- Introduction
- Creation Functions
- Structure Operations
- Element Operations
- Arithmetic Operations
- Bit Operations
- Bitwise Operations
- Equality and Membership
- Parent and Category
- Predicates on Ring Elements
- Comparison of Ring Elements
- Conjugates, Norm and Trace
- Other Elementary Functions
- AbsoluteValue(n) : RngIntElt -> RngIntElt
- Ilog2(n) : RngIntElt -> RngIntElt
- Ilog(b, n) : RngIntElt, RngIntElt -> RngIntElt
- Quotrem(m, n) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- Valuation(x, p) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- Iroot(a, n) : RngIntElt, RngIntElt -> RngIntElt
- Sign(n) : RngIntElt -> RngIntElt
- Ceiling(n) : RngIntElt -> RngIntElt
- Floor(n) : RngIntElt -> RngIntElt
- Round(n) : RngIntElt -> RngIntElt
- Truncate(n) : RngIntElt -> RngIntElt
- SquarefreeFactorization(n) : RngIntElt -> RngIntElt, RngIntElt
- Isqrt(n) : RngIntElt -> RngIntElt
- Random Numbers
- Random(a, b) : RngIntElt, RngIntElt -> RngIntElt
- Random(b) : RngIntElt -> RngIntElt
- RandomBits(n) : RngIntElt -> RngIntElt
- RandomPrime(n: parameter) : RngIntElt -> RngIntElt
- RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
- RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt
- GCD and LCM
- Arithmetic Functions
- Combinatorial Functions
- Binomial(n, r) : RngIntElt, RngIntElt -> RngIntElt
- Multinomial(n, [r1, ... rn]) : RngIntElt, [RngIntElt] -> RngIntElt
- Factorial(n) : RngIntElt -> RngIntElt
- IsFactorial(n) : RngIntElt -> BoolElt, RngIntElt
- Partitions(n) : RngIntElt -> [ [ RngIntElt ] ]
- NumberOfPartitions(n) : RngIntElt -> RngIntElt
- RestrictedPartitions(n, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
- RestrictedPartitions(n, k, M) : RngIntElt, RngIntElt, SetEnum -> [ [ RngIntElt ] ]
- StirlingFirst(n, k) : RngIntElt, RngIntElt -> RngIntElt
- StirlingSecond(n, k) : RngIntElt, RngIntElt -> RngIntElt
- Bell(n) : RngIntElt -> RngIntElt
- Fibonacci(n) : RngIntElt -> RngIntElt
- Lucas(n) : RngIntElt -> RngIntElt
- GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
- Primes and Primality Testing
- Factorization
- General Factorization
- Storing Potential Factors
- Specific Factorization Algorithms
- SetVerbose("Cunningham", b) : MonStgElt, BoolElt ->
- Cunningham(b, k, c) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
- AssertAttribute(RngInt, "CunninghamStorageLimit", l) : Cat, MonStgElt, RngIntElt ->
- TrialDivision(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
- PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
- pMinus1(n, B1) : RngIntElt, RngIntElt -> RngIntElt
- pPlus1(n, B1) : RngIntElt, RngIntElt -> RngIntElt
- SQUFOF(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
- ECM(n, B1) : RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- ECMSteps(n, L, U) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- MPQS(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
- Factorization Related Functions
- Factorization Sequences
- Modular Arithmetic
- Arithmetic Operations
- Modexp(n, k, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
- n mod m : RngIntElt, RngIntElt -> RngIntElt
- Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt
- Modsqrt(n, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
- Modorder(n, m) : RngIntElt, RngIntElt -> RngIntElt
- IsPrimitive(n, m) : RngIntElt, RngIntElt -> BoolElt
- PrimitiveRoot(m) : RngIntElt -> RngIntElt
- The Solution of Modular Equations
- Solution(a, b, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- ChineseRemainderTheorem(X, N) : [RngIntElt], [RngIntElt] -> RngIntElt
- Solution(A, B, N) : [RngIntElt], [RngIntElt],[RngIntElt] -> RngIntElt
- NormEquation(d, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt, RngIntElt
- Example RngInt_norm-equation (H19E9)
- Infinities
- Advanced Factorization Techniques: The Number Field Sieve
- The Magma Number Field Sieve Implementation
- Naive NFS
- Factoring with NFS Processes
- Data Files
- Distributing NFS Factorizations
- Magma and CWI NFS Interoperability
- Tools for Finding a Suitable Polynomial
- BaseMPolynomial(n, m, d) : RngIntElt, RngIntElt, RngIntElt -> RngMPolElt
- MurphyAlphaApproximation(F, b) : RngMPolElt, RngIntElt -> FldReElt
- OptimalSkewness(F) : RngMPolElt -> FldReElt, FldReElt
- Example RngInt_GetPoly (H19E15)
- BestTranslation(F, m, a) : RngMPolElt, RngIntElt, FldReElt, FldReElt -> RngMPolElt, RngIntElt, FldReElt, FldReElt
- PolynomialSieve(F, m, J0, J1,MaxAlpha) : RngMPolElt, RngIntElt, RngIntElt, RngIntElt, FldReElt -> List
- Bibliography
V2.28, 13 July 2023