An fmpz_mpoly_q_t represents an element of
\(\mathbb{Q}(x_1,\ldots,x_n)\) for fixed n as a pair of Flint
multivariate polynomials (fmpz_mpoly_t).
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
(fmpz_mpoly_ctx_t) specifying the number of variables n and
the monomial ordering.
An fmpz_mpoly_q_struct consists of a pair of fmpz_mpoly_struct:s. An fmpz_mpoly_q_t is defined as an array of length one of type fmpz_mpoly_q_struct, permitting an fmpz_mpoly_q_t to be passed by reference.
Macro returning a pointer to the numerator of x which can be used as an fmpz_mpoly_t.
Macro returning a pointer to the denominator of x which can be used as an fmpz_mpoly_t.
Initializes res for use, and sets its value to zero.
Clears res, freeing or recycling its allocated memory.
Swaps the values of x and y efficiently.
Sets res to the value x.
Puts the numerator and denominator of x in canonical form by removing common content and making the leading term of the denominator positive.
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).
Returns whether x is the constant 0.
Returns whether x is the constant 1.
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).
Sets res to the constant 0.
Sets res to the constant 1.
Sets res to the generator \(x_{i+1}\). Requires \(0 \le i < n\) where n is the number of variables of ctx.
The variable strings in x start with the variable of most significance at index \(0\). If x is NULL, the variables are named x1, x2, etc.
Prints res to standard output. If x is not NULL, the strings in x are used as the symbols for the variables.
Return a string, which the user is responsible for cleaning up, representing f, given an array of variable strings x.
Set res to the fraction in the null-terminated string str given an array x of variable strings.
If parsing str fails, res is set to zero, and \(-1\) is returned. Otherwise, \(0\) is returned.
The operations +, -, *, and / are permitted along with integers and the variables in x.
The character ^ must be immediately followed by the (integer) exponent.
If division by zero occurs, parsing fails.
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.
Returns whether x and y are equal.
Sets res to the negation of x.
Sets res to the sum of x and y.
Sets res to the difference of x and y.
Sets res to the product of x and y.
Sets res to the quotient of x and y. Division by zero calls flint_abort.
Sets res to the inverse of x. Division by zero calls flint_abort.
Sets res to the content of the coefficients of x.