Sturmian word: Difference between revisions
Added various BASIC dialects (BASIC256,FreeBASIC and Yabasic)
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(Added various BASIC dialects (BASIC256,FreeBASIC and Yabasic)) |
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In summary, <math>floor(k\sqrt a) = floor(mk/n)</math> where <math>m/n</math> is the first continued fraction approximant to <math>\sqrt a</math> with a denominator <math>n \geq k</math>
=={{header|BASIC}}==
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">fib = fibWord(10)
sturmian = sturmian_word(13, 21)
if left(fib, length(sturmian)) = sturmian then print sturmian
end
function invert(cadena)
for i = 1 to length(cadena)
b = mid(cadena, i, 1)
if b = "0" then
inverted += "1"
else
if b = "1" then
inverted += "0"
end if
end if
next
return inverted
end function
function sturmian_word(m, n)
sturmian = ""
if m > n then return invert(sturmian_word(n, m))
k = 1
while True
current_floor = int(k * m / n)
previous_floor = int((k - 1) * m / n)
if k * m mod n = 0 then exit while
if previous_floor = current_floor then
sturmian += "0"
else
sturmian += "10"
end if
k += 1
end while
return sturmian
end function
function fibWord(n)
Sn_1 = "0"
Sn = "01"
for i = 2 to n
tmp = Sn
Sn += Sn_1
Sn_1 = tmp
next
return Sn
end function</syntaxhighlight>
{{out}}
<pre>01001010010010100101001001010010</pre>
==={{header|FreeBASIC}}===
{{trans|Python}}
<syntaxhighlight lang="vbnet">Function invert(cadena As String) As String
Dim As String inverted, b
For i As Integer = 1 To Len(cadena)
b = Mid(cadena, i, 1)
inverted += Iif(b = "0", "1", "0")
Next
Return inverted
End Function
Function sturmian_word(m As Integer, n As Integer) As String
Dim sturmian As String
If m > n Then Return invert(sturmian_word(n, m))
Dim As Integer k = 1
Do
Dim As Integer current_floor = Int(k * m / n)
Dim As Integer previous_floor = Int((k - 1) * m / n)
If k * m Mod n = 0 Then Exit Do
sturmian += Iif(previous_floor = current_floor, "0", "10")
k += 1
Loop
Return sturmian
End Function
Function fibWord(n As Integer) As String
Dim As String Sn_1 = "0"
Dim As String Sn = "01"
For i As Integer = 2 To n
Dim As String tmp = Sn
Sn += Sn_1
Sn_1 = tmp
Next
Return Sn
End Function
Dim As String fib = fibWord(10)
Dim As String sturmian = sturmian_word(13, 21)
If Left(fib, Len(sturmian)) = sturmian Then Print sturmian
Sleep</syntaxhighlight>
{{out}}
<pre>01001010010010100101001001010010</pre>
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">fib$ = fibword$(10)
sturmian$ = sturmian_word$(13,21)
if left$(fib$,len(sturmian$)) = sturmian$ print sturmian$
end
sub invert$(cadena$)
for i = 1 to len(cadena$)
b$ = mid$(cadena$,i,1)
if b$ = "0" then
inverted$ = inverted$ +"1"
elsif b$ = "1" then
inverted$ = inverted$ +"0"
fi
next i
return inverted$
end sub
sub sturmian_word$(m,n)
sturmian$ = ""
if m > n return invert$(sturmian_word(n,m))
k = 1
while true
current_floor = int(k*m/n)
previous_floor = int((k-1)*m/n)
if mod(k*m, n) = 0 break
if previous_floor = current_floor then
sturmian$ = sturmian$ +"0"
else
sturmian$ = sturmian$ +"10"
fi
k = k +1
end while
return sturmian$
end sub
sub fibword$(n)
sn_1$ = "0"
sn$ = "01"
for i = 2 to n
tmp$ = sn$
sn$ = sn$ + sn_1$
sn_1$ = tmp$
next i
return sn$
end sub</syntaxhighlight>
{{out}}
<pre>01001010010010100101001001010010</pre>
=={{header|Julia}}==
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