+1)))
${green} 1 1
${green}- ───────── + ─────────
${green} 2⋅(x + 1) 2⋅(x - 1)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}separatevars\033[0m
(x*y)**y
${green} y
${green}(x⋅y) \033[0m
separatevars((x*y)**y, force=True)
${green} y y
${green}x ⋅y \033[0m
x*y*z*sin(x)*cos(x)+x^2*y*z^3*cos(x)
${green} 2 3
${green}x ⋅y⋅z ⋅cos(x) + x⋅y⋅z⋅sin(x)⋅cos(x)\033[0m
separatevars(x*y*z*sin(x)*cos(x)+x^2*y*z^3*cos(x))
${green} ⎛ 2⎞
${green}x⋅y⋅z⋅⎝sin(x) + x⋅z ⎠⋅cos(x)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}ratsimp\033[0m
reduce fractions to a common denominator
ratsimp(1/x + 1/y)
${green}x + y
${green}─────
${green} x⋅y \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}radsimp\033[0m
Rationalize the denominator by removing square roots
1/(1 + sqrt(2) + sqrt(3) + sqrt(5))
${green} 1
${green}────────────────
${green}1 + √2 + √3 + √5\033[0m
radsimp(1/(1 + sqrt(2) + sqrt(3) + sqrt(5)))
${green}-34⋅√10 - 26⋅√15 - 55⋅√3 - 61⋅√2 + 14⋅√30 + 93 + 46⋅√6 + 53⋅√5
${green}──────────────────────────────────────────────────────────────
${green} 71 \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand_trig\033[0m
expand_trig(sin(x + y))
${green}sin(x)⋅cos(y) + sin(y)⋅cos(x)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}trigsimp\033[0m
trigsimp(sin(x)*cos(y) + sin(y)*cos(x))
${green}sin(x + y)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand_log\033[0m
expand_log(log(x*y), force=True)
${green}log(x) + log(y)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}logcombine\033[0m
logcombine(log(x) + log(y), force=True)
${green}log(x⋅y)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}powsimp\033[0m
x**a*x**b
${green} a b
${green}x ⋅x \033[0m
powsimp(x**a*x**b)
${green} a + b
${green}x \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand_power_exp\033[0m
3**(y + 2)
${green} y + 2
${green}3 \033[0m
expand_power_exp(3**(y + 2))
${green} y
${green}9⋅3 \033[0m
pprint(expand_power_exp(Symbol('x', zero=False)**(y + 2)))
${green} 2 y
${green}x ⋅x \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand_power_base\033[0m
(x*y)**z
${green} z
${green}(x⋅y) \033[0m
expand_power_base((x*y)**z, force=True)
${green} z z
${green}x ⋅y \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}powdenest\033[0m
(x**a)**b
${green} b
${green}⎛ a⎞
${green}⎝x ⎠ \033[0m
powdenest((x**a)**b, force=True)
${green} a⋅b
${green}x \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}expand_func\033[0m
expand_func(gamma(x+3))
${green}x⋅(x + 1)⋅(x + 2)⋅Γ(x)\033[0m
expand_func(binomial(n,3))
${green}n⋅(n - 2)⋅(n - 1)
${green}─────────────────
${green} 6 \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}FUNCsimp\033[0m
gammasimp(gamma(x)*gamma(1-x))
${green} π
${green}────────
${green}sin(π⋅x)c
combsimp(binomial(n+2,k)/binomial(n,k))
${green} (n + 1)⋅(n + 2)
${green}───────────────────────
${green}(k - n - 2)⋅(k - n - 1)\033[0m
kroneckersimp( 1+KroneckerDelta(0, j) * KroneckerDelta(1, j))
${green}1\033[0m
besselsimp(z*besseli(0, z) + z*(besseli(2, z))/2 + besseli(1, z))
${green}3⋅z⋅besseli(0, z)
${green}─────────────────
${green} 2 \033[0m
hypersimp(factorial(n)**2 / factorial(2*n), n)
${green} n + 1
${green}───────────
${green}2⋅(2⋅n + 1)\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}.rewrite\033[0m
tan(x).rewrite(sin)
${green} 2
${green}2⋅sin (x)
${green}─────────
${green} sin(2⋅x)\033[0m
(cos(x)).rewrite(sin)
${green} ⎛ π⎞
${green}sin⎜x + ─⎟
${green} ⎝ 2⎠\033[0m
factorial(x).rewrite(gamma)
${green}Γ(x + 1)\033[0m
${mizu}-SEQUENCE-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}sequence\033[0m
sequence(k**2,(k,1,10))
${green}[1, 4, 9, 16, …]\033[0m
sequence(k**2,(k,1,10))[9]
${green}100\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}summation of a sequence\033[0m
Sum(k**2,(k,1,n))
${green} n
${green} ___
${green} ╲
${green} ╲ 2
${green} ╱ k
${green} ╱
${green} ‾‾‾
${green}k = 1 \033[0m
Sum(k**2,(k,1,n)).doit()
${green} 3 2
${green}n n n
${green}── + ── + ─
${green}3 2 6\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}product of a sequence\033[0m
Product(k,(k,1,10))
${green} 10
${green}─┬─┬─
${green} │ │ k
${green} │ │
${green}k = 1 \033[0m
product(k,(k,1,10))
${green}3628800\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Seki-Bernoulli number\033[0m
bernoulli(1)
${green}1/2\033[0m
bernoulli(2)
${green}1/6\033[0m
${mizu}-EQUATION-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Eq\033[0m
Eq(x^3, x^2-1)
${green} 3 2
${green}x = x - 1\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}solve\033[0m
solve(x^2+x+4)
${green}⎡ 1 √15⋅ⅈ 1 √15⋅ⅈ⎤
${green}⎢- ─ - ─────, - ─ + ─────⎥
${green}⎣ 2 2 2 2 ⎦\033[0m
solve(a*x**2+b*x+c, x)
${green}⎡ _____________ _____________⎤
${green}⎢ ╱ 2 ╱ 2 ⎥
${green}⎢-b - ╲╱ -4⋅a⋅c + b -b + ╲╱ -4⋅a⋅c + b ⎥
${green}⎢─────────────────────, ─────────────────────⎥
${green}⎣ 2⋅a 2⋅a ⎦\033[0m
solve(x**2-1,x)[0]
${green}-1\033[0m
[f]Frac
solve([2/3*x-y-1,3/7*x-2*y-5/9],[x,y])
${green}⎧ 91 11⎫
${green}⎨x: ──, y: ───⎬
${green}⎩ 57 171⎭\033[0m
solve([x+y-4,x-y-2],[x,y])
${green}{x: 3, y: 1}\033[0m
list(solve([x+y-4,x-y-2]).items())[0]
${green}(x, 3)\033[0m
list(solve([x+y-4,x-y-2],[x,y]).items())[0][1]
${green}3\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}dsolve\033[0m
variable function f
Eq(Derivative(f(t),t,2)-f(t),exp(t))
${green} 2
${green} d t
${green}───(f(t)) - f(t) = ℯ
${green} 2
${green}dt \033[0m
dsolve(Eq(f(t).diff(t, 2) - f(t), exp(t)), f(t))
${green} -t ⎛ t⎞ t
${green}f(t) = C₂⋅ℯ + ⎜C₁ + ─⎟⋅ℯ
${green} ⎝ 2⎠ \033[0m
dsolve(Eq(f(t).diff(t, 2) - f(t), exp(t)), f(t), ics={f(0):1, f(t).diff(t,1).subs(t, 0):1})
${green} -t
${green} ⎛t 3⎞ t ℯ
${green}f(t) = ⎜─ + ─⎟⋅ℯ + ───
${green} ⎝2 4⎠ 4 \033[0m
${mizu}-CALCULUS-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}differential\033[0m
diff(x^3+x^2+x+1)
${green} 2
${green}3⋅x + 2⋅x + 1\033[0m
diff(sin(x),x,3)
${green}-cos(x)\033[0m
Derivative(exp(x**2),x,3)
${green} 3⎛ ⎛ 2⎞⎞
${green} d ⎜ ⎝x ⎠⎟
${green}───⎝ℯ ⎠
${green} 3
${green}dx \033[0m
Derivative(exp(x**2),x,3).doit()
${green} ⎛ 2⎞
${green} ⎛ 2 ⎞ ⎝x ⎠
${green}4⋅x⋅⎝2⋅x + 3⎠⋅ℯ \033[0m
[c]Code
f = Function('f')
g = Function('g')
eq = (f(x) * g(x)).diff(x)
pprint(eq)
${green} d d
${green}f(x)⋅──(g(x)) + g(x)⋅──(f(x))
${green} dx dx \033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}indefinite integral\033[0m
integrate(3*x^2+2*x+1)
${green} 3 2
${green}x + x + x\033[0m
[f]Frac
Integral(3*x^2+2*x-2/3)
${green}⌠
${green}⎮ ⎛ 2 2⎞
${green}⎮ ⎜3⋅x + 2⋅x - ─⎟ dx
${green}⎮ ⎝ 3⎠
${green}⌡ \033[0m
[f]Frac
Integral(3*x^2+2*x-2/3).doit()
${green} 3 2 2⋅x
${green}x + x - ───
${green} 3 \033[0m
${violet}definite integral\033[0m
integrate(x**3,(x,0,1))
${green}1/4\033[0m
[f]Frac
Integral(2/3*x^5, (x, 0, 2/3))
${green}2/3
${green} ⌠
${green} ⎮ 5
${green} ⎮ 2⋅x
${green} ⎮ ──── dx
${green} ⎮ 3
${green} ⌡
${green} 0 \033[0m
[f]Frac
Integral(2/3*x^5, (x, 0, 2/3)).doit()
${green} 64
${green}────
${green}6561\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Taylor series\033[0m
series(sin(x),x, 0, 12)
${green} 3 5 7 9 11
${green} x x x x x ⎛ 12⎞
${green}x - ── + ─── - ──── + ────── - ──────── + O⎝x ⎠
${green} 6 120 5040 362880 39916800 \033[0m
${violet}Taylor series coefficient list\033[0m
taylor(sin, 0, 5)
${green}[0.0, 1.0, 0.0, -0.1666666666666667, 0.0, 0.008333333333333333]\033[0m
series(sin(x),x, 0, 12).removeO()
${green} 3 5 7 9 11
${green} x x x x x
${green}x - ── + ─── - ──── + ────── - ────────
${green} 6 120 5040 362880 39916800\033[0m
series(sin(x),x, 0, 12).removeO().subs(x,1)
${green}0.8414709846480680\033[0m
${mizu}-INFINITY-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}infinity\033[0m
oo
${green}∞\033[0m
Integral(1/(1+x**2), (x, -oo, oo))
${green}∞
${green}⌠
${green}⎮ 1
${green}⎮ ────── dx
${green}⎮ 2
${green}⎮ x + 1
${green}⌡
${green}-∞ \033[0m
Integral(1/(1+x**2), (x, -oo, oo)).doit()
${green}π\033[0m
integrate(1/(1+x**2), (x, -oo, oo))
${green}π\033[0m
${mizu}-LIMIT-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}limit\033[0m
limit(sin(x)/x, x, 0)
${green}1\033[0m
Limit((x^2+x-1)/(2*x^2-x+2), x, oo)
${green} ⎛ 2 ⎞
${green} ⎜ x + x - 1 ⎟
${green}lim ⎜────────────⎟
${green}x─→∞⎜ 2 ⎟
${green} ⎝2⋅x - x + 2⎠\033[0m
Limit((x^2+x-1)/(2*x^2-x+2), x, oo).doit()
${green}1/2\033[0m
limit((x^2+x-1)/(2*x^2-x+2), x, oo)
${green}1/2\033[0m
limit(tan(x), x, pi/2, '+')
${green}-∞\033[0m
limit(tan(x), x, pi/2, '-')
${green}∞\033[0m
${mizu}-MATRIX-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}Matrix\033[0m
Matrix([[1, 2], [2, 2]])
${green}⎡1 2⎤
${green}⎢ ⎥
${green}⎣2 2⎦\033[0m
Matrix([[1, 2], [2, 2]])**2
${green}⎡5 6⎤
${green}⎢ ⎥
${green}⎣6 8⎦\033[0m
eye(3)
${green}⎡1 0 0⎤
${green}⎢ ⎥
${green}⎢0 1 0⎥
${green}⎢ ⎥
${green}⎣0 0 1⎦\033[0m
zeros(3)
${green}⎡0 0 0⎤
${green}⎢ ⎥
${green}⎢0 0 0⎥
${green}⎢ ⎥
${green}⎣0 0 0⎦\033[0m
ones(3)
${green}⎡1 1 1⎤
${green}⎢ ⎥
${green}⎢1 1 1⎥
${green}⎢ ⎥
${green}⎣1 1 1⎦\033[0m
diag(1, 2, 3)
${green}⎡1 0 0⎤
${green}⎢ ⎥
${green}⎢0 2 0⎥
${green}⎢ ⎥
${green}⎣0 0 3⎦\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.det()\033[0m
Matrix([[1, 2], [2, 2]]).det()
${green}-2\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.inv()\033[0m
Matrix([[1, 2], [2, 2]]).inv()
${green}⎡-1 1 ⎤
${green}⎢ ⎥
${green}⎣1 -1/2⎦\033[0m
Matrix([[1, 2], [2, 2]])**(-1)
${green}⎡-1 1 ⎤
${green}⎢ ⎥
${green}⎣1 -1/2⎦\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.adjugate()\033[0m
Matrix([[1, 2], [3, 4]]).adjugate()
${green}⎡4 -2⎤
${green}⎢ ⎥
${green}⎣-3 1 ⎦\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.transpose()\033[0m
Matrix([[1, 2], [3, 4]]).transpose()
${green}⎡1 3⎤
${green}⎢ ⎥
${green}⎣2 4⎦\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.rank()\033[0m
Matrix([[1, 2, 3], [4, 5, 0], [0, 0, 0]]).rank()
${green}2\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.eigenvals()\033[0m
Matrix([[1, 2], [2, 2]]).eigenvals()
${green}⎧3 √17 3 √17 ⎫
${green}⎨─ - ───: 1, ─ + ───: 1⎬
${green}⎩2 2 2 2 ⎭\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}A.eigenvects()\033[0m
Matrix([[1, 2], [2, 2]]).eigenvects()
${green}⎡⎛ ⎡⎡ √17 1⎤⎤⎞ ⎛ ⎡⎡ 1 √17⎤⎤⎞⎤
${green}⎢⎜3 √17 ⎢⎢- ─── - ─⎥⎥⎟ ⎜3 √17 ⎢⎢- ─ + ───⎥⎥⎟⎥
${green}⎢⎜─ - ───, 1, ⎢⎢ 4 4⎥⎥⎟, ⎜─ + ───, 1, ⎢⎢ 4 4 ⎥⎥⎟⎥
${green}⎢⎜2 2 ⎢⎢ ⎥⎥⎟ ⎜2 2 ⎢⎢ ⎥⎥⎟⎥
${green}⎣⎝ ⎣⎣ 1 ⎦⎦⎠ ⎝ ⎣⎣ 1 ⎦⎦⎠⎦\033[0m
${mizu}-ZETA-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}zeta\033[0m
zeta(2)
${green} 2
${green}π
${green}──
${green}6 \033[0m
zeta(-1)
${green}-1/12\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}zetazero\033[0m
zetazero(1)
${green}(0.5 + 14.13472514173469j)\033[0m
${mizu}-Boolean-valued check-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}==\033[0m
1+1 == 3
${green}False\033[0m
expand((x+y)**2) == x**2+2*x*y+y**2
${green}True\033[0m
${mizu}-mpmath floating-point-\033[0m
${blue}────────────────────────────────────────────────────────────────────
(-2)**mpf("0.5")
${green}(0.0 + 1.4142135623730950488016887242096980785696718753769j)\033[0m
${mizu}-PLOT-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}from spb import * # SymPy Plotting Backends (SPB)\033[0m
${violet}import japanize_matplotlib\033[0m
${violet}import matplotlib.pyplot as plt\033[0m
plot(sin(x), (x, 0, 7), ylabel = "y")
graphics(line(sin(x)),axis_center="auto", grid=False)
p1 = plot_list([2], [4],
legend=True,
is_point = True,
line_color = "red",
show = False)
p2 = plot(x**2, (x, 0, 3),
line_color = "blue",
show = False)
(p1+p2).show()
f1 = x
f2 = x**2
f3 = sin(x)
plot((f1,"1次関数"), (f2, "2次関数"),(f3,"三角関数"),
(x, 0, 4),
rendering_kw=[{"color":"red"},{"color":"blue"},{"color":"green"}],
backend=MB, # Choromeブラウザー出力
title = "backend=MB (MatplotlibBackend)",
axis_center="auto",
grid=True,
xlabel = "x",
ylabel = "y")
f1 = x
f2 = x**2
f3 = sin(x)
plot((f1,"1次関数"), (f2, "2次関数"),(f3,"三角関数"),
(x, -2, 2),
backend=BB, # Choromeブラウザー出力
title = "backend=BB (BokehBackend)",
xlabel = "x",
ylabel = "y")
f1 = x
f2 = x**2
f3 = sin(x)
plot((f1,"1次関数"), (f2, "2次関数"),(f3,"三角関数"),
(x, -2, 2),
backend=PB, # Choromeブラウザー出力
title = "backend=PB (PlotyBackend)",
xlabel = "x",
ylabel = "y")
p = plot(sin(x), (x, -pi, pi), ylabel="sin x", axis_center="auto",backend=MB, show=False)
ax = p.ax
ax.set_xlabel("x:時間", loc="right")
ax.set_ylabel("y:長さ", loc="top", rotation=0,labelpad=-30)
plt.legend()
plt.show()
plot_parametric(2 * cos(u) + 5 * cos(2 * u / 3),
2 * sin(u) - 5 * sin(2 * u / 3),
(u, 0, 6 * pi),
aspect='equal')
${mizu}-math -- 数学関数-\033[0m
${blue}────────────────────────────────────────────────────────────────────
${violet}math.ceil(x)\033[0m
${violet}math.comb(n, k)\033[0m
${violet}math.copysign(x, y)\033[0m
x の大きさ (絶対値) で y と同じ符号の浮動小数点数を返します。
${violet}math.fabs(x)\033[0m
${violet}math.factorial(n)\033[0m
${violet}math.floor(x)\033[0m
${violet}math.fmod(x, y)\033[0m
一般には浮動小数点の場合には関数 fmod() 、整数の場合には x % y を使う方がよい
${violet}math.frexp(x)\033[0m
x の仮数と指数を (m, e) のペアとして返します
${violet}math.fsum(iterable)\033[0m
${violet}math.gcd(*integers)\033[0m
${violet}math.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)\033[0m
値 a と b が互いに近い場合 True を、そうでない場合は False を返します。
${violet}math.isfinite(x)\033[0m
${violet}math.isinf(x)\033[0m
${violet}math.isnan(x)\033[0m
${violet}math.lcm(*integers)\033[0m
${violet}math.ldexp(x, i)\033[0m
x * (2**i) を返します
${violet}math.modf(x)\033[0m
x の小数部分と整数部分を返します。
${violet}math.nextafter(x, y, steps=1)\033[0m
${violet}math.perm(n, k=None)\033[0m
${violet}math.prod(iterable, *, start=1)\033[0m
${violet}math.remainder(x, y)\033[0m
${violet}math.sumprod(p, q)\033[0m
${violet}math.trunc(x)\033[0m
${violet}math.ulp(x)\033[0m
${violet}math.cbrt(x)\033[0m
${violet}math.exp(x)\033[0m
${violet}math.exp2(x)\033[0m
${violet}math.expm1(x)\033[0m
${violet}math.log(x[, base])\033[0m
${violet}math.log1p(x)\033[0m
${violet}math.log2(x)\033[0m
${violet}math.log10(x)\033[0m
${violet}math.sqrt(x)\033[0m
${violet}math.acos(x)\033[0m
${violet}math.asin(x)\033[0m
${violet}math.atan(x)\033[0m
${violet}math.atan2(y, x)\033[0m
${violet}math.cos(x)\033[0m
${violet}math.dist(p, q)\033[0m
${violet}math.hypot(*coordinates)\033[0m
${violet}math.sin(x)\033[0m
${violet}math.tan(x)\033[0m
${violet}math.degrees(x)\033[0m
${violet}math.radians(x)\033[0m
${violet}math.acosh(x)\033[0m
${violet}math.asinh(x)\033[0m
${violet}math.atanh(x)\033[0m
${violet}math.cosh(x)\033[0m
${violet}math.sinh(x)\033[0m
${violet}math.tanh(x)\033[0m
${violet}math.erf(x)\033[0m
${violet}math.erfc(x)\033[0m
${violet}math.gamma(x)\033[0m
${violet}math.lgamma(x)\033[0m
${violet}math.pi\033[0m
${violet}math.e\033[0m
${violet}math.tau\033[0m
${violet}math.inf\033[0m
${violet}math.nan\033[0m
EOF
)
# 複数行コード ヘッダー部分 ライブラリ
EXECPRE=$(cat << EOF
import math
from mpmath import *
from pprint import pprint
mp.pretty = True
from sympy import *
from spb import * # SymPy Plotting Backends (SPB)
import japanize_matplotlib
import matplotlib.pyplot as plt
from fractions import Fraction as Frac
init_printing()
#init_printing(order='rev-lex')
var('a:z')
f = Function('f')
#
# Enter your code below
# Press ## in Last Line
#
EOF
)
# 本体
# コマンド pc
function pc(){
echo -e "${green}pc $pcversion\n\033[0mOne Line Python(SymPy) Code Calculator"
echo -e "Type [n][c][f][mpf][r][m][M][h][s][math][qq] for option"
echo -e " ${mizu}[n]\033[0mprecision n digits ${mizu}[c]\033[0mMultiple Code ${mizu}[f]\033[0mFrac ${mizu}[mpf]\033[0mmpf ${mizu}[r]\033[0mRump ${mizu}[m]\033[0mless Manual"
echo -e " ${mizu}[M]\033[0mOpen Manual ${mizu}[h]\033[0mOpen history ${mizu}[s]\033[0mOpen SymPy Web ${mizu}[math]\033[0mOpen Math module Web ${mizu}[qq]\033[0mQuit pc\n"
unset eq
unset N
mode=''
while :
do
while :
do
echo -e "One Line Code > \$eq ${mizu}[n]\033[0m${yellow}${N:-16}\033[0m${mizu}digits [c][f][mpf][r][m][M][h][s][math][qq]\033[0m"
read VAR
case "$VAR" in
n ) echo -e -n "${mizu}precision \033[0m${green}${N:-16}\033[0m${mizu}digits > \033[0m" && read N ; continue ;;
c ) mode="exec" ; break ;;
f ) mode="frac" ; break ;;
mpf ) mode="mpf" ; break ;;
r ) mode="rump" ; break ;;
m ) helppc ; continue ;;
M ) helpe ; continue ;;
h ) pcl ; continue ;;
s ) pcd && continue ;;
math ) pcmath && continue ;;
# c1 ) blue='\033[94m';violet='\033[95m';green='\033[92m';mizu='\033[96m';red='\033[91m' ; continue ;;
# c2 ) blue='\033[1;30m';violet='\033[1;30m';green='\033[1;30m';mizu='\033[1;30m'; continue ;;
qq ) mode="quit" ; break ;;
# sss ) sss ; break ;;
* ) mode="just" ; echo -n "" > $PCDIR/pceq.txt ; echo $VAR | sed -e 's%\^%**%g' > $PCDIR/pceq.txt && eq=$(<$PCDIR/pceq.txt) ; break ;;
esac
done
[ "$mode" = "exec" ] && echo -e "${green}[c]Multiple Code + ## >\033[0m" && echo "$EXECPRE" && eqq="" && IFS=$'\n' &&
while :
do
read v
eqq+=$v'\n'
if [ $v = "##" ]; then
break
fi
done
echo -e "$eqq" > $PCDIR/pceq.txt
[ "$mode" = "frac" ] && echo -e "${green}[f]eq(one liner code) >\033[0m" && read eqq && echo "$eqq" >> $PCDIR/pchistory.txt && echo $eqq | sed -e 's%[0-9]\+/[0-9]\+%Frac("&").limit_denominator()%g' -e 's%\^%**%g' > $PCDIR/pceq.txt && eq=$(<$PCDIR/pceq.txt)
[ "$mode" = "mpf" ] && echo -e "${green}[mpf]eq(one liner code) >\033[0m" && read eqq && echo $eqq | sed -e 's%[0-9]\+\.*[0-9]*%mpf("&")%g' -e 's%\^%**%g' > $PCDIR/pceq.txt && eq=$(<$PCDIR/pceq.txt)
[ "$mode" = "rump" ] && echo -e "${green}Rump"\'"s example Test\033[0m" && eq="rump"
[ "$mode" = "quit" ] && echo -e "${green}Quit pc\033[0m" && break
COMMAND=$(cat << EOF
$(echo date "+%Y.%m.%d-%H:%M:%S") >> $PCDIR/pchistory.txt
echo "$eq" >> $PCDIR/pchistory.txt
echo "" >> $PCDIR/pchistory.txt
echo -E "
import math
from fractions import Fraction as Frac
from mpmath import *
from pprint import pprint
mp.pretty = True
from sympy import *
from spb import * # SymPy Plotting Backends (SPB)
import japanize_matplotlib
import matplotlib.pyplot as plt
init_printing() #降べきの順
# init_printing(order='rev-lex') #昇べきの順
var('a:z')
f = Function('f')
GRE='$green'
RED='$red'
VIO='$violet'
END='\033[0m'
mp.dps = ${N:-16}
# mp.prec = 200
# print(GRE+'\n[0]print(eq)'+END)
# print($eq)
print(VIO+'\n[1]pprint(eq,use_unicode=False)'+END)
print(GRE,end='')
pprint($eq,use_unicode=False)
print(END,end='')
print(VIO+'\n[2]pprint(eq,use_unicode=True)'+END)
print(GRE,end='')
pprint($eq,use_unicode=True)
print(END,end='')
print(VIO+'\n[3]pprint(eval(eq), order="rev-lex")'+END)
print(GRE,end='')
pprint(eval('$eq'), order='rev-lex')
print(END,end='')
print(VIO+'\n[4]print(eval(eq))'+END)
print(GRE,end='')
print(eval('$eq'))
print(END,end='')
print(VIO+'\n[5]N(eq,${N:-16})'+END)
try:
N($eq,${N:- 16})
except AttributeError:
print(RED+'No Numerical Evaluation'+END)
else:
print(GRE,end='')
pprint(N($eq,${N:-16}))
print(END,end='')
print(VIO+'\n[6]latex(eval(eq))'+END)
try:
latex(eval('$eq'))
except AttributeError:
print(RED+'No Output in LaTeX'+END)
else:
print(GRE,end='')
print(latex(eval('$eq')))
print(END,end='')
print(VIO+'\n[7]latex(N(eq,${N:-16}))'+END)
try:
latex(N($eq,${N:-16}))
except AttributeError:
print(RED+'No Output in LaTeX'+END)
else:
print(GRE,end='')
print(latex(N($eq,${N:-16})))
print(END,end='')
print('\n')
" | python
EOF
)
# モード毎
case $mode in
just )
eval "${COMMAND}"
;;
exec )
date "+%Y.%m.%d-%H:%M:%S" >> $PCDIR/pchistory.txt
echo -e "$eqq" >> $PCDIR/pchistory.txt
echo -E "
import math
from mpmath import *
from pprint import pprint
mp.pretty = True
from sympy import *
from spb import * # SymPy Plotting Backends (SPB)
import japanize_matplotlib
import matplotlib.pyplot as plt
from fractions import Fraction as Frac
init_printing()
#init_printing(order='rev-lex')
var('a:z')
f = Function('f')
GRE='$green'
RED='$red'
VIO='$violet'
END='\033[0m'
mp.dps = ${N:- 16}
print(VIO+'\n[8]exec(eq)'+END)
f = open('$PCDIR/pceq.txt')
cmd = f.read()
print(GRE,end='')
exec(cmd)
print(END)
" | python
echo -n "" > $PCDIR/pceq.txt
;;
frac )
echo $eq && echo -n -e "${green}expression change? [n(ENTER)/y]\033[0m " ; read yn
case "$yn" in [Yy])
read eq ;;
[])
;;
[n])
;;
esac
eval echo $"$COMMAND"
;;
mpf )
echo $eq && echo -n -e "${green}expression change? [n(ENTER)/y]\033[0m " ; read yn
case "$yn" in [Yy])
read eq ;;
[])
;;
[n])
;;
esac
eval "${COMMAND}"
;;
rump )
echo -e -n "${green}precision[default:16] > \033[0m"
read N
$(echo date "+%Y.%m.%d-%H:%M:%S") >> $PCDIR/pchistory.txt
echo "$eq" >> $PCDIR/pchistory.txt
echo -E "
from mpmath import *
mp.pretty = True
a=77617
b=33096
c=333.75*b**6+a**2*(11*a**2*b**2-b**6-121*b**4-2)+5.5*b**8+a/(2*b)
print(f'Normal {c}')
def g(a, b):
return (mpf('333.75')*b**6 + a**2*(11*a**2*b**2-b**6-121*b**4-2)+mpf('5.5')*b**8+a/(mpf('2')*b))
print('{:6}'.format('mp.dps'))
for mp.dps in range(1, $N+1):
print('{:6}'.format(mp.dps),g(mpf('77617'), mpf('33096')))
print('')
" | python
esac
done
}
option[m] Manual
