Arithmetic/Rational: Difference between revisions
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=={{header|Elisa}}== |
=={{header|Elisa}}== |
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A component for Rational Numbers is defined below. |
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<lang Elisa> |
<lang Elisa> |
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component RationalNumbers; |
component RationalNumbers; |
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type Rational; |
type Rational; |
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abs(R) = Rational(abs(R.A), abs(R.B)); |
abs(R) = Rational(abs(R.A), abs(R.B)); |
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Rational(I) = Rational (I, 1); |
Rational(I) = Rational (I, 1); |
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Numerator(R) = R.A; |
Numerator(R) = R.A; |
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Denominator(R) = R.B; |
Denominator(R) = R.B; |
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<< internal definitions >> |
<< internal definitions >> |
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Normalize (A = integer, B = integer) -> Rational; |
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Normalize (A, B) = [ exception( B == 0, "Illegal Rational Number"); |
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Common = GCD(abs(A), abs(B)); |
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if B < 0 then Rational(-A / Common, -B / Common) |
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else Rational( A / Common, B / Common) ]; |
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GCD (A = integer, B = integer) -> integer; |
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GCD (A, B) = [ if A == 0 then return(B); |
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if B == 0 then return(A); |
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if A > B then GCD (B, mod(A,B)) |
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else GCD (A, mod(B,A)) ]; |
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end component RationalNumbers; |
end component RationalNumbers; |
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</lang> |
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Tests |
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<lang Elisa> |
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use RationalNumbers; |
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PerfectNumbers( Limit = integer) -> multi(integer); |
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PerfectNumbers( Limit) = |
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[ Candidate = 2 .. Limit; |
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Sum:= Rational(1,Candidate); |
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[ Divisor = 2 .. integer(sqrt(real(Candidate))); |
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if mod(Candidate, Divisor) == 0 then |
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Sum := Sum + Rational(1, Divisor) + Rational(Divisor, Candidate); |
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]; |
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if Sum == Rational(1,1) then Candidate |
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]; |
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PerfectNumbers(10000)? |
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</lang> |
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Output |
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<lang Elisa> |
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6 |
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28 |
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496 |
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8128 |
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</lang> |
</lang> |
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