Data.Number.Flint.Fmpq.MPoly

Multivariate polynomials over the rational numbers

data FmpqMPoly

Constructors

FmpqMPoly !(ForeignPtr CFmpqMPoly)

data CFmpqMPoly

Constructors

CFmpqMPoly (Ptr CFmpq) CFmpzMPoly

Instances

Storable CFmpqMPoly

Defined in Data.Number.Flint.Fmpq.MPoly.FFI

Methods

sizeOf :: CFmpqMPoly -> Int

alignment :: CFmpqMPoly -> Int

peekElemOff :: Ptr CFmpqMPoly -> Int -> IO CFmpqMPoly

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

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

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

peek :: Ptr CFmpqMPoly -> IO CFmpqMPoly

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

newFmpqMPoly :: FmpqMPolyCtx -> IO FmpqMPoly

withFmpqMPoly :: FmpqMPoly -> (Ptr CFmpqMPoly -> IO a) -> IO (FmpqMPoly, a)

Context object

data FmpqMPolyCtx

Constructors

FmpqMPolyCtx !(ForeignPtr CFmpqMPolyCtx)

data CFmpqMPolyCtx

Instances

Storable CFmpqMPolyCtx

Defined in Data.Number.Flint.Fmpq.MPoly.FFI

Methods

sizeOf :: CFmpqMPolyCtx -> Int

alignment :: CFmpqMPolyCtx -> Int

peekElemOff :: Ptr CFmpqMPolyCtx -> Int -> IO CFmpqMPolyCtx

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

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

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

peek :: Ptr CFmpqMPolyCtx -> IO CFmpqMPolyCtx

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

newFmpqMPolyCtx :: CLong -> Ptr COrdering -> IO FmpqMPolyCtx

Create a new FmpqMPolyCtx

withFmpqMPolyCtx :: FmpqMPolyCtx -> (Ptr CFmpqMPolyCtx -> IO a) -> IO (FmpqMPolyCtx, a)

Use a FmpqMPolyCtx

fmpq_mpoly_ctx_init :: Ptr CFmpqMPolyCtx -> CLong -> Ptr COrdering -> IO ()

fmpq_mpoly_ctx_init ctx nvars ord

Initialise a context object for a polynomial ring with the given number of variables and the given ordering. The possibilities for the ordering are ORD_LEX, ORD_DEGLEX and ORD_DEGREVLEX.

fmpq_mpoly_ctx_nvars :: Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_ctx_nvars ctx

Return the number of variables used to initialize the context.

fmpq_mpoly_ctx_ord :: Ptr CFmpqMPolyCtx -> IO (Ptr COrdering)

fmpq_mpoly_ctx_ord ctx

Return the ordering used to initialize the context.

fmpq_mpoly_ctx_clear :: Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_ctx_clear ctx

Release up any space allocated by ctx.

Memory management

fmpq_mpoly_init :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_init A ctx

Initialise A for use with the given and initialised context object. Its value is set to zero.

fmpq_mpoly_init2 :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_init2 A alloc ctx

Initialise A for use with the given and initialised context object. Its value is set to zero. It is allocated with space for alloc terms and at least MPOLY_MIN_BITS bits for the exponents.

fmpq_mpoly_init3 :: Ptr CFmpqMPoly -> CLong -> CFBitCnt -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_init3 A alloc bits ctx

Initialise A for use with the given and initialised context object. Its value is set to zero. It is allocated with space for alloc terms and bits bits for the exponents.

fmpq_mpoly_fit_length :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_fit_length A len ctx

Ensure that A has space for at least len terms.

fmpq_mpoly_fit_bits :: Ptr CFmpqMPoly -> CFBitCnt -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_fit_bits A bits ctx

Ensure that the exponent fields of A have at least bits bits.

fmpq_mpoly_realloc :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_realloc A alloc ctx

Reallocate A to have space for alloc terms. Assumes the current length of the polynomial is not greater than alloc.

fmpq_mpoly_clear :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_clear A ctx

Release any space allocated for A.

Input/Output

fmpq_mpoly_get_str_pretty :: Ptr CFmpqMPoly -> Ptr (Ptr CChar) -> Ptr CFmpqMPolyCtx -> IO CString

fmpq_mpoly_get_str_pretty A x ctx

Return a string, which the user is responsible for cleaning up, representing A, given an array of variable strings x.

fmpq_mpoly_fprint_pretty :: Ptr CFile -> Ptr CFmpqMPoly -> Ptr (Ptr CChar) -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_fprint_pretty file A x ctx

Print a string representing A to file.

fmpq_mpoly_print_pretty :: Ptr CFmpqMPoly -> Ptr (Ptr CChar) -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_print_pretty A x ctx

Print a string representing A to stdout. foreign import ccall "fmpq_mpoly.h fmpq_mpoly_print_pretty"

fmpq_mpoly_set_str_pretty :: Ptr CFmpqMPoly -> CString -> Ptr (Ptr CChar) -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_set_str_pretty A str x ctx

Set A to the polynomial in the null-terminates string str given an array x of variable strings. If parsing str fails, A 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 any division is not exact, parsing fails.

Basic manipulation

fmpq_mpoly_gen :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_gen A var ctx

Set A to the variable of index var, where var = 0 corresponds to the variable with the most significance with respect to the ordering.

fmpq_mpoly_is_gen :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_gen A var ctx

If \(var \ge 0\), return \(1\) if A is equal to the \(var\)-th generator, otherwise return \(0\). If \(var < 0\), return \(1\) if the polynomial is equal to any generator, otherwise return \(0\).

fmpq_mpoly_set :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set A B ctx

Set A to B.

fmpq_mpoly_equal :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_equal A B ctx

Return \(1\) if A is equal to B, else return \(0\).

fmpq_mpoly_swap :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_swap A B ctx

Efficiently swap A and B.

Constants

fmpq_mpoly_is_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_fmpq A ctx

Return \(1\) if A is a constant, else return \(0\).

fmpq_mpoly_get_fmpq :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_fmpq c A ctx

Assuming that A is a constant, set c to this constant. This function throws if A is not a constant.

fmpq_mpoly_set_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_fmpq A c ctx

fmpq_mpoly_set_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_fmpz A c ctx

fmpq_mpoly_set_ui :: Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_ui A c ctx

fmpq_mpoly_set_si :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_si A c ctx

Set A to the constant c.

fmpq_mpoly_zero :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_zero A ctx

Set A to the constant \(0\).

fmpq_mpoly_one :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_one A ctx

Set A to the constant \(1\).

fmpq_mpoly_equal_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_equal_fmpq A c ctx

fmpq_mpoly_equal_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_equal_fmpz A c ctx

fmpq_mpoly_equal_ui :: Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_equal_ui A c ctx

fmpq_mpoly_equal_si :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_equal_si A c ctx

Return \(1\) if A is equal to the constant c, else return \(0\).

fmpq_mpoly_is_zero :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_zero A ctx

Return \(1\) if A is equal to the constant \(0\), else return \(0\).

fmpq_mpoly_is_one :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_one A ctx

Return \(1\) if A is equal to the constant \(1\), else return \(0\).

Degrees

fmpq_mpoly_degrees_fit_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_degrees_fit_si A ctx

Return \(1\) if the degrees of A with respect to each variable fit into an slong, otherwise return \(0\).

fmpq_mpoly_degrees_fmpz :: Ptr (Ptr CFmpz) -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_degrees_fmpz degs A ctx

fmpq_mpoly_degrees_si :: Ptr CLong -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_degrees_si degs A ctx

Set degs to the degrees of A with respect to each variable. If A is zero, all degrees are set to \(-1\).

fmpq_mpoly_degree_fmpz :: Ptr CFmpz -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_degree_fmpz deg A var ctx

fmpq_mpoly_degree_si :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_degree_si A var ctx

Either return or set deg to the degree of A with respect to the variable of index var. If A is zero, the degree is defined to be \(-1\).

fmpq_mpoly_total_degree_fits_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_total_degree_fits_si A ctx

Return \(1\) if the total degree of A fits into an slong, otherwise return \(0\).

fmpq_mpoly_total_degree_fmpz :: Ptr CFmpz -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_total_degree_fmpz tdeg A ctx

fmpq_mpoly_total_degree_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_total_degree_si A ctx

Either return or set tdeg to the total degree of A. If A is zero, the total degree is defined to be \(-1\).

fmpq_mpoly_used_vars :: Ptr CInt -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_used_vars used A ctx

For each variable index i, set used[i] to nonzero if the variable of index i appears in A and to zero otherwise.

Coefficients

fmpq_mpoly_get_denominator :: Ptr CFmpz -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_denominator d A ctx

Set d to the denominator of A, the smallest positive integer \(d\) such that \(d \times A\) has integer coefficients.

fmpq_mpoly_get_coeff_fmpq_monomial :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_coeff_fmpq_monomial c A M ctx

Assuming that M is a monomial, set c to the coefficient of the corresponding monomial in A. This function throws if M is not a monomial.

fmpq_mpoly_set_coeff_fmpq_monomial :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_coeff_fmpq_monomial A c M ctx

Assuming that M is a monomial, set the coefficient of the corresponding monomial in A to c. This function throws if M is not a monomial.

fmpq_mpoly_get_coeff_fmpq_fmpz :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_coeff_fmpq_fmpz c A exp ctx

fmpq_mpoly_get_coeff_fmpq_ui :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_coeff_fmpq_ui c A exp ctx

Set c to the coefficient of the monomial with exponent exp.

fmpq_mpoly_set_coeff_fmpq_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_coeff_fmpq_fmpz A c exp ctx

fmpq_mpoly_set_coeff_fmpq_ui :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_coeff_fmpq_ui A c exp ctx

Set the coefficient of the monomial with exponent exp to c.

fmpq_mpoly_get_coeff_vars_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CLong -> Ptr CULong -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_coeff_vars_ui C A vars exps length ctx

Set C to the coefficient of A with respect to the variables in vars with powers in the corresponding array exps. Both vars and exps point to array of length length. It is assumed that \(0 < length \le nvars(A)\) and that the variables in vars are distinct.

Comparison

fmpq_mpoly_cmp :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_cmp A B ctx

Return \(1\) (resp. \(-1\), or \(0\)) if A is after (resp. before, same as) B in some arbitrary but fixed total ordering of the polynomials. This ordering agrees with the usual ordering of monomials when A and B are both monomials.

Container operations

fmpq_mpoly_content_ref :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO (Ptr CFmpq)

fmpq_mpoly_content_ref A ctx

Return a reference to the content of A.

fmpq_mpoly_zpoly_ref :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO (Ptr (Ptr CFmpzMPoly))

fmpq_mpoly_zpoly_ref A ctx

Return a reference to the integer polynomial of A.

fmpq_mpoly_zpoly_term_coeff_ref :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO (Ptr CFmpz)

fmpq_mpoly_zpoly_term_coeff_ref A i ctx

Return a reference to the coefficient of index i of the integer polynomial of A.

fmpq_mpoly_is_canonical :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_canonical A ctx

Return \(1\) if A is in canonical form. Otherwise, return \(0\). An fmpq_mpoly_t is represented as the product of an fmpq_t content and an fmpz_mpoly_t zpoly. The representation is considered canonical when either (1) both content and zpoly are zero, or (2) both content and zpoly are nonzero and canonical and zpoly is reduced. A nonzero zpoly is considered reduced when the coefficients have GCD one and the leading coefficient is positive.

fmpq_mpoly_length :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_length A ctx

Return the number of terms stored in A. If the polynomial is in canonical form, this will be the number of nonzero coefficients.

fmpq_mpoly_resize :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_resize A new_length ctx

Set the length of A to new_length. Terms are either deleted from the end, or new zero terms are appended.

fmpq_mpoly_get_term_coeff_fmpq :: Ptr CFmpq -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term_coeff_fmpq c A i ctx

Set c to coefficient of index i

fmpq_mpoly_set_term_coeff_fmpq :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_term_coeff_fmpq A i c ctx

Set the coefficient of index i to c.

fmpq_mpoly_term_exp_fits_si :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_term_exp_fits_si A i ctx

fmpq_mpoly_term_exp_fits_ui :: Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_term_exp_fits_ui A i ctx

Return \(1\) if all entries of the exponent vector of the term of index i fit into an slong (resp. a ulong). Otherwise, return \(0\).

fmpq_mpoly_get_term_exp_fmpz :: Ptr (Ptr CFmpz) -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term_exp_fmpz exps A i ctx

fmpq_mpoly_get_term_exp_ui :: Ptr CULong -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term_exp_ui exps A i ctx

fmpq_mpoly_get_term_exp_si :: Ptr CLong -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term_exp_si exps A i ctx

Set exp to the exponent vector of the term of index i. The _ui (resp. _si) version throws if any entry does not fit into a ulong (resp. slong).

fmpq_mpoly_get_term_var_exp_ui :: Ptr CFmpqMPoly -> CLong -> CLong -> Ptr CFmpqMPolyCtx -> IO CULong

fmpq_mpoly_get_term_var_exp_ui A i var ctx

fmpq_mpoly_get_term_var_exp_si :: Ptr CFmpqMPoly -> CLong -> CLong -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_get_term_var_exp_si A i var ctx

Return the exponent of the variable var of the term of index i. This function throws if the exponent does not fit into a ulong (resp. slong).

fmpq_mpoly_set_term_exp_fmpz :: Ptr CFmpqMPoly -> CLong -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_term_exp_fmpz A i exps ctx

fmpq_mpoly_set_term_exp_ui :: Ptr CFmpqMPoly -> CLong -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_set_term_exp_ui A i exps ctx

Set the exponent vector of the term of index i to exp.

fmpq_mpoly_get_term :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term M A i ctx

Set M to the term of index i in A.

fmpq_mpoly_get_term_monomial :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_get_term_monomial M A i ctx

Set M to the monomial of the term of index i in A. The coefficient of M will be one.

fmpq_mpoly_push_term_fmpq_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_fmpq_fmpz A c exp ctx

fmpq_mpoly_push_term_fmpz_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_fmpz_fmpz A c exp ctx

fmpq_mpoly_push_term_ui_fmpz :: Ptr CFmpqMPoly -> CULong -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_ui_fmpz A c exp ctx

fmpq_mpoly_push_term_si_fmpz :: Ptr CFmpqMPoly -> CLong -> Ptr (Ptr CFmpz) -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_si_fmpz A c exp ctx

fmpq_mpoly_push_term_fmpq_ui :: Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_fmpq_ui A c exp ctx

fmpq_mpoly_push_term_fmpz_ui :: Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_fmpz_ui A c exp ctx

fmpq_mpoly_push_term_ui_ui :: Ptr CFmpqMPoly -> CULong -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_ui_ui A c exp ctx

fmpq_mpoly_push_term_si_ui :: Ptr CFmpqMPoly -> CLong -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_push_term_si_ui A c exp ctx

Append a term to A with coefficient c and exponent vector exp. This function should run in constant average time if the terms pushed have bounded denominator.

fmpq_mpoly_reduce :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_reduce A ctx

Factor out necessary content from A->zpoly so that it is reduced. If the terms of A were nonzero and sorted with distinct exponents to begin with, the result will be in canonical form.

fmpq_mpoly_sort_terms :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sort_terms A ctx

Sort the internal A->zpoly into the canonical ordering dictated by the ordering in ctx. This function does not combine like terms, nor does it delete terms with coefficient zero, nor does it reduce.

fmpq_mpoly_combine_like_terms :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_combine_like_terms A ctx

Combine adjacent like terms in the internal A->zpoly and then factor out content via a call to fmpq_mpoly_reduce. If the terms of A were sorted to begin with, the result will be in canonical form.

Random generation

fmpq_mpoly_randtest_bound :: Ptr CFmpqMPoly -> Ptr CFRandState -> CLong -> CMpLimb -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_randtest_bound A state length coeff_bits exp_bound ctx

Generate a random polynomial with length up to length and exponents in the range [0, exp_bound - 1]. The exponents of each variable are generated by calls to n_randint(state, exp_bound).

fmpq_mpoly_randtest_bounds :: Ptr CFmpqMPoly -> Ptr CFRandState -> CLong -> CMpLimb -> Ptr CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_randtest_bounds A state length coeff_bits exp_bounds ctx

Generate a random polynomial with length up to length and exponents in the range [0, exp_bounds[i] - 1]. The exponents of the variable of index i are generated by calls to n_randint(state, exp_bounds[i]).

fmpq_mpoly_randtest_bits :: Ptr CFmpqMPoly -> Ptr CFRandState -> CLong -> CMpLimb -> CMpLimb -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_randtest_bits A state length coeff_bits exp_bits ctx

Generate a random polynomial with length up to length and exponents whose packed form does not exceed the given bit count.

The parameter coeff_bits to the three functions fmpq_mpoly_randtest_{bound|bounds|bits} is merely a suggestion for the approximate bit count of the resulting coefficients.

Addition/Subtraction

fmpq_mpoly_add_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_add_fmpq A B c ctx

fmpq_mpoly_add_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_add_fmpz A B c ctx

fmpq_mpoly_add_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_add_ui A B c ctx

fmpq_mpoly_add_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_add_si A B c ctx

Set A to \(B + c\).

fmpq_mpoly_sub_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sub_fmpq A B c ctx

fmpq_mpoly_sub_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sub_fmpz A B c ctx

fmpq_mpoly_sub_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sub_ui A B c ctx

fmpq_mpoly_sub_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sub_si A B c ctx

Set A to \(B - c\).

fmpq_mpoly_add :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_add A B C ctx

Set A to \(B + C\).

fmpq_mpoly_sub :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_sub A B C ctx

Set A to \(B - C\).

Scalar operations

fmpq_mpoly_neg :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_neg A B ctx

Set A to \(-B\).

fmpq_mpoly_scalar_mul_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_mul_fmpq A B c ctx

fmpq_mpoly_scalar_mul_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_mul_fmpz A B c ctx

fmpq_mpoly_scalar_mul_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_mul_ui A B c ctx

fmpq_mpoly_scalar_mul_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_mul_si A B c ctx

Set A to \(B \times c\).

fmpq_mpoly_scalar_div_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_div_fmpq A B c ctx

fmpq_mpoly_scalar_div_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_div_fmpz A B c ctx

fmpq_mpoly_scalar_div_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_div_ui A B c ctx

fmpq_mpoly_scalar_div_si :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_scalar_div_si A B c ctx

Set A to \(B/c\).

fmpq_mpoly_make_monic :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_make_monic A B ctx

Set A to B divided by the leading coefficient of B. This throws if B is zero.

All of these functions run quickly if A and B are aliased.

Differentiation/Integration

fmpq_mpoly_derivative :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_derivative A B var ctx

Set A to the derivative of B with respect to the variable of index var.

fmpq_mpoly_integral :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_integral A B var ctx

Set A to the integral with the fewest number of terms of B with respect to the variable of index var.

Evaluation

fmpq_mpoly_evaluate_all_fmpq :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr (Ptr CFmpq) -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_evaluate_all_fmpq ev A vals ctx

Set ev to the evaluation of A where the variables are replaced by the corresponding elements of the array vals. Return \(1\) for success and \(0\) for failure.

fmpq_mpoly_evaluate_one_fmpq :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpq -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_evaluate_one_fmpq A B var val ctx

Set A to the evaluation of B where the variable of index var is replaced by val. Return \(1\) for success and \(0\) for failure.

fmpq_mpoly_compose_fmpq_poly :: Ptr CFmpqPoly -> Ptr CFmpqMPoly -> Ptr (Ptr (Ptr (Ptr CFmpqPoly))) -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_compose_fmpq_poly A B C ctxB

Set A to the evaluation of B where the variables are replaced by the corresponding elements of the array C. The context object of B is ctxB. Return \(1\) for success and \(0\) for failure.

fmpq_mpoly_compose_fmpq_mpoly :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr (Ptr (Ptr CFmpqMPoly)) -> Ptr CFmpqMPolyCtx -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_compose_fmpq_mpoly A B C ctxB ctxAC

Set A to the evaluation of B where the variables are replaced by the corresponding elements of the array C. Both A and the elements of C have context object ctxAC, while B has context object ctxB. Neither A nor B is allowed to alias any other polynomial. Return \(1\) for success and \(0\) for failure.

fmpq_mpoly_compose_fmpq_mpoly_gen :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CLong -> Ptr CFmpqMPolyCtx -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_compose_fmpq_mpoly_gen A B c ctxB ctxAC

Set A to the evaluation of B where the variable of index i in ctxB is replaced by the variable of index c[i] in ctxAC. The length of the array C is the number of variables in ctxB. If any c[i] is negative, the corresponding variable of B is replaced by zero. Otherwise, it is expected that c[i] is less than the number of variables in ctxAC.

Multiplication

fmpq_mpoly_mul :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_mul A B C ctx

Set A to \(B \times C\).

Powering

fmpq_mpoly_pow_fmpz :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpz -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_pow_fmpz A B k ctx

Set A to B raised to the k-th power. Return \(1\) for success and \(0\) for failure.

fmpq_mpoly_pow_ui :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CULong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_pow_ui A B k ctx

Set A to B raised to the k-th power. Return \(1\) for success and \(0\) for failure.

Division

fmpq_mpoly_divides :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_divides Q A B ctx

If A is divisible by B, set Q to the exact quotient and return \(1\). Otherwise, set Q to zero and return \(0\). Note that the function fmpq_mpoly_div may be faster if the quotient is known to be exact.

fmpq_mpoly_div :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_div Q A B ctx

Set Q to the quotient of A by B, discarding the remainder.

fmpq_mpoly_divrem :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_divrem Q R A B ctx

Set Q and R to the quotient and remainder of A divided by B.

fmpq_mpoly_divrem_ideal :: Ptr (Ptr (Ptr CFmpqMPoly)) -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr (Ptr (Ptr CFmpqMPoly)) -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_divrem_ideal Q R A B len ctx

This function is as per fmpq_mpoly_divrem except that it takes an array of divisor polynomials B and it returns an array of quotient polynomials Q. The number of divisor (and hence quotient) polynomials is given by len.

Greatest Common Divisor

fmpq_mpoly_content :: Ptr CFmpq -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_content g A ctx

Set g to the (nonnegative) gcd of the coefficients of A.

fmpq_mpoly_term_content :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_term_content M A ctx

Set M to the GCD of the terms of A. If A is zero, M will be zero. Otherwise, M will be a monomial with coefficient one.

fmpq_mpoly_content_vars :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CLong -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_content_vars g A vars vars_length ctx

Set g to the GCD of the coefficients of A when viewed as a polynomial in the variables vars. Return \(1\) for success and \(0\) for failure. Upon success, g will be independent of the variables vars.

fmpq_mpoly_gcd :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd G A B ctx

Try to set G to the monic GCD of A and B. The GCD of zero and zero is defined to be zero. If the return is \(1\) the function was successful. Otherwise the return is \(0\) and G is left untouched.

fmpq_mpoly_gcd_cofactors :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_cofactors G Abar Bbar A B ctx

Do the operation of fmpq_mpoly_gcd and also compute \(Abar = A/G\) and \(Bbar = B/G\) if successful.

fmpq_mpoly_gcd_brown :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_brown G A B ctx

fmpq_mpoly_gcd_hensel :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_hensel G A B ctx

fmpq_mpoly_gcd_subresultant :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_subresultant G A B ctx

fmpq_mpoly_gcd_zippel :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_zippel G A B ctx

fmpq_mpoly_gcd_zippel2 :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_gcd_zippel2 G A B ctx

Try to set G to the GCD of A and B using various algorithms.

fmpq_mpoly_resultant :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_resultant R A B var ctx

Try to set R to the resultant of A and B with respect to the variable of index var.

fmpq_mpoly_discriminant :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_discriminant D A var ctx

Try to set D to the discriminant of A with respect to the variable of index var.

Square Root

fmpq_mpoly_sqrt :: Ptr CFmpqMPoly -> Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_sqrt Q A ctx

If A is a perfect square return \(1\) and set Q to the square root with positive leading coefficient. Otherwise return \(0\) and set Q to zero.

fmpq_mpoly_is_square :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_is_square A ctx

Return \(1\) if A is a perfect square, otherwise return \(0\).

Univariate Functions

fmpq_mpoly_univar_init :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_univar_init A ctx

Initialize A.

fmpq_mpoly_univar_clear :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_univar_clear A ctx

Clear A.

fmpq_mpoly_univar_swap :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_univar_swap A B ctx

Swap A and B.

fmpq_mpoly_to_univar :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPoly -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_to_univar A B var ctx

Set A to a univariate form of B by pulling out the variable of index var. The coefficients of A will still belong to the content ctx but will not depend on the variable of index var.

fmpq_mpoly_from_univar :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyUniVar -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_from_univar A B var ctx

Set A to the normal form of B by putting in the variable of index var. This function is undefined if the coefficients of B depend on the variable of index var.

fmpq_mpoly_univar_degree_fits_si :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyCtx -> IO CInt

fmpq_mpoly_univar_degree_fits_si A ctx

Return \(1\) if the degree of A with respect to the main variable fits an slong. Otherwise, return \(0\).

fmpq_mpoly_univar_length :: Ptr CFmpqMPolyUniVar -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_univar_length A ctx

Return the number of terms in A with respect to the main variable.

fmpq_mpoly_univar_get_term_exp_si :: Ptr CFmpqMPolyUniVar -> CLong -> Ptr CFmpqMPolyCtx -> IO CLong

fmpq_mpoly_univar_get_term_exp_si A i ctx

Return the exponent of the term of index i of A.

fmpq_mpoly_univar_get_term_coeff :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyUniVar -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_univar_get_term_coeff c A i ctx

fmpq_mpoly_univar_swap_term_coeff :: Ptr CFmpqMPoly -> Ptr CFmpqMPolyUniVar -> CLong -> Ptr CFmpqMPolyCtx -> IO ()

fmpq_mpoly_univar_swap_term_coeff c A i ctx

Set (resp. swap) c to (resp. with) the coefficient of the term of index i of A.