针对方程"ax^3+bx^2+cx+d=0"的求根程序。
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控件只需一个Command1，结果显示在“立即”中。
代码如下。（参考）
========================
Private Sub Command1_Click()
Dim x1r As Double, x1i As Double, x2r As Double, x2i As Double, x3r As Double, x3i As Double
Dim ret As String
Const eq = "ax^3+bx^2+cx+d=0"
a = InputBox("请输入a", eq)
b = InputBox("请输入b", eq)
c = InputBox("请输入c", eq)
d = InputBox("请输入d", eq)
ret = CubicEquation(a, b, c, d, x1r, x1i, x2r, x2i, x3r, x3i) '5x^3+4x^2+3x-12=0
Debug.Print "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" ret
Debug.Print x1r; " + "; x1i; " i"
Debug.Print x2r; " + "; x2i; " i"
Debug.Print x3r; " + "; x3i; " i"
End Sub
Private Function CubicEquation _
(ByVal a As Double, ByVal b As Double, ByVal c As Double, ByVal d As Double, _
x1r As Double, x1i As Double, x2r As Double, x2i As Double, x3r As Double, x3i As Double) As String
'Cubic equation(v2.2), coded by btef (please let this line remain)
Dim e As Double, f As Double, g As Double, h As Double, delta As Double
Dim r As Double, sita As Double, pi As Double, rr As Double, ri As Double
If a = 0 Then
CubicEquation = "Not a cubic equation: a = 0"
Exit Function
End If
'pi = 3.14159265358979
pi = 4 * Atn(1)
b = b / a 'simplify to a=1: x^3+bx^2+cx+d=0
c = c / a
d = d / a
e = -b ^ 2 / 3 + c 'substitute x=y-b/3: y^3+ey+f=0
f = (2 * b ^ 2 - 9 * c) * b / 27 + d
If e = 0 And f = 0 Then
x1r = -b / 3
x2r = x1r
x3r = x1r
CubicEquation = "3 same real roots:"
ElseIf e = 0 Then 'need to deal with e = 0, or it will cause z = 0 later.
r = -f 'y^3+f=0, y^3=-f
r = Cur(r)
x1r = r - b / 3 'a real root
If r 0 Then 'r never = 0 since g=f/2, f never = 0 there
sita = 2 * pi / 3
x2r = r * Cos(sita) - b / 3
x2i = r * Sin(sita)
Else
sita = pi / 3
x2r = -r * Cos(sita) - b / 3
x2i = -r * Sin(sita)
End If
x3r = x2r
x3i = -x2i
CubicEquation = "1 real root and 2 image roots:"
Else 'substitute y=z-e/3/z: (z^3)^2+fz^3-(e/3)^3=0, z^3=-g+sqr(delta)
g = f / 2 '-q-sqr(delta) is ignored
h = e / 3
delta = g ^ 2 + h ^ 3
If delta 0 Then
r = Sqr(g ^ 2 - delta)
sita = Argument(-g, Sqr(-delta)) 'z^3=r(con(sita)+isin(sita))
r = Cur(r)
rr = r - h / r
sita = sita / 3 'z1=r(cos(sita)+isin(sita))
x1r = rr * Cos(sita) - b / 3 'y1=(r-h/r)cos(sita)+i(r+h/r)sin(sita), x1=y1-b/3
sita = sita + 2 * pi / 3 'no image part since r+h/r = 0
x2r = rr * Cos(sita) - b / 3
sita = sita + 2 * pi / 3
x3r = rr * Cos(sita) - b / 3
CubicEquation = "3 real roots:"
Else 'delta = 0
r = -g + Sqr(delta)
r = Cur(r)
rr = r - h / r
ri = r + h / r
If ri = 0 Then
CubicEquation = "3 real roots:"
Else
CubicEquation = "1 real root and 2 image roots:"
End If
x1r = rr - b / 3 'a real root
If r 0 Then 'r never = 0 since g=f/2, f never = 0 there
sita = 2 * pi / 3
x2r = rr * Cos(sita) - b / 3
x2i = ri * Sin(sita)
Else 'r 0
sita = pi / 3
x2r = -rr * Cos(sita) - b / 3
x2i = -ri * Sin(sita)
End If
x3r = x2r
x3i = -x2i
End If
End If
End Function
Private Function Cur(v As Double) As Double
If v 0 Then
Cur = -(-v) ^ (1 / 3)
Else
Cur = v ^ (1 / 3)
End If
End Function
Private Function Argument(a As Double, b As Double) As Double
Dim sita As Double, pi As Double
'pi = 3.14159265358979
pi = 4 * Atn(1)
If a = 0 Then
If b = 0 Then
Argument = pi / 2
Else
Argument = -pi / 2
End If
Else
sita = Atn(Abs(b / a))
If a 0 Then
If b = 0 Then
Argument = sita
Else
Argument = -sita
End If
ElseIf a 0 Then
If b = 0 Then
Argument = pi - sita
Else
Argument = pi + sita
End If
End If
End If
End Function
(-b+(b^2-4ac))/(2a) (-b+(b^2-4ac))/(2a) 是2个根
Delta = b * b - 4 * a * c '求得b*b-4*a*c并存放在变量Delta中
If Delta = 0 Then '如果Delta的值为0
Re = -b / (2 * a)
b * b - 4 * a * c＝b^2-4ac=0
-b/(2a)是唯一解
Dim s1!, s2!, a$ '为小数点的叠加，s1,s2必须定义为单精度型
Dim flag As Boolean 'flag它是过程及的变量，在通用里必须声明
'在数字按钮控件单击数组单击事件中获取操作数（没有区分是哪一个操作数）
Private Sub Command1_Click(Index As Integer)
x = Text1.Text
If flag = True Or x = "0" Then '查看数字是否输入完毕或者是否清零了
Text1.Text = CStr(Index) 'CStr将数值转换字符
Else
Text1.Text = Text1.Text + CStr(Index) '"+"在这里这个是对字符串的操作的叠加，CStr(Index)是接的数据
End If
flag = False '时刻准备数字的输入
End Sub
'2.单击运算符，确定s1，并且要选定运算
Private Sub Command2_Click(Index As Integer)
flag = True
s1 = Val(Text1.Text)
Select Case Index
Case 0
a = "+"
Case 1
a = "-"
Case 2
a = "*"
Case 3
a = "/"
End Select
End Sub
'3."="的单击事件
Private Sub Command3_Click()
flag = True
s2 = Val(Text1.Text)
Select Case a
Case "+"
Text1.Text = s1 + s2
Case "-"
Text1.Text = s1 - s2
Case "*"
Text1.Text = s1 * s2
Case "/"
Text1.Text = s1 / s2 '分母不能为0
End Select
s1 = 0: s2 = 0: a = ""
End Sub
'4.清屏
Private Sub Command4_Click()
Text1.Text = "0"
s1 = 0
s2 = 0
a = ""
flag = False
End Sub
'5.删除最后输入的一个字符，换句话说，将本文框中的字符串取字符（从左往右取left(string,length)），将最后一个字符不取就先行
Private Sub Command5_Click()
If Text1.Text = "" Then
Else
Command5.Enabled = True
Text1.Text = Left(Text1.Text, Len(Text1.Text) - 1)
'len求字符串的长度，left(text1.len(text1)-1减1是取字符串从左往右减去一个字符串
End If
End Sub
'小数点 1）显示出"."(注意前面输入过的整数必须显示) 2）小数后能继续接受数字的输入
Private Sub Command6_Click()
Text1 = Text1 "."
End Sub
'7加入正负号--单击“+、-”,产生一个"-"，而且处于一种等待数字输入的一种状态
Private Sub Command7_Click()
Dim temp As Double
temp = -Val(Text1.Text)
Text1.Text = temp
If d = " " Then s1 = temp Else s2 = temp
End Sub
Private Sub Command8_Click() '退出
End
End Sub
Private Sub Form_Load() '窗体初始化
Text1.Text = 0
Text1.Locked = True
End Sub
解一元一次方程：
设置4个文本框，分别代表一元一次方程中的参数k,b,x,y
分别命名txtk,txtb,txtx,txty.计算按钮命名为cmdCalc。
在代码窗口里粘贴如下代码:
Private Sub cmdCalc_Click()
Dim k, b As Long
k = txtk.Text
b = txtb.Text
If txtx.Text = "x" Then
MsgBox "x的值为:" (txty.Text - b) / k
ElseIf txty.Text = "y" Then
MsgBox "y的值为:" k * txtx.Text + b
End If
End Sub
计算时求x则在txtx那里输入一个x，
求y则在txty那里输入一个y，
在各文本框中输入参数，
然后按下按钮，
就有提示框弹出，显示结果。
一元二次方程：
privat sub command1_click()
dim a,b,c,x1,x2,d as sigle
a=val(textl.text)
b=val(text2.text)
c=val(text3.text)
d=b^2-4*a*c
if d0 then
x1=(-b+sqr(d))/(2*a)
x2=(-b-sqr(d))/(2*a)
else if d=0 then
x1=(-b/2*a)
x2=x1
else msgbox"方程没有实根"
end if
text4.text="x1=" x1 "" "x2=" x2
end sub
sub min(byref a() as integer)
dim i,j as interger
for i=1 to 9
for j=i+1 to 10
if a a(i)a(j) then
t=a(j)
a(i)=a(j)
a(j)=t
end if
next
next
end sub
private sub command_(click)
dim b(1 to 10) as interger
dim a(1 to 10) as interger
randomize
for i=1 to 10
a(i)=int(rnd*90)+10
list1.additem a(i)
b(i)=int(rnd*90)+ 10
list2.additem b(i)
next
call min(a)
call min(b)
if a(1)b(1) then
m=a(1)
else
m=b(1)
end if
text1.text="A,B种的最小值：" vbcrlf m
end sub
一元三次方程：
针对方程"ax^3+bx^2+cx+d=0"的求根程序。
控件只需一个Command1，结果显示在“立即”中。
代码如下。（参考）
========================
Private Sub Command1_Click()
Dim x1r As Double, x1i As Double, x2r As Double, x2i As Double, x3r As Double, x3i As Double
Dim ret As String
Const eq = "ax^3+bx^2+cx+d=0"
a = InputBox("请输入a", eq)
b = InputBox("请输入b", eq)
c = InputBox("请输入c", eq)
d = InputBox("请输入d", eq)
ret = CubicEquation(a, b, c, d, x1r, x1i, x2r, x2i, x3r, x3i) '5x^3+4x^2+3x-12=0
Debug.Print "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~" ret
Debug.Print x1r; " + "; x1i; " i"
Debug.Print x2r; " + "; x2i; " i"
Debug.Print x3r; " + "; x3i; " i"
End Sub
Private Function CubicEquation _
(ByVal a As Double, ByVal b As Double, ByVal c As Double, ByVal d As Double, _
x1r As Double, x1i As Double, x2r As Double, x2i As Double, x3r As Double, x3i As Double) As String
'Cubic equation(v2.2), coded by btef (please let this line remain)
Dim e As Double, f As Double, g As Double, h As Double, delta As Double
Dim r As Double, sita As Double, pi As Double, rr As Double, ri As Double
If a = 0 Then
CubicEquation = "Not a cubic equation: a = 0"
Exit Function
End If
'pi = 3.14159265358979
pi = 4 * Atn(1)
b = b / a 'simplify to a=1: x^3+bx^2+cx+d=0
c = c / a
d = d / a
e = -b ^ 2 / 3 + c 'substitute x=y-b/3: y^3+ey+f=0
f = (2 * b ^ 2 - 9 * c) * b / 27 + d
If e = 0 And f = 0 Then
x1r = -b / 3
x2r = x1r
x3r = x1r
CubicEquation = "3 same real roots:"
ElseIf e = 0 Then 'need to deal with e = 0, or it will cause z = 0 later.
r = -f 'y^3+f=0, y^3=-f
r = Cur(r)
x1r = r - b / 3 'a real root
If r 0 Then 'r never = 0 since g=f/2, f never = 0 there
sita = 2 * pi / 3
x2r = r * Cos(sita) - b / 3
x2i = r * Sin(sita)
Else
sita = pi / 3
x2r = -r * Cos(sita) - b / 3
x2i = -r * Sin(sita)
End If
x3r = x2r
x3i = -x2i
CubicEquation = "1 real root and 2 image roots:"
Else 'substitute y=z-e/3/z: (z^3)^2+fz^3-(e/3)^3=0, z^3=-g+sqr(delta)
g = f / 2 '-q-sqr(delta) is ignored
h = e / 3
delta = g ^ 2 + h ^ 3
If delta 0 Then
r = Sqr(g ^ 2 - delta)
sita = Argument(-g, Sqr(-delta)) 'z^3=r(con(sita)+isin(sita))
r = Cur(r)
rr = r - h / r
sita = sita / 3 'z1=r(cos(sita)+isin(sita))
x1r = rr * Cos(sita) - b / 3 'y1=(r-h/r)cos(sita)+i(r+h/r)sin(sita), x1=y1-b/3
sita = sita + 2 * pi / 3 'no image part since r+h/r = 0
x2r = rr * Cos(sita) - b / 3
sita = sita + 2 * pi / 3
x3r = rr * Cos(sita) - b / 3
CubicEquation = "3 real roots:"
Else 'delta = 0
r = -g + Sqr(delta)
r = Cur(r)
rr = r - h / r
ri = r + h / r
If ri = 0 Then
CubicEquation = "3 real roots:"
Else
CubicEquation = "1 real root and 2 image roots:"
End If
x1r = rr - b / 3 'a real root
If r 0 Then 'r never = 0 since g=f/2, f never = 0 there
sita = 2 * pi / 3
x2r = rr * Cos(sita) - b / 3
x2i = ri * Sin(sita)
Else 'r 0
sita = pi / 3
x2r = -rr * Cos(sita) - b / 3
x2i = -ri * Sin(sita)
End If
x3r = x2r
x3i = -x2i
End If
End If
End Function
Private Function Cur(v As Double) As Double
If v 0 Then
Cur = -(-v) ^ (1 / 3)
Else
Cur = v ^ (1 / 3)
End If
End Function
Private Function Argument(a As Double, b As Double) As Double
Dim sita As Double, pi As Double
'pi = 3.14159265358979
pi = 4 * Atn(1)
If a = 0 Then
If b = 0 Then
Argument = pi / 2
Else
Argument = -pi / 2
End If
Else
sita = Atn(Abs(b / a))
If a 0 Then
If b = 0 Then
Argument = sita
Else
Argument = -sita
End If
ElseIf a 0 Then
If b = 0 Then
Argument = pi - sita
Else
Argument = pi + sita
End If
End If
End If
End Function
二元一次方程：
Dim a, b, c As Integer
Dim x, y As Single
Dim d As Double
a = Val(InputBox("输入二次项系数"))
b = Val(InputBox("输入一次项系数"))
c = Val(InputBox("输入常数项"))
d = b ^ 2 - 4 * a * c
If d 0 Then
MsgBox "方程无解"
ElseIf d = 0 Then
x = -b / (2 * a)
MsgBox "方程有一个解：" x
Else
x = (-b + Sqr(d)) / (2 * a)
y = (-b - Sqr(d)) / (2 * a)
MsgBox "方程有两个解：" x "和" y
End If
三元一次方程：
方程组如下,
ax+by+cz=d
a'x+b'y+c'z=d'
a"x+b"y+c"z=d"
其中x,y,z为未知数,a,a',a",b,b',b",c,c',c",d,d',d",为用户输入的数值
解N元一次方程，indat为N+1行、N列的数组，outdat为N个元素的数组
Public Sub 解方程(ByRef InDat() As Double, ByVal InDatCount As Long, ByRef OutDat() As Double, ByRef OutDatCount As Long)
Dim Xt() As Double
Dim Dt As Double
Dim Ss As Long
Dim OtSCount As Long
Dim XtOut() As Double
If InDatCount 1 Then
ReDim Xt(1 To InDatCount - 1, 1 To InDatCount) As Double
For j = 1 To InDatCount - 1 '行
For i = 2 To InDatCount + 1 '列
Xt(j, i - 1) = InDat(j, i) * InDat(InDatCount, 1) / InDat(1, 1) - InDat(InDatCount, i)
Next i
Next j
OtSCount = 0
解方程 Xt, InDatCount - 1, XtOut, OtSCount
Dt = 0
For i = 1 To InDatCount - 1
Dt = Dt + InDat(InDatCount, i + 1) * XtOut(i)
Next i
Dt = Dt + InDat(InDatCount, i + 1)
ReDim Preserve OutDat(1 To 1 + OtSCount) As Double
OutDat(1) = -Dt / InDat(InDatCount, 1)
For i = 2 To OtSCount + 1
OutDat(i) = XtOut(i - 1)
Next i
OutDatCount = 1 + OtSCount
Else
ReDim OutDat(1 To 1) As Double
If InDat(1, 1) 0 Then
OutDat(1) = -InDat(1, 2) / InDat(1, 1)
Else
OutDat(1) = 0
End If
OutDatCount = 1
End If
End Sub
VB的运算顺序是：先乘除、后加减，有括号的先算括号内，有负号的先算负号。
请你比较一下这个运算中x和y的值：
Dim n As Single = 4
Dim x As Single
Dim y As Single
x = n + 1
x = x / n
x = x - 1
x = Math.Sqrt(x)
y = Math.Sqrt((n + 1) / n - 1)
这样就会发现，你的代码中括号的位置错了。
正确的应该是： Math.Sqrt((n + 1) / n - 1)
Private Sub Command1_Click()
Dim A, B, C
A = 10
B = 3
C = f(A) / (f(B) * f(A - B))
Print C
End Sub
Private Function f(n)
Dim I As Integer
f = 1
For I = 1 To n
f = f * I
Next I
End Function