Continued fraction: Difference between revisions
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(Removed Liberty Basic code: Incorrect task) |
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2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274 |
2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274 |
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</lang> |
</lang> |
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=={{header|Liberty BASIC}}== |
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<lang lb> |
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dim terms(100) |
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input "Enter a number:";n$ |
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if instr(n$,"/")=0 then |
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n$=castToFraction$(val(n$)) |
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end if |
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if castToReal(n$)<=0 then notice "N must be positive!":end |
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print "["; |
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if termoverride=0 then |
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nterms=1 |
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[start] |
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term=int2(n$):n$=subtract$(n$,castToFraction$(term)) |
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print term; |
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terms(nterms)=term |
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if equal(n$,"0/1")=0 then n$=reciprocal$(n$) |
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if compare(n$,"1/100")=1 and nterms<100 then print ",";:nterms=nterms+1:goto [start] |
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print "]" |
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end if |
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print "Convergents:" |
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for x=1 to nterms |
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sum=terms(x) |
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sum$=castToFraction$(terms(x)) |
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for y=x-1 to 1 step -1 |
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sum=terms(y)+1/sum |
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sum$=add$(castToFraction$(terms(y)),reciprocal$(sum$)) |
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next y |
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print sum$;"=";sum |
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next x |
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function int2(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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int2=int(aNumerator/aDenominator) |
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end function |
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function abs$(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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bNumerator=abs(aNumerator) |
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bDenominator=abs(aDenominator) |
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b$=str$(bNumerator)+"/"+str$(bDenominator) |
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abs$=simplify$(b$) |
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end function |
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function negate$(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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bNumerator=-1*aNumerator |
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bDenominator=aDenominator |
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b$=str$(bNumerator)+"/"+str$(bDenominator) |
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negate$=simplify$(b$) |
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end function |
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function add$(a$,b$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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bNumerator=val(word$(b$,1,"/")) |
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bDenominator=val(word$(b$,2,"/")) |
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cNumerator=(aNumerator*bDenominator+bNumerator*aDenominator) |
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cDenominator=aDenominator*bDenominator |
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c$=str$(cNumerator)+"/"+str$(cDenominator) |
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add$=simplify$(c$) |
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end function |
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function subtract$(a$,b$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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bNumerator=val(word$(b$,1,"/")) |
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bDenominator=val(word$(b$,2,"/")) |
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cNumerator=(aNumerator*bDenominator-bNumerator*aDenominator) |
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cDenominator=aDenominator*bDenominator |
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c$=str$(cNumerator)+"/"+str$(cDenominator) |
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subtract$=simplify$(c$) |
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end function |
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function multiply$(a$,b$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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bNumerator=val(word$(b$,1,"/")) |
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bDenominator=val(word$(b$,2,"/")) |
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cNumerator=aNumerator*bNumerator |
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cDenominator=aDenominator*bDenominator |
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c$=str$(cNumerator)+"/"+str$(cDenominator) |
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multiply$=simplify$(c$) |
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end function |
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function divide$(a$,b$) |
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divide$=multiply$(a$,reciprocal$(b$)) |
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end function |
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function simplify$(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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gcd=GCD(aNumerator,aDenominator) |
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if aNumerator<0 and aDenominator<0 then gcd=-1*gcd |
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bNumerator=aNumerator/gcd |
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bDenominator=aDenominator/gcd |
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b$=str$(bNumerator)+"/"+str$(bDenominator) |
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simplify$=b$ |
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end function |
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function reciprocal$(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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reciprocal$=str$(aDenominator)+"/"+str$(aNumerator) |
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end function |
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function equal(a$,b$) |
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if simplify$(a$)=simplify$(b$) then equal=1:else equal=0 |
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end function |
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function castToFraction$(a) |
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do |
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exp=exp+1 |
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a=a*10 |
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loop until abs(a-int(a+0.001))<0.001 |
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castToFraction$=simplify$(str$(a)+"/"+str$(10^exp)) |
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end function |
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function castToReal(a$) |
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aNumerator=val(word$(a$,1,"/")) |
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aDenominator=val(word$(a$,2,"/")) |
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castToReal=aNumerator/aDenominator |
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end function |
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function castToInt(a$) |
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castToInt=int(castToReal(a$)) |
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end function |
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function compare(a$,b$) |
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if abs$(subtract$(a$,b$))=subtract$(a$,b$) then compare=1:else compare=-1 |
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end function |
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function GCD(a,b) |
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if a=0 then |
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GCD=1 |
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else |
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if a>=b then |
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while b |
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c = a |
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a = b |
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b = c mod b |
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GCD = abs(a) |
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wend |
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else |
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GCD=GCD(b,a) |
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end if |
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end if |
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end function |
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</lang> |
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=={{header|Mathematica}}== |
=={{header|Mathematica}}== |
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<lang Mathematica> |
<lang Mathematica> |
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