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| Option Explicit
Public Const cP$ = "+": Public Const cD$ = "/": Public Const cM$ = "_": Public Const cO$ = "(": Public Const cF$ = ")"
Public Const cD0$ = "Bad Entry"
Public Const cR$ = "?"
Function SmQ$(x$, y$)
'addition Q->Q
Dim p$(1 To 2, 1 To 3), b%(1 To 2, 1 To 2), c$(1 To 5), i%
For i = 1 To 3
p(1, i) = IdnQ(x, i): p(2, i) = IdnQ(y, i)
Next i
b(1, 1) = SgnQ(x): b(2, 1) = SgnQ(y)
c(1) = PrdN(p(1, 2), p(2, 3)): c(2) = PrdN(p(1, 3), p(2, 2)): c(3) = PrdN(p(1, 3), p(2, 3))
If b(1, 1) = b(2, 1) Then
c(4) = SmmN(c(1), c(2)): b(1, 2) = b(1, 1): c(5) = SmmN(p(1, 1), p(2, 1)): b(2, 2) = b(1, 1)
If XsYn(c(4), c(3)) Then
c(4) = DffN(c(4), c(3)): c(5) = SmmN(c(5), 1)
End If
Else
c(4) = DffN(c(1), c(2)): b(1, 2) = IIf(XsYn(c(1), c(2)), b(1, 1), b(2, 1))
c(5) = DffN(p(1, 1), p(2, 1)): b(2, 2) = IIf(XsYn(p(1, 1), p(2, 1)), b(1, 1), b(2, 1))
End If
If Not CBool(c(4)) Then
SmQ = IIf(b(2, 2), c(5), IIf(Not CBool(c(5)), 0, cM & c(5)))
Else
c(1) = c(3): c(3) = SmpN(c(4), c(3), 2): c(4) = SmpN(c(4), c(1), 1)
If Not CBool(c(5)) Then
SmQ = IIf(b(1, 2), 0 & cP & c(4) & cD & c(3), cM & cO & 0 & cP & c(4) & cD & c(3) & cF)
Else
If b(2, 2) = b(1, 2) Then
SmQ = IIf(b(2, 2), c(5) & cP & c(4) & cD & c(3), cM & cO & c(5) & cP & c(4) & cD & c(3) & cF)
Else
If b(2, 2) Then
SmQ = DffN(c(5), 1) & cP & DffN(c(3), c(4)) & cD & c(3)
Else
SmQ = cM & cO & DffN(c(5), 1) & cP & DffN(c(3), c(4)) & cD & c(3) & cF
End If
End If
End If
End If
End Function
Function PrQ$(x$, y$)
'multiplication Q->Q
Dim p$(1 To 2, 1 To 3), b%, c$(1 To 4), i%
For i = 1 To 3
p(1, i) = IdnQ(x, i): p(2, i) = IdnQ(y, i)
Next i
b = SgnQ(x) Eqv SgnQ(y)
c(1) = PrdN(p(1, 3), p(2, 3))
c(2) = SmmN(SmmN(SmmN(PrdN(PrdN(p(1, 1), p(2, 1)), c(1)), PrdN(PrdN(p(1, 1), p(2, 2)), p(1, 3))), _
PrdN(PrdN(p(2, 1), p(1, 2)), p(2, 3))), PrdN(p(1, 2), p(2, 2)))
c(3) = DvnN(c(2), c(1), 1): c(2) = DvnN(c(2), c(1), 2)
If XsYn(c(2), c(1)) Then
c(3) = SmmN(c(3), 1): c(2) = DffN(c(2), c(1))
End If
If b Then
If Not CBool(c(2)) Then
PrQ = c(3)
Else
c(4) = c(1): c(1) = SmpN(c(2), c(1), 2): c(2) = SmpN(c(2), c(4), 1)
PrQ = c(3) & cP & c(2) & cD & c(1)
End If
Else
If Not CBool(c(2)) Then
PrQ = IIf(c(3) <> 0, cM & c(3), c(3))
Else
c(4) = c(1): c(1) = SmpN(c(2), c(1), 2): c(2) = SmpN(c(2), c(4), 1)
PrQ = cM & cO & c(3) & cP & c(2) & cD & c(1) & cF
End If
End If
End Function
Function SsQ$(x$, y$)
'soustraction Q->Q
SsQ = SmQ(x, PrQ(y, "_1"))
End Function
Function DvQ$(x$, y$)
'division Q->Q
Dim p$(1 To 3), b%, i%
If y = "0" Then
DvQ = cD0
Else
For i = 1 To 3
p(i) = IdnQ(y, i)
Next i
b = SgnQ(y): p(1) = SmmN(PrdN(p(1), p(3)), p(2)): p(2) = p(3)
If b Then
DvQ = PrQ(x, 0 & cP & p(2) & cD & p(1))
Else
DvQ = PrQ(x, cM & cO & 0 & cP & p(2) & cD & p(1) & cF)
End If
End If
End Function
Private Function SgnQ%(x$)
'signe (true=0,+,false=-) Q
If Left(x, 1) <> cM Then SgnQ = True
End Function
Private Function Sp0n$(x$)
'supprime les 0 à gauche N
Dim i%
i = 1
Do Until x = "" Or Left(x, 1) <> 0
x = Right(x, Len(x) - 1): i = i + 1
Loop
Sp0n = IIf(x <> "", x, 0)
End Function
Private Function IdnQ$(x$, Arg%)
'partie entiere (1), numérateur (2) diviseur (3) Q
Dim pD&, pA&
pD = InStr(1, x, cD): pA = InStr(1, x, cP)
Select Case Arg
Case 1
If SgnQ(x) Then
If pD > 0 Then
IdnQ = Left(x, pA - 1)
Else
IdnQ = x
End If
Else
If pD > 0 Then
IdnQ = Right(Left(x, pA - 1), pA - 3)
Else
IdnQ = Right(x, Len(x) - 1)
End If
End If
Case 2
If pD = 0 Then
IdnQ = 0
Else
IdnQ = Right(Left(x, pD - 1), pD - 1 - pA)
End If
Case 3
If pD = 0 Then
IdnQ = 1
Else
If SgnQ(x) Then
IdnQ = Right(x, Len(x) - pD)
Else
IdnQ = Left(Right(x, Len(x) - pD), Len(x) - pD - 1)
End If
End If
End Select
IdnQ = Sp0n(IdnQ)
End Function
Private Function XsYn%(x$, y$)
'N->x>=y?, suppose Sp0n fait
Dim Cx%, Cy%, i%
Select Case Len(x)
Case Is > Len(y)
XsYn = True
Case Len(y)
For i = 1 To Len(x)
Cx = Right(Left(x, i), 1): Cy = Right(Left(y, i), 1)
If Cx > Cy Then
XsYn = True: Exit Function
End If
If Cy > Cx Then Exit Function
Next i
XsYn = True
End Select
End Function
Private Function SmmN$(x$, y$)
'N->x+y, suppose Sup0 fait
Dim r%, i%, Cx%, Cy%, Cz%
For i = 1 To WorksheetFunction.Max(Len(x), Len(y))
Cx = Left(Right(x, i), 1): If i > Len(x) Then Cx = 0
Cy = Left(Right(y, i), 1): If i > Len(y) Then Cy = 0
Cz = Cx + Cy + r
If Cz < 10 Then
r = 0
Else
Cz = Cz - 10: r = 1
End If
SmmN = Cz & SmmN
Next i
SmmN = Sp0n(r & SmmN)
End Function
Private Function DffN$(ByVal x$, ByVal y$)
'N->Abs(x-y), suppose Sup0 fait
Dim z$, Cx%, Cy%, r%, i%, Cz%
If Not XsYn(x, y) Then
z = x: x = y: y = z
End If
For i = 1 To WorksheetFunction.Max(Len(x), Len(y))
Cx = Left(Right(x, i), 1): Cy = Left(Right(y, i), 1)
If i > WorksheetFunction.Min(Len(x), Len(y)) Then Cy = 0
Cz = Cx - Cy - r
If Cx < Cy + r Then
Cz = Cz + 10: r = 1
Else
r = 0
End If
DffN = Cz & DffN
Next i
DffN = Sp0n(DffN)
End Function
Private Function PrdN$(ByVal x$, ByVal y$)
'N->x*y, suppose Sup0 fait
Dim z$, r%, Cx%, Cy%, i%, j%, Cz%, k%, Rs1$, Rs2$
PrdN = 0
If Not XsYn(x, y) Then
z = x: x = y: y = z
End If
For i = 1 To WorksheetFunction.Min(Len(x), Len(y))
Rs1 = "": r = 0: Cx = Left(Right(y, i), 1)
For j = 1 To WorksheetFunction.Max(Len(x), Len(y))
Cy = Left(Right(x, j), 1): Cz = (Cx * Cy) + r: r = Int(Cz / 10): Cz = Cz - 10 * r: Rs1 = Cz & Rs1
Next j
Rs2 = IIf(r > 0, r & Rs1, Rs1)
For k = 2 To i
Rs2 = Rs2 & 0
Next k
PrdN = SmmN(Rs2, PrdN)
Next i
PrdN = Sp0n(PrdN)
End Function
Private Function DvnN$(x$, y$, Arg%)
'(1) int(x/y), (2) x mod y, suppose Sup0 fait (N)
Dim Cx$, i%, j%, v$, RsE$, RsR$
If Not XsYn(x, y) Then
DvnN = IIf(Arg = 1, 0, x): Exit Function
End If
Cx = Left(x, Len(y))
For i = Len(y) To Len(x)
For j = 0 To 9
If Not XsYn(Cx, PrdN(j + 1, y)) Then
RsE = RsE & j: v = DffN(Cx, PrdN(j, y))
If i < Len(x) Then Cx = Sp0n(v & Right(Left(x, i + 1), 1))
Exit For
End If
Next j
Next i
RsE = Sp0n(RsE)
DvnN = Sp0n(IIf(Arg = 1, RsE, v))
End Function
Private Function SmpN$(x$, y$, Arg%)
'(1) x/pgcd(x,y),(2) y/pgcd(x,y), suppose Sup0 fait (N)
Dim a$, b$, c$
a = x: b = y
Do While DvnN(a, b, 2) <> 0
c = a: a = b: b = DvnN(c, b, 2)
Loop
Select Case Arg
Case 1
SmpN = DvnN(x, b, 1)
Case 2
SmpN = DvnN(y, b, 1)
End Select
End Function |
Opérations sur les grands nombres dans Q
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