Integers mod n : detailed table of contents¶
- nmod.h – integers mod n (word-size n)
- nmod_vec.h – vectors over integers mod n (word-size n)
- nmod_mat.h – matrices over integers mod n (word-size n)
- Types, macros and constants
- Memory management
- Basic properties and manipulation
- Window
- Concatenate
- Printing
- Random matrix generation
- Comparison
- Transposition and permutations
- Addition and subtraction
- Matrix-scalar arithmetic
- Matrix multiplication
- Matrix Exponentiation
- Trace
- Determinant and rank
- Inverse
- Triangular solving
- Nonsingular square solving
- LU decomposition
- Reduced row echelon form
- Nullspace
- Transforms
- Characteristic polynomial
- Minimal polynomial
- Strong echelon form and Howell form
- nmod_poly.h – univariate polynomials over integers mod n (word-size n)
- Simple example
- Types, macros and constants
- Memory management
- Polynomial properties
- Assignment and basic manipulation
- Randomization
- Getting and setting coefficients
- Input and output
- Comparison
- Shifting
- Addition and subtraction
- Scalar multiplication and division
- Bit packing and unpacking
- KS2/KS4 Reduction
- Multiplication
- Powering
- Division
- Divisibility testing
- Derivative and integral
- Evaluation
- Multipoint evaluation
- Interpolation
- Composition
- Taylor shift
- Modular composition
- Greatest common divisor
- Discriminant
- Power series composition
- Power series reversion
- Square roots
- Power sums
- Transcendental functions
- Special polynomials
- Products
- Subproduct trees
- Inflation and deflation
- Chinese Remaindering
- Berlekamp-Massey Algorithm
- nmod_poly_mat.h – matrices of univariate polynomials over integers mod n (word-size n)
- nmod_poly_factor.h – factorisation of univariate polynomials over integers mod n (word-size n)
- nmod_mpoly.h – multivariate polynomials over integers mod n (word-size n)
- Types, macros and constants
- Context object
- Memory management
- Input/Output
- Basic manipulation
- Constants
- Degrees
- Coefficients
- Comparison
- Container operations
- Random generation
- Addition/Subtraction
- Scalar operations
- Differentiation
- Evaluation
- Multiplication
- Powering
- Division
- Greatest Common Divisor
- Square Root
- Univariate Functions
- Internal Functions
- nmod_mpoly_factor.h – factorisation of multivariate polynomials over integers mod n (word-size n)
- mpn_mod.h – integers mod n (packed multi-word n)
- fmpz_mod.h – arithmetic modulo integers
- fmpz_mod_vec.h – vectors over integers mod n
- fmpz_mod_mat.h – matrices over integers mod n
- Types, macros and constants
- Element access
- Memory management
- Random generation
- Windows and concatenation
- Input and output
- Comparison
- Set and transpose
- Conversions
- Addition and subtraction
- Scalar arithmetic
- Matrix multiplication
- Trace
- Gaussian elimination
- Strong echelon form and Howell form
- Inverse
- LU decomposition
- Triangular solving
- Solving
- Transforms
- Characteristic polynomial
- Minimal polynomial
- fmpz_mod_poly.h – polynomials over integers mod n
- Simple example
- Types, macros and constants
- Memory management
- Randomisation
- Attributes
- Assignment and basic manipulation
- Conversion
- Comparison
- Getting and setting coefficients
- Shifting
- Addition and subtraction
- Scalar multiplication and division
- Multiplication
- Products
- Division
- Divisibility testing
- Power series inversion
- Power series division
- Greatest common divisor
- Minpoly
- Resultant
- Discriminant
- Derivative
- Evaluation
- Multipoint evaluation
- Composition
- Square roots
- Modular composition
- Subproduct trees
- Radix conversion
- Input and output
- Inflation and deflation
- Berlekamp-Massey Algorithm
- fmpz_mod_poly_factor.h – factorisation of polynomials over integers mod n
- fmpz_mod_mpoly.h – polynomials over the integers mod n
- Types, macros and constants
- Context object
- Memory management
- Input/Output
- Basic manipulation
- Constants
- Degrees
- Coefficients
- Comparison
- Container operations
- Random generation
- Addition/Subtraction
- Scalar operations
- Differentiation
- Evaluation
- Multiplication
- Powering
- Division
- Greatest Common Divisor
- Square Root
- Univariate Functions
- Internal Functions
- fmpz_mod_mpoly_factor.h – factorisation of multivariate polynomials over the integers mod n