Struct libslide::math::poly::Poly

pub struct Poly {
    pub vec: Vec<isize>,
}

A polynomial in integer space Z. TODO: Currently, this container only services polynomials with non-negative degrees.

Fields

vec: Vec<isize>

Underlying polynomial coefficient representation. The degree of each coefficient is its index in the vector.

Implementations

impl Poly

pub fn new(vec: Vec<isize>) -> Self

Creates a new Poly from a vector of coefficients, with the degree of each coefficient being its index in the vector.

pub fn empty() -> Self

Creates an empty Poly.

pub fn is_zero(&self) -> bool

Returns whether the polynomial is equivalent to 0.

pub fn is_one(&self) -> bool

Returns whether the polynomial is equivalent to 1.

pub fn deg(&self) -> usize

Returns the degree of the polynomial.

pub fn primitive(self) -> Self

Returns the primitive polynomial of self over the integers.

Examples:

// 6x^2 + 4x + 2 -> 3x^2 + 2x + 1
assert_eq!(poly![2, 4, 6], poly![1, 2, 3]);

fn add_term(self, coeff: isize, pow: usize) -> Self

Adds a term of form coeffx^pow to self.

Examples:

// (x + 2) + 3x^2 -> 3x^2 + x + 2
assert_eq!(poly![2, 1].add_term(3, 2), poly![2, 1, 3]);

fn mul_term(self, coeff: isize, pow: usize) -> Self

Multiplies a term of form coeffx^pow to self.

Examples:

// (x + 2) * 3x^2 -> 3x^3 + 6x^2
assert_eq!(poly![2, 1].mul_term(3, 2), poly![0, 0, 6, 3]);

pub fn mul_scalar(self, c: isize) -> Self

Multiplies each term in the polynomial by a scalar.

pub fn div_scalar(self, c: isize) -> Result<Self, &'static str>

Divides each term in the polynomial by a scalar. If the scalar divisor is 0, an error is returned.

fn sub(self, other: Self) -> Self

Subtracts other from self, yielding a new polynomial.

Examples:

// (x + 2) - (3x^2 + 2x) -> -3x^2 - x + 2
assert_eq!(poly![2, 1].sub(poly![0, 2, 3]), poly![2, -1, -3]);

fn truncate_zeros(self) -> Self

Removes leading zero terms in a polynomial.

pub fn div(self, other: Poly) -> Result<(Self, Self), &'static str>

Divides one polynomial by another, returning a tuple of (quotient, remainder) or an error if division failed.

Examples:

// (x^2 - 4) / (x + 2) -> ((x - 2), 0)
assert_eq!(poly![-4, 0, 1].div(poly![2, 1]), Ok((poly![-2, 1], poly![])));

// (x^2 - 2x) / (x + 1) -> ((x - 3), 3)
assert_eq!(poly![-2, 0, 1].div(poly![1, 1]), Ok((poly![-3, 1], poly![3])));

pub fn max_norm(&self) -> usize

Returns the max norm of a polynomial. This is equivalent to the largest absolute value of each term's coefficient.

pub fn lc(&self) -> isize

Returns the leading coefficient, i.e. the coefficient of the highest-degree term, of the polynomial. If the polynomial is empty, the leading coefficient is 0.

pub fn eval(&self, x: isize) -> isize

Evaluates the polynomial at a value x.

Examples:

// (x^2 - 4)(1) -> -3
assert_eq!(poly![-4, 0, 1].eval(1), -3);

pub fn from_expr(
    expr: RcExpr,
    relative_to: Option<RcExpr>
) -> Result<(Self, Option<RcExpr>), String>

Transforms an expression into a polynomial relative to some term. If relative_to is not none, the constructed polynomial will be relative to that term. Otherwise, the polynomial will be relative to the term in the expression sequence.

If transformation is successful, the return value is a tuple of (polynomial, relative term). Transformation may fail for a number of reasons, including the expression containing a non-unique term, consisting of non-integer coefficients, or non-integer exponents.

Examples

from_expr("x + 2x^2", None) == Some(poly![0, 1, 2], Some(Var("x")))
from_expr("5", None) == Some(poly![5], None)
from_expr("x + 2x^2", Some(Var("x"))) == Some(poly![0, 1, 2], Some(Var("x")))
from_expr("y + 2y^2", Some(Var("x"))) == None
from_expr("2.5x", None) == None
from_expr("x^{2.5}", None) == None
from_expr("x^{-2}", None) == None

pub fn to_expr(&self, relative_to: RcExpr, span: Span) -> RcExpr

Converts a Poly polynomial, relative to some term, into an expression.

A artificial span the elements of the converted expression are derived from must be provided. In general, span should be the span of an expression previously converted the Poly this method is called on.

Examples

poly![1, 2, 3].to_expr("x") == "3 * (x ^ 2) + 2 * x + 1"

pub fn to_string(&self, var: &str) -> String

Prints the Poly as a polynomial string.

Trait Implementations

impl Clone for Poly

fn clone(&self) -> Poly

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Poly

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Poly

fn default() -> Poly

Returns the "default value" for a type.

impl Eq for Poly

impl<'_> From<&'_ Vec<isize>> for Poly

fn from(v: &Vec<isize>) -> Poly

Performs the conversion.

impl From<Vec<isize>> for Poly

fn from(v: Vec<isize>) -> Poly

Performs the conversion.

impl PartialEq<Poly> for Poly

fn eq(&self, other: &Poly) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Poly) -> bool

This method tests for !=.

impl StructuralEq for Poly

impl StructuralPartialEq for Poly