Flint2-0.1.0.5: Haskell bindings for the flint library for number theory
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Number.Flint.Fmpz.MPoly.Q

Description

An FmpzMPolyQ represents an element of :math:`mathbb{Q}(x_1,ldots,x_n)` for fixed n as a pair of Flint multivariate polynomials (FmpzMPolyQ). Instances are always kept in canonical form by ensuring that the GCD of numerator and denominator is 1 and that the coefficient of the leading term of the denominator is positive.

The user must create a multivariate polynomial context (FmpzMPolyCtx) specifying the number of variables n and the monomial ordering.

Synopsis

Multivariate rational functions over Q

Types

Memory management

fmpz_mpoly_q_init :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_init res ctx

Initializes res for use, and sets its value to zero.

fmpz_mpoly_q_clear :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_clear res ctx

Clears res, freeing or recycling its allocated memory.

Assignment

fmpz_mpoly_q_swap :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_swap x y ctx

Swaps the values of x and y efficiently.

fmpz_mpoly_q_set :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_set res x ctx

Sets res to the value x.

Canonicalisation

fmpz_mpoly_q_canonicalise :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_canonicalise x ctx

Puts the numerator and denominator of x in canonical form by removing common content and making the leading term of the denominator positive.

fmpz_mpoly_q_is_canonical :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_is_canonical x ctx

Returns whether x is in canonical form.

In addition to verifying that the numerator and denominator have no common content and that the leading term of the denominator is positive, this function checks that the denominator is nonzero and that the numerator and denominator have correctly sorted terms (these properties should normally hold; verifying them provides an extra consistency check for test code).

Properties

fmpz_mpoly_q_is_zero :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_is_zero x ctx

Returns whether x is the constant 0.

fmpz_mpoly_q_is_one :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_is_one x ctx

Returns whether x is the constant 1.

fmpz_mpoly_q_used_vars :: Ptr CInt -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_used_vars used f ctx

For each variable, sets the corresponding entry in used to the boolean flag indicating whether that variable appears in the rational function (respectively its numerator or denominator).

Special values

fmpz_mpoly_q_zero :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_zero res ctx

Sets res to the constant 0.

fmpz_mpoly_q_one :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_one res ctx

Sets res to the constant 1.

fmpz_mpoly_q_gen :: Ptr CFmpzMPolyQ -> CLong -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_gen res i ctx

Sets res to the generator \(x_{i+1}\). Requires \(0 \le i < n\) where n is the number of variables of ctx.

Input and output

fmpz_mpoly_q_get_str_pretty :: Ptr CFmpzMPolyQ -> Ptr (Ptr CChar) -> Ptr CFmpzMPolyCtx -> IO CString Source #

fmpz_mpoly_q_get_str_pretty f x ctx

Returns string representation of f. If x is not NULL, the strings in x are used as the symbols for the variables.

fmpz_mpoly_q_fprint_pretty :: Ptr CFile -> Ptr CFmpzMPolyQ -> Ptr (Ptr CChar) -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_fprint_pretty out f x ctx

Prints f to file out. If x is not NULL, the strings in x are used as the symbols for the variables.

fmpz_mpoly_q_print_pretty :: Ptr CFmpzMPolyQ -> Ptr (Ptr CChar) -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_print_pretty f x ctx

Prints f to standard output. If x is not NULL, the strings in x are used as the symbols for the variables.

Random generation

fmpz_mpoly_q_randtest :: Ptr CFmpzMPolyQ -> Ptr CFRandState -> CLong -> CMpLimb -> CLong -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_randtest res state length coeff_bits exp_bound ctx

Sets res to a random rational function where both numerator and denominator have up to length terms, coefficients up to size coeff_bits, and exponents strictly smaller than exp_bound.

Comparisons

fmpz_mpoly_q_equal :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO CInt Source #

fmpz_mpoly_q_equal x y ctx

Returns whether x and y are equal.

Arithmetic

fmpz_mpoly_q_neg :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_neg res x ctx

Sets res to the negation of x.

fmpz_mpoly_q_add :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_add res x y ctx

Sets res to the sum of x and y.

fmpz_mpoly_q_sub :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_sub res x y ctx

Sets res to the difference of x and y.

fmpz_mpoly_q_mul :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_mul res x y ctx

Sets res to the product of x and y.

fmpz_mpoly_q_div :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_div res x y ctx

Sets res to the quotient of x and y. Division by zero calls flint_abort.

fmpz_mpoly_q_inv :: Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyQ -> Ptr CFmpzMPolyCtx -> IO () Source #

fmpz_mpoly_q_inv res x ctx

Sets res to the inverse of x. Division by zero calls flint_abort.

Content

_fmpz_mpoly_q_content :: Ptr CFmpz -> Ptr CFmpz -> Ptr CFmpzMPoly -> Ptr CFmpzMPoly -> Ptr CFmpzMPolyCtx -> IO () Source #

_fmpz_mpoly_q_content num den xnum xden ctx

Sets res to the content of the coefficients of x.