Modinv(m,n): inverse of m modulo n, only valid when m and n are coprime, meaning that they do not have common factors.): Least common multiple of these integers. ): Greatest common divisor of these integers. Example: P(4) = 5 because the number 4 can be partitioned in 5 different ways: 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1. P(n): Unrestricted Partition Number (number of decompositions of n into sums of integers without regard to order).where each element equals the sum of the previous two members of the sequence. F(n): Fibonacci number F n from the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.B(n): Previous probable prime before n.p#: primorial (product of all primes less or equal than p).(all numbers greater than zero) where k is the number of exclamation marks. It is the product of n times n − k times n − 2k. !: multiple factorial ( n must be greater than or equal to zero). n!: factorial ( n must be greater than or equal to zero).Otherwise, a SHR b shifts a left the number of bits specified by − b. SHL or >: When b ≥ 0, a SHR b shifts a right the number of bits specified by b.Positive (negative) numbers are prepended with an infinite number of bits set to zero (one). The operations are done in binary (base 2). The operators return zero for false and -1 for true. ^ or ** for exponentiation (the exponent must be greater than or equal to zero).% for modulus (remainder of the integer division).
You can use the following operators and parentheses for the expressions: When the program displays convergents, it stops before if it runs out of memory. If b is negative, the result is not a real number, so it cannot be represented as a continued fraction.įor rational numbers the calculator finds the coefficients and the numerator and denominator of all convergents, but for quadratic irrationalities the calculator stops after the 100000th convergent if the period is larger. If you need the square root to subtract the number at the left, just negate both a and c. The calculator accepts numbers of up to 10000 digits. You can type numbers or numerical expressions on the input boxes. Is the best rational approximation to the argument x with denominator less or equal to B n and matches the value obtained by developing only the first n coefficients of the continued fraction. This calculator can find the continued fraction expansions of rational numbers and quadratic irrationalities.Īpart from the coefficients a n, the program allows to find the convergent A n/ B n.
#Negative and positive fractions calculator plus#
If the number is a quadratic irrationality of the form fraction whether the numerator is a plus the square root of b and the denominator is c , If the number to be represented is rational, there is a finite number of terms in the continued fraction. X is equal to a sub 0 plus double slash a sub 1, a sub 2, a sub 3, etcetera double slash X is equal to a sub 0 plus 1 over a sub 1 plus 1 over a sub 2 plus 1 over a sub 3 plus etcetera This Web application shows the continued fraction expansion of rational numbers and quadratic irrationalities.Īny real number x can be represented uniquely by a continued fraction:
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