【数C】ExcelVBAで行列でできる不定方程式の解法【ゆっくり解説】

ExcelVBAで行列でできる不定方程式の解法マクロを作る
この動画のマクロはWindows11/Office2016で作成してます。

不定方程式の解法マクロ
Excel futei.xlsm
Google 不定方程式を解いてみる

Sub macro()
    a = 23
    b = 31
    c = 1

    kai = tokutei(a, b)
    
    Debug.Print "解  x= "; kai(1, 1) * c, "  y= "; kai(1, 2) * c
End Sub

Function tokutei(a, b)
    rt = ""
    
    'a,bの符号を正にする
    m_norm = Evaluate("{" & Sgn(a) & ",0;0," & Sgn(b) & "}")
    
    v = Evaluate("{" & a & ";" & b & "}")   'aとbの列ベクトル
    
    v = WorksheetFunction.MMult(m_norm, v)
    
    Do
        r = Int(v(1, 1) / v(2, 1))
        q = v(1, 1) Mod v(2, 1)
        If q = 0 Then
            '割り切れた
            Debug.Print "ユークリッドの互除法0"
            Debug.Print "|" & Right("    " & v(1, 1), 4); "| = |"; Right("    " & r, 4); "  0 ||" & Right("    " & v(2, 1), 4); " |"
            Debug.Print "|" & Right("    " & v(2, 1), 4); "|   |   0 -1 ||"; Right("     " & q, 4); " |"
            Debug.Print "最大公約数GCM", v(2, 1)
            rt = r & "," & rt
            Exit Do
        Else
            Debug.Print "ユークリッドの互除法1"
            Debug.Print "|" & Right("    " & v(1, 1), 4); "| = |"; Right("    " & r, 4); "  0 ||" & Right("    " & v(2, 1), 4); " |"
            Debug.Print "|" & Right("    " & v(2, 1), 4); "|   |   0 -1 ||"; Right("     " & q, 4); " |"
            Debug.Print
            
            v(1, 1) = v(2, 1)
            v(2, 1) = q
            If rt = "" Then
                rt = r
            Else
                rt = r & "," & rt
            End If
        End If
        DoEvents
    Loop
    
    Debug.Print "商の並び  ", rt
    r = Split(rt, ",")
    
    p = [{1,0;0,1}] '単位行列
    
    For i = 0 To UBound(r) + 1
        '逆行列をかけていく
        
        If i > UBound(r) Then
            s = m_norm
        Else
            s = Evaluate("{0,1;1,-" & r(i) & "}")
        End If
        p0 = WorksheetFunction.MMult(p, s)
        Debug.Print "|" & Right("    " & p(1, 1), 4); "  "; Right("    " & p(1, 2), 4); "| * |" & Right("    " & s(1, 1), 4); "  "; Right("    " & s(1, 2), 4); "| = |" & Right("    " & p0(1, 1), 4); "  "; Right("    " & p0(1, 2), 4); "|"
        Debug.Print "|" & Right("    " & p(2, 1), 4); "  "; Right("    " & p(2, 2), 4); "|   |" & Right("    " & s(2, 1), 4); "  "; Right("    " & s(2, 2), 4); "|   |" & Right("    " & p0(2, 1), 4); "  "; Right("    " & p0(2, 2), 4); "|"
        Debug.Print
        p = p0
        DoEvents
    Next

    tokutei = p
End Function