RationalPolynomial

`RationalPolynomial`

RationalPolynomial()

A Symbolica rational polynomial.

Methods

Name	Description
`__add__`	Add two rational polynomials `self` and `rhs`, returning the result.
`__copy__`	Copy the rational polynomial.
`__eq__`	Check if two rational polynomials are equal.
`__floordiv__`	Divide the polynomial `self` by `rhs`, rounding down, returning the result.
`__ge__`	Check if the polynomial is greater than or equal to an integer.
`__gt__`	Check if the rational polynomial is greater than an integer.
`__le__`	Check if the rational polynomial is less than or equal to an integer.
`__lt__`	Check if the rational polynomial is less than an integer.
`__mul__`	Multiply two rational polynomials `self` and `rhs`, returning the result.
`__ne__`	Check if two rational polynomials are not equal.
`__neg__`	Negate the rational polynomial.
`__new__`	Create a new rational polynomial from a numerator and denominator polynomial.
`__str__`	Print the rational polynomial in a human-readable format.
`__sub__`	Subtract rational polynomials `rhs` from `self`, returning the result.
`__truediv__`	Divide the rational polynomial `self` by `rhs` if possible, returning the result.
`apart`	Compute the partial fraction decomposition in `x`
`denominator`	Get the denominator.
`derivative`	Take a derivative in `x`.
`gcd`	Compute the greatest common divisor (GCD) of two rational polynomials.
`get_variables`	Get the list of variables in the internal ordering of the polynomial.
`numerator`	Get the numerator.
`parse`	Parse a rational polynomial from a string
`to_expression`	Convert the polynomial to an expression.
`to_finite_field`	Convert the coefficients of the rational polynomial to a finite field with prime `prime`.
`to_latex`	Convert the rational polynomial into a LaTeX string.

`add`

RationalPolynomial.__add__(rhs: RationalPolynomial) -> RationalPolynomial

Add two rational polynomials self and rhs, returning the result.

`copy`

RationalPolynomial.__copy__() -> RationalPolynomial

Copy the rational polynomial.

`eq`

RationalPolynomial.__eq__(rhs: Polynomial | int) -> bool

Check if two rational polynomials are equal.

`floordiv`

RationalPolynomial.__floordiv__(rhs: Polynomial) -> Polynomial

Divide the polynomial self by rhs, rounding down, returning the result.

`ge`

RationalPolynomial.__ge__(rhs: int) -> bool

Check if the polynomial is greater than or equal to an integer.

`gt`

RationalPolynomial.__gt__(rhs: int) -> bool

Check if the rational polynomial is greater than an integer.

`le`

RationalPolynomial.__le__(rhs: int) -> bool

Check if the rational polynomial is less than or equal to an integer.

`lt`

RationalPolynomial.__lt__(rhs: int) -> bool

Check if the rational polynomial is less than an integer.

`mul`

RationalPolynomial.__mul__(rhs: RationalPolynomial) -> RationalPolynomial

Multiply two rational polynomials self and rhs, returning the result.

`ne`

RationalPolynomial.__ne__(rhs: Polynomial | int) -> bool

Check if two rational polynomials are not equal.

`neg`

RationalPolynomial.__neg__() -> RationalPolynomial

Negate the rational polynomial.

`new`

RationalPolynomial.__new__(num: Polynomial, den: Polynomial) -> RationalPolynomial

Create a new rational polynomial from a numerator and denominator polynomial.

`str`

RationalPolynomial.__str__() -> str

Print the rational polynomial in a human-readable format.

`sub`

RationalPolynomial.__sub__(rhs: RationalPolynomial) -> RationalPolynomial

Subtract rational polynomials rhs from self, returning the result.

`truediv`

RationalPolynomial.__truediv__(rhs: RationalPolynomial) -> RationalPolynomial

Divide the rational polynomial self by rhs if possible, returning the result.

`apart`

RationalPolynomial.apart(x: Optional[Expression] = None) -> List[RationalPolynomial]

Compute the partial fraction decomposition in x.

If None is passed, the expression will be decomposed in all variables which involves a potentially expensive Groebner basis computation.

Examples

from symbolica import *
x = S('x')
p = E('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
for pp in p.apart(x):
    print(pp)

`denominator`

RationalPolynomial.denominator() -> Polynomial

Get the denominator.

`derivative`

RationalPolynomial.derivative(x: Expression) -> RationalPolynomial

Take a derivative in x.

Examples

from symbolica import *
x = S('x')
p = E('1/((x+y)*(x^2+x*y+1)(x+1))').to_rational_polynomial()
print(p.derivative(x))

`gcd`

RationalPolynomial.gcd(rhs: RationalPolynomial) -> RationalPolynomial

Compute the greatest common divisor (GCD) of two rational polynomials.

`get_variables`

RationalPolynomial.get_variables() -> Sequence[Expression]

Get the list of variables in the internal ordering of the polynomial.

`numerator`

RationalPolynomial.numerator() -> Polynomial

Get the numerator.

`parse`

RationalPolynomial.parse(
    input: str,
    vars: Sequence[str],
    default_namespace: str | None = None,
) -> RationalPolynomial

Parse a rational polynomial from a string. The list of all the variables must be provided.

If this requirements is too strict, use Expression.to_polynomial() instead.

Examples

e = RationalPolynomial.parse('(3/4*x^2+y+y*4)/(1+x)', ['x', 'y'])

Raises

ValueError: If the input is not a valid Symbolica rational polynomial.

`to_expression`

RationalPolynomial.to_expression() -> Expression

Convert the polynomial to an expression.

Examples

from symbolica import *
e = E('(x*y+2*x+x^2)/(x^7+y+1)')
p = e.to_polynomial()
print((e - p.to_expression()).expand())

`to_finite_field`

RationalPolynomial.to_finite_field(prime: int) -> FiniteFieldRationalPolynomial

Convert the coefficients of the rational polynomial to a finite field with prime prime.

`to_latex`

RationalPolynomial.to_latex() -> str

Convert the rational polynomial into a LaTeX string.