fmpz_poly_q.h

Brings rop into canonical form by dividing the numerator and the denominator by their gcd in $\mathbb{Z}[x]$ and making the leading coefficient of the denominator positive. The denominator must be nonzero; a zero denominator causes an exception (FLINT_ERROR).

Returns whether op is in canonical form.

Initialises rop as the zero function $0/1$, allocating its numerator and denominator.

Frees the memory used by rop.

Sets rop to op.

Sets rop to the constant function op.

Swaps op1 and op2 efficiently, by exchanging the pointers to the numerators and the denominators.

Set rop to 0 or 1.

Sets rop to $-\mathit{op}$.

Sets rop to $1/\mathit{op}$, by exchanging numerator and denominator and fixing the sign. Raises an exception (FLINT_ERROR) if op is zero.

Set poly to a random rational function, the canonical form of $a/b$ with $a$ a random polynomial of length at most len1 and coefficients of at most bits1 bits (fmpz_poly_randtest) and $b$ a random nonzero polynomial of length at most len2 and at most bits2 bits. In the _not_zero version $a$ is nonzero as well. Lengths and bit sizes less than 1 are replaced by 1 where a nonzero polynomial is needed.

Return whether op is 0, respectively 1.

Returns whether op1 and op2 are equal. Since the canonical form is unique, this compares numerators and denominators.

Set rop to $\mathit{op1} + \mathit{op2}$, respectively $\mathit{op1} - \mathit{op2}$, by Henrici's algorithm: with $g$ the gcd of the denominators, only $\gcd(\text{numerator}, g)$ has to be cancelled.

Set rop to $\mathit{rop} + \mathit{op}$, respectively $\mathit{rop} - \mathit{op}$. fmpz_poly_q_add and fmpz_poly_q_sub call these when the output is aliased with the first input.

Set rop to $\mathit{rop} + \mathit{op1} \cdot \mathit{op2}$, respectively $\mathit{rop} - \mathit{op1} \cdot \mathit{op2}$, using a temporary for the product.

Set rop to $x \cdot \mathit{op}$.

Set rop to $\mathit{op} / x$. A zero $x$ raises an exception (FLINT_DIVZERO).

Sets rop to $\mathit{op1} \cdot \mathit{op2}$. Writing $\mathit{op1} = a/b$ and $\mathit{op2} = c/d$, Henrici's algorithm cancels $\gcd(a, d)$ and $\gcd(c, b)$ before multiplying, which gives the canonical result directly.

Sets rop to $\mathit{op1} / \mathit{op2}$, computed like the product with $\mathit{op2}$ inverted. A zero op2 raises an exception (FLINT_DIVZERO).

Sets rop to $\mathit{op}^{\mathit{exp}}$, by raising the numerator and the denominator to the power exp. For exp = 0 the result is 1, also when op is zero.

Sets rop to the derivative of op.

If the denominator of f does not vanish at the rational number $a$, sets rop to $f(a)$ and returns 0. Otherwise returns a nonzero value and leaves rop unchanged.

Sets rop to the rational function described by s, in the format above, and canonicalises it. Returns 0 on success and a nonzero value if s is not valid, in which case the value of rop is unspecified. A denominator string that describes the zero polynomial raises an exception.

Return the string representation of op, in the plain format or in the pretty format with the variable name x. The string is allocated with flint_malloc and must be freed with flint_free.

Print the plain or the pretty representation of op to standard output, and return 1.