Last update:
April 29, 2017, 01:05

## B2B Code Show: Polyplotter

##### by dodicat

From dodicat:

Basically the roots of a real polynomial can be found by iterating,
by QR algorithm, for the eigenvalues of the companion matrix of the
polynomial. The roots are shown with any real roots marked real, of course. The polynomial is sketched, it can be scaled up by a click on the  interface, the roots are drawn onto the sketch.  New coefficients for a different polynomial can be edited at runtime.
```'POLY PLOTTER and roots (AUG 2012)
#define WIN_INCLUDEALL
#Include "windows.bi"
#include "fbgfx.bi"
#include "string.bi"
Type complex
As Double re,im
End Type
'======================= All procedures =========================
Declare Sub balance(A()As Double,d() As Double)
Declare Sub GET_HESSENBERG(A() As Double)
Declare Sub ITERATE_BY_QR(A() As Double,wr() As Double,wi() As Double)
Declare Sub GET_EIGENVALUES(A() As Double,Eigen() As complex)
Declare Sub makecompanion(polynomium() As Double,mat() As Double)
Declare Sub equalize(m1() As Double,m2() As Double)
Declare Function decround ( a As Double, b As Integer) As Double
Declare Function _poly(coff() As Double,number As Double)As Double
Declare Function lenint(num As Ulongint) As Integer
Declare Sub getrange(n As Integer)
Declare Sub drawplot(k As Double=1)
Declare Sub plotclick()
Declare Sub scaleupclick
Declare Function seeterms(pol() As Double)As String
'=========  Globals ========================
Dim Shared n As Integer                        'DIMENSION OF POLYNOMIAL
Dim Shared As Double PLOT_GRADE =20000
Dim Shared As Integer xres,yres
Dim Shared As Double minx,maxx,miny,maxy,x
Dim Shared runplot As Integer
Screen 19,32,FB.GFX_ALWAYS_ON_TOP
Screencontrol FB.SET_WINDOW_POS,0,0
Screeninfo xres,yres
Windowtitle "POLYNOMIAL PLOTTER"
'============== Plotting macros ======================
#macro _window(topleftX,topleftY,bottomrightX,bottomrightY)
minx=topleftX
maxx=bottomrightX
miny=bottomrightY
maxy=topleftY
#endmacro
#macro _axis(colour)
Line(0,(yres-(miny/(miny-maxy))*yres))-(xres,(yres-(miny/(miny-maxy))*yres)),colour 'x axis
Line(((minx/(minx-maxx))*xres),0)-(((minx/(minx-maxx))*xres),yres),colour 'y axis
Draw String(0,(yres-(miny/(miny-maxy))*yres)),Format(decround(minx,2)),colour
Draw String(xres-8-8*(Len(Format(decround(maxx,2)))),(yres-(miny/(miny-maxy))*yres)),Format(decround(maxx,2)),colour
Draw String (xres/2,0),Format(decround(maxy,2)),colour
Draw String (xres/2,yres-16),Format(decround(miny,2)),colour
#endmacro
#macro grid(colour)
Scope
Dim As Integer l
If Abs(minx)<Abs(maxx) Then
Else
End If
l=lenint(l)
For z As Double=0 To minx Step Sgn(minx)*(10^(l-1))
Line((((minx-z)/(minx-maxx))*xres),0)-((((minx-z)/(minx-maxx))*xres),yres),colour 'y axis
Next z
l=lenint(l)
For z As Double=0 To maxx Step Sgn(maxx)*(10^(l-1))
Line((((minx-z)/(minx-maxx))*xres),0)-((((minx-z)/(minx-maxx))*xres),yres),colour 'y axis
Next z
If Abs(miny)<Abs(maxy) Then
Else
End If
l=lenint(l)
For z As Double=0 To miny Step Sgn(miny)*(10^(l-1))
Line(0,(yres-((miny-z)/(miny-maxy))*yres))-(xres,(yres-((miny-z)/(miny-maxy))*yres)),colour '
Next z
l=lenint(l)
For z As Double=0 To maxy Step Sgn(maxy)*(10^(l-1))
Line(0,(yres-((miny-z)/(miny-maxy))*yres))-(xres,(yres-((miny-z)/(miny-maxy))*yres)),colour '
Next z
End If
End Scope
#endmacro
#macro sketch(_function,colour)
For x =minx To maxx Step (maxx-minx)/PLOT_GRADE
Dim As Double x1=Cdbl(xres)*(x-minx)/(maxx-minx)
Dim As Double y1=Cdbl(yres)*(_function-maxy)/(miny-maxy)
Pset(x1,y1),colour
Next x
#endmacro
#macro mark(x1,y1,colour)
Dim As Double xx1= Cdbl(xres)*(x1-minx)/(maxx-minx)
Dim As Double yy1=Cdbl(yres)*(y1-maxy)/(miny-maxy)
Circle (xx1,yy1),5,colour,,,,f
#endmacro
' ***************** END PLOTTING MACROS ********************
'=============== Set up Win Gui =============================
Paint (0,0),Rgb(200,200,200)
Dim As MSG msg
Dim Shared As HWND hWnd,hwnd2,Poly_input1,Poly_input2,plot,roots_output,note,scaleup,scaledown
Dim Shared As String outtext,errorflag,rootstring
errorflag=""
Redim Shared As Double poly(0),copypoly(0)
Dim Shared As String s3
Dim dx As Integer=250
'*******************************************************
hWnd=CreateWindowEx( 0, "#32770", "Coefficients", WS_OVERLAPPEDWINDOW Or WS_VISIBLE, 200+dx, 200, 500+dx, 600, 0, 0, 0, 0 )
Dim s As String= "Enter Coefficients, highest power first."+Chr(13)+Chr(10)
Dim s2 As String="When all entered, click PLOT"
s=s+s2
roots_output = CreateWindowEx( 0, "EDIT", "", ws_border Or WS_VISIBLE Or WS_CHILD Or WS_HSCROLL Or WS_VSCROLL Or ES_AUTOHSCROLL Or ES_AUTOVSCROLL Or ES_MULTILINE Or ES_READONLY, 220, 80, 450, 400, hWnd, 0, 0, 0 )
note = CreateWindowEx( 0, "EDIT",s, ws_border Or WS_VISIBLE Or WS_CHILD Or WS_HSCROLL Or WS_VSCROLL Or ES_AUTOHSCROLL Or ES_AUTOVSCROLL Or ES_MULTILINE Or ES_READONLY, 110, 20, 300, 60, hWnd, 0, 0, 0 )
Poly_input2 = CreateWindowEx( 0, "EDIT","", ws_border Or WS_VISIBLE Or WS_CHILD Or WS_HSCROLL Or WS_VSCROLL Or ES_AUTOHSCROLL Or ES_AUTOVSCROLL Or ES_MULTILINE, 10, 80, 200, 400, hWnd, 0, 0, 0 )
plot= CreateWindowEx( 0, "BUTTON", "Plot", WS_VISIBLE Or WS_CHILD, 20, 20 , 70, 30, hWnd, 0, 0, 0 )
scaleup=CreateWindowEx( 0, "BUTTON", "Scaleup", WS_VISIBLE Or WS_CHILD, 20, 20+500 , 70, 30, hWnd, 0, 0, 0 )
s3="INSTRUCTIONS for use:"+Chr(13)+Chr(10)
s3=s3+"Print coefficients carefully and realistically"+Chr(13)+Chr(10)
s3=s3+"Example -3, not -03 or not -0 for 0 or not 0.8 for .8"+Chr(13)+Chr(10)
s3=s3+"No un-needed + signs"+Chr(13)+Chr(10)
s3=s3+"E.g. +.78"+Chr(13)+Chr(10)
s3=s3+"No numbers in form 3.5e-5, you must write .000035 in this case"+Chr(13)+Chr(10)
s3=s3+"Press enter at each new entry, "
s3=s3+"including the last entry"+Chr(13)+Chr(10)
s3=s3+"Edit previous entries if required"+Chr(13)+Chr(10)
s3=s3+"No need to press enter in this case"+Chr(13)+Chr(10)
s3=s3+"First coefficient (highest power) must not be 0"
setWindowText(roots_output,s3)
Dim As String starttext
starttext="16"+Chr(13)+Chr(10)+"0"+Chr(13)+Chr(10)+"-20"+Chr(13)+Chr(10)
starttext=starttext+"0"+Chr(13)+Chr(10)+"5"+Chr(13)+Chr(10)+"0"+Chr(13)+Chr(10)
setwindowtext(poly_input2,starttext)
Draw String (50,50),"Start example is Chebyshev polynomial degree 5 ",Rgb(0,0,200)
'=======================  Working Loop ==========================
start:
While GetMessage( @msg, 0, 0, 0 )
TranslateMessage( @msg )
DispatchMessage( @msg )
Select Case msg.hwnd
Case hWnd
Select Case msg.message
Case 273
End
End Select
'__________________
Case plot
Select Case msg.message
Case WM_LBUTTONDOWN
plotclick()
Goto go
End Select
'______________________
Case scaleup
Select Case msg.message
Case WM_LBUTTONDOWN
If runplot>=1 Then
scaleupclick()
End If
End Select
'__________________________

End Select
Wend
'==================== PROCEDURES ============================
Sub scaleupclick
Static k As Double
k=k+.001
drawplot(1+k)
End Sub
Sub plotclick()
#macro remove(s,char)
Scope
Dim temp As String
Dim As Integer asci=Asc(char)
For i As Long =0 To Len(s)-1
If s[i]<>asci Then temp=temp+Chr\$(s[i])
Next i
s= temp
End Scope
#endmacro
#macro Replace(s,char,newchar)
Scope
Dim temp As String=String(Len(s),newchar)
Dim As Integer asci=Asc(char)
For i As Long =0 To Len(s)-1
If s[i]<>asci Then temp[i]=s[i]
Next i
s= temp
End Scope
#endmacro

Dim charcount As Integer
charcount = GetWindowTextLength(Poly_input2)
outtext = String(charcount," ")
GetWindowText(Poly_input2,outtext,charcount)
remove(outtext,Chr(0))
outtext=Rtrim(outtext,Chr(10))
outtext=Rtrim(outtext,Chr(13))
outtext=Rtrim(outtext,Chr(10))
replace(outtext,Chr(10),"*")
replace(outtext,Chr(13),"*")
outtext=outtext+Chr(0)
Redim poly(charcount)
Redim copypoly(charcount)
Dim count As Integer
For z As Integer=0 To Ubound(poly)
count=count+1
outtext=Ltrim(outtext,"+") 'just incase
poly(z)=Val(outtext)
copypoly(z)=poly(z)
outtext=Ltrim(outtext,Format(poly(z)))
outtext=Ltrim(outtext,"*")
If outtext=Chr(0) Then
outtext=Rtrim(outtext,Chr(0))
Exit For
End If
Next z
Redim Preserve poly(count-1)
Redim Preserve copypoly(count-1)
If poly(0)=0 Then
messagebox(NULL,"The first coefficient should not be 0","ERROR",MB_OK)
errorflag="ERROR"+Chr(13)+Chr(10)
errorflag=errorflag+"First coefficient"+Chr(13)+Chr(10)
errorflag=errorflag+"can't be 0"
Else
errorflag=""
End If

'REVERSE POLY
Dim As Long lb,ub:lb=Lbound(poly):ub=Ubound(poly)
For z As Integer=Lb To Int((lb+Ub)/2)
Swap poly(z),poly(ub+lb-z)
Swap copypoly(z),copypoly(ub+lb-z)
Next z

outtext=s3+Chr(13)+Chr(10)
outtext=outtext+errorflag

setWindowText(roots_output,outtext)
End Sub
go:
n=Ubound(poly)
If n<=0 Then errorflag="no"
Redim companion(0,0) As Double
Redim Shared As complex roots(0)
If errorflag="" Then
Dim As Double val1=poly(n)
For z As Integer=n To 0 Step -1 'prepare to form companion matrix
Next z
Print

makecompanion(poly(),companion())

GET_EIGENVALUES(companion(),roots())
getrange(n)

drawplot(.1)

End If 'errorflag=""
Goto start
Sub getrange(n As Integer)
' get plotting parameters
maxx=-1e50
minx=1e50
maxy=-1e50
miny=1e50
For z As Integer=1 To n
If maxx<roots(z).re Then maxx=roots(z).re 'get x range
If minx>roots(z).re Then minx=roots(z).re
Next z
If maxx=0 And minx=0 Then
For z As Integer=1 To n
If maxx<roots(z).im Then maxx=roots(z).im 'if no real roots, get x range on imaginary roots
If minx>roots(z).im Then minx=roots(z).im
Next z
End If
If maxx=0 And minx=0 Then 'if roots are all totally zero
Print "DEFAULT X LIMITS"
maxx=1
minx=-1
End If

If minx=maxx Then
minx=minx-.1*Abs(minx)
maxx=maxx+.1*Abs(maxx)
End If
Dim As Double polyval
For z As Double=minx To maxx Step (maxx-minx)/1000 'get y range
polyval=_poly(copypoly(),z)
If maxy< polyval Then maxy=polyval
If miny>polyval Then miny=polyval
Next z

For z As Double=1 To n
If maxy< roots(z).im Then maxy=roots(z).im 'extend to cover imaginary roots
If miny>roots(z).im Then miny=roots(z).im
Next z

End Sub
Sub drawplot(k As Double=1)

Dim As Double xhalf,yhalf,range
xhalf=Abs(maxx-minx)/2
yhalf=Abs(maxy-miny)/2
range=Abs(maxx-minx)
If range<1 Then k=10*k
maxx=(maxx+xhalf*k)
minx=(minx-xhalf*k)
maxy=(maxy+yhalf*k)
miny=(miny-yhalf*k)
Cls
Paint (0,0),Rgb(200,200,200)

runplot=runplot+1
_window(minx,maxy,maxx,miny)

grid(Rgb(180,180,180))'draw grid

_axis(Rgb(200,0,0))   'draw axis
Dim As String cplex,polystring
For z As Integer=n To 0 Step -1  'write coefficients
polystring=polystring+Format(copypoly(z))+","
Next z
Dim As Uinteger col  'write roots

Draw String(.01*xres,16),"COEFFICIENTS "+"("+polystring+")"+" (degree "+Str(n)+")"

Draw String(.3*xres,32), "ROOTS marked (blue = real) (white = imaginary)"
rootstring="ROOTS:"+Chr(13)+Chr(10)
For x As Integer=1 To n         'seperate real from imaginary
cplex=" , "+Str(roots(x).im)+" i"
col=Rgb(255,255,255)
If  Val(Str(roots(x).im))=0  Then
cplex=" (real root)"
col=Rgb(0,0,200)
End If
rootstring=rootstring+Str(roots(x).re)+cplex+Chr(13)+Chr(10)
setWindowText(roots_output,rootstring)
Next x
setWindowText(note,seeterms(copypoly()))
Sketch(_poly(copypoly(),x),Rgb(0,200,0))   'draw the curve

For z As Double=1 To n                     'mark the roots
mark(roots(z).re,roots(z).im,Rgb(255*Abs(Sgn(roots(z).im)),255*Abs(Sgn(roots(z).im)),255))
Next z

End Sub
'START PROCEDURES FOR EIGENVALUES
#macro EXC(m)
d(m) = 1# * j
If j <> m Then
For ii As Integer = 1 To k
f = A(ii, j)
A(ii, j) = A(ii, m)
A(ii, m) = f
Next ii
For ii As Integer = l To n
f = A(j, ii)
A(j, ii) = A(m, ii)
A(m, ii) = f
Next ii
End If
#endmacro
Sub balance(A() As Double,d() As Double)
Dim n As Integer = Ubound(A)
Dim As Double b = 2
Dim As Integer low,ihi,noconv
Dim As Integer i,j,k,l,m
Dim As Double b2,c,f,g,r,s

Dim As Double zero=0
b2 = b * b
l = 1
k = n

lab1: For j = k To 1 Step -1
r = ZERO
For i = 1 To j - 1
r = r + Abs(A(j, i))
Next i
For i = j + 1 To k
r = r + Abs(A(j, i))
Next i
If (r = 0) Then
m = k
Exc(k)
k = k - 1
Goto lab1
End If
Next j
lab2: For j = l To k
c = ZERO
For i = l To j - 1
c = c + Abs(A(i, j))
Next i
For i = j + 1 To k
c = c + Abs(A(i, j))
Next i
If (c = 0) Then
m = l: Exc(l)
l = l + 1
Goto lab2
End If
Next j
low = l
ihi = k
For i = 1 To k
d(i) = 1#
Next i
lab3:  noconv = 0
For i = l To k
c = ZERO
r = c
For j = l To i - 1
c = c + Abs(A(j, i))
r = r + Abs(A(i, j))
Next j
For j = i + 1 To k
c = c + Abs(A(j, i))
r = r + Abs(A(i, j))
Next j
g = r / b
f = 1#
s = c + r
lab4: If c < g Then
f = f * b
c = c * b2
Goto lab4
End If
g = r * b
lab5: If c >= g Then
f = f / b
c = c / b2
Goto lab5
End If
If (c + r) / f < .95 * s Then
g = 1# / f
d(i) = d (i) * f
noconv = 1
For j = l To n
A(i, j) = A(i, j) * g
Next j
For j = 1 To k
A(j, i) = A(j, i) * f
Next j
End If
Next i
If noconv = 1 Then Goto lab3
End Sub
Sub GET_HESSENBERG(A() As Double)

Dim n As Integer=Ubound(a)
Dim As Integer m,j,i
Dim As Double y,x,ZERO=0
If n > 2 Then
For m = 2 To n - 1
x = ZERO
i = m
For j = m To n
If Abs(A(j, m - 1)) > Abs(x) Then
x = A(j, m - 1)
i = j
End If 'IF Abs
Next j 'FOR j= m TO n
If i <> m Then
For j = m - 1 To n
y = A(i, j)
A(i, j) = A(m, j)
A(m, j) = y
Next j
For j = 1 To n
y = A(j, i)
A(j, i) = A(j, m)
A(j, m) = y
Next j
End If 'IF i <> m
If x <> ZERO Then
For i = m + 1 To n
y = A(i, m - 1)
If y <> ZERO Then
y = y / x
A(i, m - 1) = y
For j = m To n
A(i, j) = A(i, j) - y * A(m, j)
Next j
For j = 1 To n
A(j, m) = A(j, m) + y * A(j, i)
Next j
End If  'IF y
Next i  'FOR i
End If  'IF x
Next m  'FOR m
End If 'if n>2
End Sub
Sub ITERATE_BY_QR(A() As Double,wr() As Double,wi() As Double)
Dim As Double y,r,u,v,mmin
Dim As String res
Dim sign As Double
Dim As Double ZERO=0
Dim n As Integer=Ubound(A)
Dim As Double anorm,itsmx,t,its,s,x,p,q,nn,z,w
Dim As Integer i,j,l,m,k
Dim As Double aa,bb
#macro _SIGN(aa,bb)
If bb < 0 Then
Sign = -Abs(aa)
Else
Sign = Abs(aa)
End If
#endmacro
itsmx = 50

anorm = Abs(A(1, 1))
For i = 2 To n
For j = i - 1 To n
anorm = anorm + Abs(A(i, j))
Next j
Next i
nn = n
t = ZERO

label4: its = 0
label2: For l = nn To 2 Step -1
s = Abs(A(l - 1, l - 1)) + Abs(A(l, l))
If (s = 0!) Then s = anorm
If ((Abs(A(l, l - 1)) + s) = s) Then Goto label3
Next l
l = 1
label3: x = A(nn, nn)
If (l = nn) Then
wr(nn) = x + t
wi(nn) = ZERO
nn = nn - 1
Else
y = A(nn - 1, nn - 1)
w = A(nn, nn - 1) * A(nn - 1, nn)
If (l = nn - 1) Then
p = .5# * (y - x)
q = p * p + w
z = Sqr(Abs(q))
x = x + t
If q >= ZERO Then
aa = z: bb = p:  _SIGN(aa,bb)
z = p + Sign

wr(nn) = x + z
wr(nn - 1) = wr(nn)
If z <> ZERO Then wr(nn) = x - w / z

wi(nn) = ZERO
wi(nn - 1) = ZERO
Else
wr(nn) = x + p
wr(nn - 1) = wr(nn)
wi(nn) = z
wi(nn - 1) = -z
End If
nn = nn - 2
Else
If its = itsmx Then
Print " Pause"
Print " Too many iterations!"
Input res
End If
If (its = 10) Or (its = 20) Then
t = t + x
For i = 1 To nn
A(i, i) = A(i, i) - x
Next i
s = Abs(A(nn, nn - 1)) + Abs(A(nn - 1, nn - 2))
x = .75# * s
y = x
w = -.4375# * s * s
End If
its = its + 1
For m = nn - 2 To 1 Step -1
z = A(m, m)
r = x - z
s = y - z
p = (r * s - w) / A(m + 1, m) + A(m, m + 1)
q = A(m + 1, m + 1) - z - r - s
r = A(m + 2, m + 1)
s = Abs(p) + Abs(q) + Abs(r)
p = p / s
q = q / s
r = r / s
If m = 1 Then Goto label1
u = Abs(A(m, m - 1)) * (Abs(q) + Abs(r))
v = Abs(p) * (Abs(A(m - 1, m - 1)) + Abs(z) + Abs(A(m + 1, m + 1)))
If u + v = v Then Goto label1
Next m
label1:  For i = m + 2 To nn
A(i, i - 2) = ZERO
If i <> (m + 2) Then A(i, i - 3) = ZERO
Next i
For k = m To nn - 1
If k <> m Then
p = A(k, k - 1)
q = A(k + 1, k - 1)
r = ZERO
If k <> (nn - 1) Then r = A(k + 2, k - 1)
x = Abs(p) + Abs(q) + Abs(r)
If x <> ZERO Then
p = p / x
q = q / x
r = r / x
End If
End If
aa = Sqr(p * p + q * q + r * r): bb = p:  _SIGN(aa,bb)'GOSUB 2900
s = Sign
If s <> ZERO Then
If k = m Then
If l <> m Then A(k, k - 1) = -A(k, k - 1)
Else
A(k, k - 1) = -s * x
End If
p = p + s
x = p / s
y = q / s
z = r / s
q = q / p
r = r / p
For j = k To nn
p = A(k, j) + q * A(k + 1, j)
If k <> (nn - 1) Then
p = p + r * A(k + 2, j)
A(k + 2, j) = A(k + 2, j) - p * z
End If
A(k + 1, j) = A(k + 1, j) - p * y
A(k, j) = A(k, j) - p * x
Next j
If nn < k + 3 Then
mmin = nn
Else
mmin = k + 3
End If
For i = 1 To mmin
p = x * A(i, k) + y * A(i, k + 1)
If k <> (nn - 1) Then
p = p + z * A(i, k + 2)
A(i, k + 2) = A(i, k + 2) - p * r
End If
A(i, k + 1) = A(i, k + 1) - p * q
A(i, k) = A(i, k) - p
Next i
End If
Next k
Goto label2:
End If
End If
If nn >= 1 Then Goto label4:
End Sub
Sub GET_EIGENVALUES(MAT() As Double,Eig() As complex)

Dim n As Integer=Ubound(MAT)
Redim Eig(n)
Dim As Double A(n,n)
equalize(A(),MAT())
Dim As Double wr(n),wi(n),d(n)
balance(a(),d())
GET_HESSENBERG(A())
ITERATE_BY_QR(A(),wr(),wi())
For i As Integer = 1 To n
Eig(i).re= wr(i):Eig(i).im= wi(i)
Next i
End Sub
Sub makecompanion(polynomium() As Double,mat() As Double)
Dim As Integer di=Ubound(polynomium)
Dim As Double one,_null=0
one=1:
Redim mat (1 To di,1 To di) As Double

For a As Integer=1 To di
mat(1,di)=_null-polynomium(0)
For b As Integer=1 To di
If a=b+1 Then mat(a,b)=one
If b>1 Then
mat(b,di)=_null-polynomium(b-1)
End If
Next b
Next a
End Sub
Sub equalize(m1() As Double,m2() As Double)
For x As Integer=1 To Ubound(m1)
For y As Integer=1 To Ubound(m1)
m1(x,y)=m2(x,y)
Next y
Next x
End Sub
Function decround ( a As Double, b As Integer) As Double
Dim y As Double
Dim i As Double
Dim r As Double
y = (Abs(a) - Int(Abs(a))) * (10 ^ b)
i = Int(y)
y = y - i
If y >= .5 Then i = i + 1
i = i / (10 ^ b)
r = Int(Abs(a)) + i
If a < 0 Then r = -r
decround = r
End Function
Function lenint(num As Ulongint) As Integer
Dim As Double x=1
Dim As Integer l=1
Do
x=x*10
Select Case num>=x
Case -1
l=l+1
Case 0
Exit Select
End Select
Loop Until x>=18446744073709551615
Return l
End Function
Function _poly(coff() As Double,number As Double)As Double
Dim count As Integer                'evaluates the polynomial
Dim pol As Double
Dim deg As Integer=Ubound(coff)
pol = 0
For count = 1 To DEG + 1
pol = pol + coff(count-1) * ((number) ^ (count - 1))
Next count
_poly = pol
End Function
Function seeterms(pol() As Double)As String
Redim As Double coff(1 To Ubound(pol)+1)
For z As Integer=0 To Ubound(pol)'+1
coff(z+1)=pol(z)
Next z
Dim result As String
result=result+"P(x) = "
Dim DEG As Integer=Ubound(coff)-1
Dim sgnstr As String
For j As Integer=DEG+1 To 1 Step -1

If coff(j) <> 0 Then
If Sgn(coff(j)) = 1 Then
sgnstr = "+"
result=result+"+"
End If

If Sgn(coff(j)) = -1 Then
sgnstr = ""
result=result+""
End If
If j - 1 = 0 Then
result=result+Format(coff(j))
End If

If Abs(coff(j)) <> 1 Then
If j - 1 = 1 Then
result=result+Format(coff(j))+"x "
End If

End If
If Abs(coff(j)) <> 1 Then
If j - 1 > 1 Then
result=result+Format(coff(j))+"x^"+(Format(j - 1))+" "
End If

End If
If coff(j) = 1 Then
If j - 1 > 1 Then
result=result+"x^"+(Format(j - 1))+" "
End If

If j - 1 = 1 Then
result=result+"x "
End If
End If

If coff(j) = -1 Then
If j - 1 = 1 Then
result=result+"-x "
End If

If j - 1 > 1 Then
result=result+"-x^"+(Format(j - 1))
End If
End If
End If
Next j
Return result
End Function```

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