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predecessorOfPairOfNeighborsInFm m (successor, rightNeighborOfSuccessor) checkPair
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-- If checkPair == True, then to check whether the input pair is indeed a pair of neighboring fractions in the sequence Fm
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| m <1=-1%1-- "N/A: Order m of the sequence should be > 0"
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| successor >= rightNeighborOfSuccessor =-1%2-- "N/A We should have successor < rightNeighborOfSuccessor"
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| successor >= rightNeighborOfSuccessor =-1%2-- "N/A: We should have successor < rightNeighborOfSuccessor"
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| successor <=0%1|| successor >=1%1=-1%3--"N/A: successor should be between (0 % 1) (excluded) and (1 % 1) (excluded)"
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| denominator successor > m =-1%4--"N/A: Denominator of the successor should not exceed the order m of the sequence"
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| rightNeighborOfSuccessor >1%1=-1%5--"N/A: rightNeighborOfSuccessor should be between successor (excluded) and (1 % 1) (included)"
@@ -684,7 +684,7 @@ predecessorOfPairOfNeighborsInFml m l (successor, rightNeighborOfSuccessor) chec
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-- If checkPair == True, then to check whether the input pair is indeed a pair of neighboring fractions in the sequence Fml
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| m <2=-1%1-- "N/A: Parameter m of the sequence should be > 1"
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| l <=0|| l >= m =-1%2--"N/A: Parameter l should be between 0 (excluded) and m (excluded)"
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| successor >= rightNeighborOfSuccessor =-1%3-- "N/A We should have successor < rightNeighborOfSuccessor"
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| successor >= rightNeighborOfSuccessor =-1%3-- "N/A: We should have successor < rightNeighborOfSuccessor"
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| successor <=0%1|| successor >1%1=-1%4--"N/A: successor should be between (0 % 1) (excluded) and (1 % 1) (included)"
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| denominator successor > m =-1%5--"N/A: Denominator of the successor should not exceed the parameter m of the sequence"
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| l < numerator successor =-1%6--"N/A: Numerator of the successor should be between 1 (included) and l (included)"
@@ -770,7 +770,7 @@ predecessorOfPairOfNeighborsInGml m l (successor, rightNeighborOfSuccessor) chec
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-- If checkPair == True, then to check whether the input pair is indeed a pair of neighboring fractions in the sequence Gml
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| m <2=-1%1-- "N/A: Parameter m of the sequence should be > 1"
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| l <=0|| l >= m =-1%2--"N/A: Parameter l should be between 0 (excluded) and m (excluded)"
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-
| successor >= rightNeighborOfSuccessor =-1%3-- "N/A We should have successor < rightNeighborOfSuccessor"
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| successor >= rightNeighborOfSuccessor =-1%3-- "N/A: We should have successor < rightNeighborOfSuccessor"
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| successor <=0%1|| successor >1%1=-1%4--"N/A: successor should be between (0 % 1) (excluded) and (1 % 1) (included)"
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| denominator successor > m =-1%5--"N/A: Denominator of the successor should not exceed the parameter m of the sequence"
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| l + denominator successor - m > numerator successor =-1%6--"N/A: The quantity (l + denominator - m) should not exceed the numerator of the successor"
@@ -864,7 +864,7 @@ predecessorOfPairOfNeighborsInFBnm n m (successor, rightNeighborOfSuccessor) che
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-- If checkPair == True, then to check whether the input pair is indeed a pair of neighboring fractions in the sequence FBnm
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| n <2=-1%1-- "N/A: Parameter n of the sequence should be > 1"
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| m <1|| m >= n =-1%2-- "N/A: Parameter m of the sequence should be between 0 (excluded) and n (excluded)"
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| successor >= rightNeighborOfSuccessor =-1%3-- "N/A We should have successor < rightNeighborOfSuccessor"
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| successor >= rightNeighborOfSuccessor =-1%3-- "N/A: We should have successor < rightNeighborOfSuccessor"
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| successor <=0%1|| successor >=1%1=-1%4--"N/A: successor should be between (0 % 1) (excluded) and (1 % 1) (excluded)"
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| denominator successor > n =-1%5--"N/A: Denominator of the successor should not exceed n"
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| m + denominator successor - n > numerator successor ||
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