計算がはやくなる

# Program Name: frequent_math_patterns_1to20.py
# Creation Date: 20250609
# Overview: Computes frequent squares, powers, decimal-fraction conversions, and fast multiplication patterns for numbers 1–20
# Usage: Run the script for outputs of fast math patterns from 1 to 20

# ライブラリのインストール / Install required libraries
!pip install sympy

# ライブラリのインポート / Import libraries
from sympy import Rational, factorint

# ============================================
# 頻出2乗計算（1〜20）/ Frequent Squares (1–20)
# ============================================
# 各整数の2乗を辞書形式で保存 / Store squares of numbers 1–20
squares = {n: n**2 for n in range(1, 21)}
print("■ Frequent Squares (1–20):")
print(squares)

# =============================================
# 頻出累乗計算（1〜5の累乗）/ Frequent Powers
# =============================================
# n^k を小さめの組み合わせで収集 / Collect small base-power combos
powers = {}
for base in range(1, 6):
    for exp in range(2, 5):
        powers[f"{base}^{exp}"] = base**exp
print("\n■ Frequent Powers (base 1–5, exp 2–4):")
print(powers)

# ==========================================================
# 小数⇔分数変換：0.05〜1.0までの0.05刻み / Decimal-Fraction
# ==========================================================
# 0.05 刻みで小数から分数へ変換 / Convert 0.05 steps to fractions
decimals = [round(0.05 * i, 2) for i in range(1, 21)]
fractions = {d: Rational(d).limit_denominator() for d in decimals}
print("\n■ Decimal to Fraction (0.05 – 1.0):")
print(fractions)

# ======================================================
# 偶数×5の倍数の速算 / Even × Multiple of 5 (≤ 20)
# ======================================================
even_numbers = [n for n in range(2, 21, 2)]  # 2, 4, ..., 20
multiple_of_5 = [n for n in range(5, 21, 5)]  # 5, 10, 15, 20
even_5_products = {(a, b): a * b for a in even_numbers for b in multiple_of_5}
print("\n■ Fast Multiplication: Even × Multiple of 5:")
print(even_5_products)

# =====================================================
# (4の倍数)×25 の速算（≤20）/ Multiple of 4 × 25
# =====================================================
multiple_of_4 = [n for n in range(4, 21, 4)]  # 4, 8, 12, 16, 20
result_25 = {f"{x}×25": x * 25 for x in multiple_of_4}
print("\n■ Fast Multiplication: Multiple of 4 × 25:")
print(result_25)

# =====================================================
# (8の倍数)×125 の速算（≤20）/ Multiple of 8 × 125
# =====================================================
multiple_of_8 = [n for n in range(8, 21, 8)]  # 8, 16
result_125 = {f"{x}×125": x * 125 for x in multiple_of_8}
print("\n■ Fast Multiplication: Multiple of 8 × 125:")
print(result_125)

# ================================================
# 恒等式 A²-B² = (A+B)(A-B) の確認
# Identity: A² - B² = (A + B)(A - B)
# ================================================
A = 25
B = 5
lhs = A**2 - B**2
rhs = (A + B) * (A - B)
print("\n■ Identity A² - B² = (A+B)(A−B):")
print(f"A={A}, B={B}, A²−B²={lhs}, (A+B)(A−B)={rhs}")

# ======================================================
# A² = (A+B)(A−B) + B² の展開公式の変形利用 / Identity
# ======================================================
transformed = (A + B)*(A - B) + B**2
print("\n■ Transformed Identity A² = (A+B)(A−B) + B²:")
print(f"(A+B)(A−B) + B² = {transformed}, A² = {A**2}")

# ====================================
# 公約数：a = 171, b = 133 の差を素因数分解
# Prime factorization of a - b
# ====================================
a = 171
b = 133
difference = a - b
factorization = factorint(difference)
print("\n■ a - b =", difference)
print("■ Prime Factorization of a - b:")
print(factorization)

# Program Name: sakuranbozan.py
# Creation Date: 20250609
# Overview: General implementation of "Sakuranbo-zan" for both addition and subtraction, emphasizing place value strategies
# Usage: Use sakuranbo_add(a, b) or sakuranbo_sub(a, b)

# -------------------------------
# さくらんぼ算（加法）/ Sakuranbo-style Addition
# -------------------------------
def sakuranbo_add(a, b):
    print(f"\n■ さくらんぼ算（加法）: {a} + {b}")
    
    to_10 = 10 - (a % 10)  # 10にするためにbから取る数 / portion to complete 10 from a
    if to_10 > b:
        # 繰り上がりなし / no carrying
        result = a + b
        print(f"→ {a} + {b} = {result}（繰り上がりなし / no carrying）")
    else:
        left = to_10
        right = b - to_10
        step1 = a + left
        step2 = step1 + right
        print(f"→ {b} を {left} と {right} に分ける（さくらんぼ分解 / cherry split）")
        print(f"→ {a} + {left} = {step1}（10のかたまり / made 10）")
        print(f"→ {step1} + {right} = {step2}")
        print(f"✅ 結果 / result: {a} + {b} = {step2}")

# -------------------------------
# さくらんぼ算（減法）/ Sakuranbo-style Subtraction
# -------------------------------
def sakuranbo_sub(a, b):
    print(f"\n■ さくらんぼ算（減法）: {a} - {b}")

    if a < b:
        print(f"⚠ {a} < {b}：負の数になります / result will be negative")
        print(f"→ {a} - {b} = {a - b}")
        return

    ones_a = a % 10
    if ones_a >= b % 10 or b < 10:
        # 一の位で引ける / no borrowing
        result = a - b
        print(f"→ {a} - {b} = {result}（繰り下がりなし / no borrowing）")
    else:
        # 繰り下がり必要 / borrowing needed
        print(f"→ {a} の一の位：{ones_a}，{b} の一の位：{b%10}")
        need = b % 10 - ones_a
        print(f"→ 一の位が足りないので十の位から {need} 借りる / need to borrow {need}")
        new_ones = 10 + ones_a - (b % 10)
        new_tens = (a // 10 - 1) * 10 - (b // 10) * 10
        result = new_tens + new_ones
        print(f"→ 新しい一の位：{new_ones}，新しい十の位：{new_tens}")
        print(f"✅ 結果 / result: {a} - {b} = {a - b}")

# -------------------------------
# 実行例 / Examples
# -------------------------------
sakuranbo_add(8, 7)     # 繰り上がりあり
sakuranbo_add(6, 3)     # 繰り上がりなし
sakuranbo_add(9, 1)     # ちょうど10

sakuranbo_sub(13, 8)    # 繰り下がりあり
sakuranbo_sub(15, 4)    # 繰り下がりなし
sakuranbo_sub(57, 19)   # 複雑な繰り下がり
sakuranbo_sub(9, 13)    # 負の数

# 📘 Google Colab 用：二次関数のプロットと式の素因数分解
# F(x) = Ax^2 + Bx + C 形式で描画と計算を行う

# 必要ライブラリのインポート
import numpy as np
import matplotlib.pyplot as plt
from sympy import factorint, sqrt, simplify

# --- 定数定義（A, B, C） ---
A = 1
B = 6
C = 8

# --- 関数定義 ---
def F(x):
    return A * x**2 + B * x + C

# --- プロット（F(x)） ---
x_vals = np.linspace(-10, 2, 400)
y_vals = F(x_vals)

plt.figure(figsize=(8, 5))
plt.plot(x_vals, y_vals, label=f"F(x) = {A}x² + {B}x + {C}")
plt.axhline(0, color='gray', linewidth=0.5)
plt.axvline(0, color='gray', linewidth=0.5)
plt.title("Quadratic Function Plot")
plt.xlabel("x")
plt.ylabel("F(x)")
plt.grid(True)
plt.legend()
plt.show()

# --- 式の計算と素因数分解 ---
exprs = {
    "A": A,
    "B": B,
    "C": C,
    "B^2 - 4AC": B**2 - 4*A*C,
    "2A": 2*A,
    "B / (2A)": B / (2*A),
    "sqrt(B^2 - 4AC)": sqrt(B**2 - 4*A*C),
    "sqrt(B^2 - 4AC) / (2A)": sqrt(B**2 - 4*A*C) / (2*A)
}

print("🔎 素因数分解または簡約表現:")
for label, value in exprs.items():
    if isinstance(value, (int, float)) and float(value).is_integer():
        factors = factorint(int(value))
        print(f"{label}: {int(value)} -> {factors}")
    else:
        simplified = simplify(value)
        print(f"{label}: {simplified}")