Module arithmetic 

Traits for arithmetic on UnsignedPolynomials.

Modules

canonicalize_unit

Implementations of CanonicalizeUnit and CanonicalizeUnitAssign, which bring a polynomial into canonical unit form.

compose_power_of_x

Implementations of ComposePowerOfX and ComposePowerOfXAssign, for substituting a power of the variable into a polynomial.

content

Implementations of Content, PrimitivePart, PrimitivePartAssign, and ContentAndPrimitivePart, which compute the GCD of a polynomial’s coefficients and the polynomial divided by it.

deflate_power_of_x

Implementations of DeflatePowerOfX and DeflatePowerOfXAssign, for undoing the substitution of a power of the variable into a polynomial.

div_power_of_x

Implementations of DivPowerOfX and DivPowerOfXAssign, for dividing a polynomial by a power of its variable and discarding the remainder.

evaluate

Implementations of ModEvaluate and ModPowerOf2Evaluate, which evaluate a polynomial at a value modulo a value or a power of 2.

exponent_gcd

An implementation of ExponentGcd, the greatest common divisor of the exponents at which a polynomial has nonzero coefficients.

height

An implementation of Height, the largest of a polynomial’s coefficients.

is_unit

An implementation of IsUnit, a trait for determining whether a number is a unit of its ring.

mod_add

Implementations of ModAdd and ModAddAssign, for adding two polynomials modulo a value.

mod_add_truncated

Implementations of ModAddTruncated and ModAddTruncatedAssign, for adding two polynomials modulo a value and keeping only their low coefficients.

mod_derivative

Implementations of ModDerivative and ModDerivativeAssign, for differentiating a polynomial modulo a number.

mod_integral

Implementations of ModIntegral and ModIntegralAssign, for integrating a polynomial modulo a value.

mod_is_reduced

An implementation of ModIsReduced, which checks whether every coefficient of a polynomial is less than a given modulus.

mod_make_monic

Implementations of ModMakeMonic and ModMakeMonicAssign, which make a polynomial monic modulo a value.

mod_mul

Implementations of ModMul and ModMulAssign, for multiplying two polynomials modulo a value.

mod_mul_truncated

Implementations of ModMulTruncated and ModMulTruncatedAssign, for multiplying two polynomials modulo a value and keeping the low coefficients of the product.

mod_neg

Implementations of ModNeg and ModNegAssign, which negate a polynomial modulo a number.

mod_nth_derivative

Implementations of ModNthDerivative and ModNthDerivativeAssign, for differentiating a polynomial any number of times modulo a number.

mod_op

Implementations of Mod, ModAssign, Rem and RemAssign, which reduce every coefficient of a polynomial modulo a number.

mod_pow

Implementations of ModPow and ModPowAssign, for raising a polynomial to a power modulo a number.

mod_pow_truncated

Implementations of ModPowTruncated and ModPowTruncatedAssign, for raising a polynomial to a power modulo a number and keeping only the low coefficients.

mod_power_of_2

Implementations of ModPowerOf2 and ModPowerOf2Assign, which reduce every coefficient of a polynomial modulo a power of 2.

mod_power_of_2_add

Implementations of ModPowerOf2Add and ModPowerOf2AddAssign, for adding two polynomials modulo $2^k$.

mod_power_of_2_add_truncated

Implementations of ModPowerOf2AddTruncated and ModPowerOf2AddTruncatedAssign, for adding two polynomials modulo $2^k$ and keeping only their low coefficients.

mod_power_of_2_derivative

Implementations of ModPowerOf2Derivative and ModPowerOf2DerivativeAssign, for differentiating a polynomial modulo a power of 2.

mod_power_of_2_integral

Implementations of ModPowerOf2Integral and ModPowerOf2IntegralAssign, for integrating a polynomial modulo $2^k$.

mod_power_of_2_is_reduced

An implementation of ModPowerOf2IsReduced, which checks whether every coefficient of a polynomial is less than a given power of 2.

mod_power_of_2_mul

Implementations of ModPowerOf2Mul and ModPowerOf2MulAssign, for multiplying two polynomials modulo $2^k$.

mod_power_of_2_mul_truncated

Implementations of ModPowerOf2MulTruncated and ModPowerOf2MulTruncatedAssign, for multiplying two polynomials modulo $2^k$ and keeping the low coefficients of the product.

mod_power_of_2_neg

Implementations of ModPowerOf2Neg and ModPowerOf2NegAssign, which negate a polynomial modulo a power of 2.

mod_power_of_2_nth_derivative

Implementations of ModPowerOf2NthDerivative and ModPowerOf2NthDerivativeAssign, for differentiating a polynomial any number of times modulo a power of 2.

mod_power_of_2_pow

Implementations of ModPowerOf2Pow and ModPowerOf2PowAssign, for raising a polynomial to a power modulo a power of 2.

mod_power_of_2_pow_truncated

Implementations of ModPowerOf2PowTruncated and ModPowerOf2PowTruncatedAssign, for raising a polynomial to a power modulo a power of 2 and keeping only the low coefficients.

mod_power_of_2_shl

Implementations of ModPowerOf2Shl and ModPowerOf2ShlAssign, for left-shifting a polynomial modulo a power of 2.

mod_power_of_2_square

Implementations of ModPowerOf2Square and ModPowerOf2SquareAssign, for squaring a polynomial modulo $2^k$.

mod_power_of_2_square_truncated

Implementations of ModPowerOf2SquareTruncated and ModPowerOf2SquareTruncatedAssign, for squaring a polynomial modulo $2^k$ and keeping the low coefficients of the square.

mod_power_of_2_sub

Implementations of ModPowerOf2Sub and ModPowerOf2SubAssign, for subtracting one polynomial from another modulo $2^k$.

mod_power_of_2_sub_truncated

Implementations of ModPowerOf2SubTruncated and ModPowerOf2SubTruncatedAssign, for subtracting one polynomial from another modulo $2^k$ and keeping only their low coefficients.

mod_shl

Implementations of ModShl and ModShlAssign, for left-shifting a polynomial modulo a number.

mod_square

Implementations of ModSquare and ModSquareAssign, for squaring a polynomial modulo a value.

mod_square_truncated

Implementations of ModSquareTruncated and ModSquareTruncatedAssign, for squaring a polynomial modulo a value and keeping the low coefficients of the square.

mod_sub

Implementations of ModSub and ModSubAssign, for subtracting one polynomial from another modulo a value.

mod_sub_truncated

Implementations of ModSubTruncated and ModSubTruncatedAssign, for subtracting one polynomial from another modulo a value and keeping only their low coefficients.

mul_power_of_x

Implementations of MulPowerOfX and MulPowerOfXAssign, for multiplying a polynomial by a power of its variable.