The only extraordinary arithmetic operations on integers are mod and div.
The quotient q of the division with remainder n=qm + r, where 0 <= r<m or m<r <= 0 (depending on the sign of m), for integers n and m != 0.
The remainder r of the division with remainder n=qm + r, where 0 <= r<m or m<r <= 0 (depending on the sign of m), for integers n and m != 0.
Assuming that the integer n is exactly divisible by the integer d, return the exact quotient of n by d (as an integer). An error results if d does not divide n exactly.
True if the integer n is even, otherwise false.
True if the integer n is odd, otherwise false.
True if and only if the integer n is divisible by the integer d; if true, the quotient of n by d is also returned.
True if the non-negative integer n is the square of an integer, false otherwise. If n is a square, its positive square root is also returned.
True if the non-zero integer n is not divisible by the square of any prime, false otherwise.
If the integer n>1 is a power n=b^k of an integer b, with k>1, this function returns true, the minimal positive b and its associated k; if it is not such integer power the function returns false.
If the integer n>1 is k-th power (k>1) of some integer b, so n=b^k, this function returns true, and b; if it is not a k-th integer power the function returns false.
Proof: BoolElt Default: true
True iff the integer n is a prime. A rigorous primality test and proof will be used (unless the parameter Proof is false; see the section on Primes and Factorization for a complete description of this function).
> { p : p in [10^10+3..10^10+1000 by 4] |
> IsPrime(p) and IsPrime((p-1) div 2) };
{ 10000000259, 10000000643 }
Returns true if and only if a is integral, which is of course true for every integer n.
Returns true if n fits in a single word in the internal representation of integers in Magma, that is, if | n|<2^(30), false otherwise.
The complex conjugate of n, which will be the integer n itself.
The conjugate of n, which will be the integer n itself.
The norm (in Q) of n, which will be the integer n itself.
The Euclidean norm (length) of n, which will equal the absolute value of n.
The trace (in Q) of n, which will be the integer n itself.
Returns the minimal polynomial of the integer n, which is the monic linear polynomial with constant coefficient n in a univariate polynomial ring R over the integers. (If R has not been created before with a name for its indeterminate, $.1-n will be returned.)
Absolute value of the integer n.
The integral part of the logarithm to the base two of the positive integer n.
The integral part of the logarithm to the base b of the positive integer n (i.e., the largest integer k such that b^k <= n). b must be greater than or equal to two.
Returns both the quotient q and remainder r obtained upon dividing the integer m by the integer n, that is, m = q.n + r, with 0 <= r < |n|.
The valuation of the integer x at the prime p. This is the largest integer v for which p^v divides x. If x = 0 then v = Infinity. The optional second return value is the integer u such that x = p^v u.
A random integer lying in the interval [a, b], where a, b are positive integers and a <= b.
A random integer lying in the interval [0, b], where b is a positive integer.
A random integer m such that 0 <= m < 2^n, where n is a small positive integer (i.e. so m has n random bits with a probability of 1/2 for each bit).
A integer m such that 0 <= m < 2^n, and the binary expansion of n consists of consecutive strings of zeros or ones each of random length in the range [a ... b].
Given a positive integer a, return the integer b= Floor(root n of a), i.e. the integral part of the n-th root of a. (To obtain the root itself (as a real number), a has to be coerced into a real field, and Root can be applied.)
Returns -1, 0 or 1 depending upon whether the integer n is negative, zero or positive, respectively.
The ceiling of the integer n, that is, n itself.
The floor of the integer n, that is, n itself.
This function rounds the integer n to itself.
This function returns the integer truncation of the integer n, that is, n itself.
Given a non-negative integer n, return a squarefree integer x as well as a positive integer y, such that n=xy^2.
Given a positive integer n, return the integer Floor(sqrt n), i.e., the integral part of the square root of the integer n.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]