Data.Number.Flint.Fmpz.Poly.Q

Rational functions over the rational numbers

data FmpzPolyQ

Constructors

FmpzPolyQ !(ForeignPtr CFmpzPolyQ)

Instances

Enum FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

succ :: FmpzPolyQ -> FmpzPolyQ

pred :: FmpzPolyQ -> FmpzPolyQ

toEnum :: Int -> FmpzPolyQ

fromEnum :: FmpzPolyQ -> Int

enumFrom :: FmpzPolyQ -> [FmpzPolyQ]

enumFromThen :: FmpzPolyQ -> FmpzPolyQ -> [FmpzPolyQ]

enumFromTo :: FmpzPolyQ -> FmpzPolyQ -> [FmpzPolyQ]

enumFromThenTo :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ -> [FmpzPolyQ]

Num FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

(+) :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ

(-) :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ

(*) :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ

negate :: FmpzPolyQ -> FmpzPolyQ

abs :: FmpzPolyQ -> FmpzPolyQ

signum :: FmpzPolyQ -> FmpzPolyQ

fromInteger :: Integer -> FmpzPolyQ

Real FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

toRational :: FmpzPolyQ -> Rational

Show FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

showsPrec :: Int -> FmpzPolyQ -> ShowS

show :: FmpzPolyQ -> String

showList :: [FmpzPolyQ] -> ShowS

Eq FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

(==) :: FmpzPolyQ -> FmpzPolyQ -> Bool

(/=) :: FmpzPolyQ -> FmpzPolyQ -> Bool

Ord FmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

compare :: FmpzPolyQ -> FmpzPolyQ -> Ordering

(<) :: FmpzPolyQ -> FmpzPolyQ -> Bool

(<=) :: FmpzPolyQ -> FmpzPolyQ -> Bool

(>) :: FmpzPolyQ -> FmpzPolyQ -> Bool

(>=) :: FmpzPolyQ -> FmpzPolyQ -> Bool

max :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ

min :: FmpzPolyQ -> FmpzPolyQ -> FmpzPolyQ

Quotient FmpzPolyQ FmpzPoly

Defined in Data.Number.Flint.Fmpz.Poly.Q.Instances

Methods

(//) :: FmpzPoly -> FmpzPoly -> FmpzPolyQ

numerator :: FmpzPolyQ -> FmpzPoly

denominator :: FmpzPolyQ -> FmpzPoly

data CFmpzPolyQ

Constructors

CFmpzPolyQ (Ptr CFmpzPoly) (Ptr CFmpzPoly)

Instances

Storable CFmpzPolyQ

Defined in Data.Number.Flint.Fmpz.Poly.Q.FFI

Methods

sizeOf :: CFmpzPolyQ -> Int

alignment :: CFmpzPolyQ -> Int

peekElemOff :: Ptr CFmpzPolyQ -> Int -> IO CFmpzPolyQ

pokeElemOff :: Ptr CFmpzPolyQ -> Int -> CFmpzPolyQ -> IO ()

peekByteOff :: Ptr b -> Int -> IO CFmpzPolyQ

pokeByteOff :: Ptr b -> Int -> CFmpzPolyQ -> IO ()

peek :: Ptr CFmpzPolyQ -> IO CFmpzPolyQ

poke :: Ptr CFmpzPolyQ -> CFmpzPolyQ -> IO ()

newFmpzPolyQ :: IO FmpzPolyQ

withFmpzPolyQ :: FmpzPolyQ -> (Ptr CFmpzPolyQ -> IO a) -> IO (FmpzPolyQ, a)

withNewFmpzPolyQ :: (Ptr CFmpzPolyQ -> IO a) -> IO (FmpzPolyQ, a)

withFmpzPolyQNum :: FmpzPolyQ -> (Ptr CFmpzPoly -> IO t) -> IO (FmpzPolyQ, t)

withFmpzPolyQDen :: FmpzPolyQ -> (Ptr CFmpzPoly -> IO t) -> IO (FmpzPolyQ, t)

Memory management

fmpz_poly_q_init :: Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_init rop

Initialises rop.

fmpz_poly_q_clear :: Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_clear rop

Clears the object rop.

fmpz_poly_q_canonicalise :: Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_canonicalise rop

Brings rop into canonical form, only assuming that the denominator is non-zero.

fmpz_poly_q_is_canonical :: Ptr CFmpzPolyQ -> IO CInt

fmpz_poly_q_is_canonical op

Checks whether the rational function op is in canonical form.

Randomisation

fmpz_poly_q_randtest :: Ptr CFmpzPolyQ -> Ptr CFRandState -> CLong -> CFBitCnt -> CLong -> CFBitCnt -> IO ()

fmpz_poly_q_randtest poly state len1 bits1 len2 bits2

Sets poly to a random rational function.

fmpz_poly_q_randtest_not_zero :: Ptr CFmpzPolyQ -> Ptr CFRandState -> CLong -> CFBitCnt -> CLong -> CFBitCnt -> IO ()

fmpz_poly_q_randtest_not_zero poly state len1 bits1 len2 bits2

Sets poly to a random non-zero rational function.

Assignment

fmpz_poly_q_set :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_set rop op

Sets the element rop to the same value as the element op.

fmpz_poly_q_set_si :: Ptr CFmpzPolyQ -> CLong -> IO ()

fmpz_poly_q_set_si rop op

Sets the element rop to the value given by the slong op.

fmpz_poly_q_swap :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_swap op1 op2

Swaps the elements op1 and op2.

This is done efficiently by swapping pointers.

fmpz_poly_q_zero :: Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_zero rop

Sets rop to zero.

fmpz_poly_q_one :: Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_one rop

Sets rop to one.

fmpz_poly_q_neg :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_neg rop op

Sets the element rop to the additive inverse of op.

fmpz_poly_q_inv :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_inv rop op

Sets the element rop to the multiplicative inverse of op.

Assumes that the element op is non-zero.

Comparison

fmpz_poly_q_is_zero :: Ptr CFmpzPolyQ -> IO CInt

fmpz_poly_q_is_zero op

Returns whether the element op is zero.

fmpz_poly_q_is_one :: Ptr CFmpzPolyQ -> IO CInt

fmpz_poly_q_is_one op

Returns whether the element rop is equal to the constant polynomial \(1\).

fmpz_poly_q_equal :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO CInt

fmpz_poly_q_equal op1 op2

Returns whether the two elements op1 and op2 are equal.

Addition and subtraction

fmpz_poly_q_add :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_add rop op1 op2

Sets rop to the sum of op1 and op2.

fmpz_poly_q_sub :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_sub rop op1 op2

Sets rop to the difference of op1 and op2.

fmpz_poly_q_addmul :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_addmul rop op1 op2

Adds the product of op1 and op2 to rop.

fmpz_poly_q_submul :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_submul rop op1 op2

Subtracts the product of op1 and op2 from rop.

Scalar multiplication and division

fmpz_poly_q_scalar_mul_si :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> CLong -> IO ()

fmpz_poly_q_scalar_mul_si rop op x

Sets rop to the product of the rational function op and the slong integer \(x\).

fmpz_poly_q_scalar_mul_fmpz :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpz -> IO ()

fmpz_poly_q_scalar_mul_fmpz rop op x

Sets rop to the product of the rational function op and the fmpz_t integer \(x\).

fmpz_poly_q_scalar_mul_fmpq :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpq -> IO ()

fmpz_poly_q_scalar_mul_fmpq rop op x

Sets rop to the product of the rational function op and the fmpq_t rational \(x\).

fmpz_poly_q_scalar_div_si :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> CLong -> IO ()

fmpz_poly_q_scalar_div_si rop op x

Sets rop to the quotient of the rational function op and the slong integer \(x\).

fmpz_poly_q_scalar_div_fmpz :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpz -> IO ()

fmpz_poly_q_scalar_div_fmpz rop op x

Sets rop to the quotient of the rational function op and the fmpz_t integer \(x\).

fmpz_poly_q_scalar_div_fmpq :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpq -> IO ()

fmpz_poly_q_scalar_div_fmpq rop op x

Sets rop to the quotient of the rational function op and the fmpq_t rational \(x\).

Multiplication and division

fmpz_poly_q_mul :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_mul rop op1 op2

Sets rop to the product of op1 and op2.

fmpz_poly_q_div :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_div rop op1 op2

Sets rop to the quotient of op1 and op2.

Powering

fmpz_poly_q_pow :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> CULong -> IO ()

fmpz_poly_q_pow rop op exp

Sets rop to the exp-th power of op.

The corner case of exp == 0 is handled by setting rop to the constant function \(1\). Note that this includes the case \(0^0 = 1\).

Derivative

fmpz_poly_q_derivative :: Ptr CFmpzPolyQ -> Ptr CFmpzPolyQ -> IO ()

fmpz_poly_q_derivative rop op

Sets rop to the derivative of op.

Evaluation

fmpz_poly_q_evaluate_fmpq :: Ptr CFmpq -> Ptr CFmpzPolyQ -> Ptr CFmpq -> IO CInt

fmpz_poly_q_evaluate_fmpq rop f a

Sets rop to \(f\) evaluated at the rational \(a\).

If the denominator evaluates to zero at \(a\), returns non-zero and does not modify any of the variables. Otherwise, returns \(0\) and sets rop to the rational \(f(a)\).

Input and output

fmpz_poly_q_set_str :: Ptr CFmpzPolyQ -> CString -> IO CInt

fmpz_poly_q_set_str rop s

Sets rop to the rational function given by the string s. The following three methods enable users to construct elements of type fmpz_poly_q_t from strings or to obtain string representations of such elements. The format used is based on the FLINT format for integer polynomials of type fmpz_poly_t, which we recall first: A non-zero polynomial \(a_0 + a_1 X + \dotsb + a_n X^n\) of length n + 1 is represented by the string "n+1 a_0 a_1 ... a_n", where there are two space characters following the length and single space characters separating the individual coefficients. There is no leading or trailing white-space. The zero polynomial is simply represented by "0". We adapt this notation for rational functions as follows. We denote the zero function by "0". Given a non-zero function with numerator and denominator string representations num and den, respectively, we use the string num/den to represent the rational function, unless the denominator is equal to one, in which case we simply use num. There is also a _pretty variant available, which bases the string parts for the numerator and denominator on the output of the function fmpz_poly_get_str_pretty and introduces parentheses where necessary. Note that currently these functions are not optimised for performance and are intended to be used only for debugging purposes or one-off input and output, rather than as a low-level parser.

fmpz_poly_q_get_str :: Ptr CFmpzPolyQ -> IO CString

fmpz_poly_q_get_str op

Returns the string representation of the rational function op.

fmpz_poly_q_get_str_pretty :: Ptr CFmpzPolyQ -> CString -> IO CString

fmpz_poly_q_get_str_pretty op x

Returns the pretty string representation of the rational function op.

fmpz_poly_q_print :: Ptr CFmpzPolyQ -> IO CInt

fmpz_poly_q_print op

Prints the representation of the rational function op to stdout.

fmpz_poly_q_print_pretty :: Ptr CFmpzPolyQ -> CString -> IO CInt

fmpz_poly_q_print_pretty op x

Prints the pretty representation of the rational function op to stdout.