Data.Number.Flint.Fmpz.Mod.MPoly

Multivariate polynomials over the integers mod n

data FmpzModMPoly

Constructors

FmpzModMPoly !(ForeignPtr CFmpzModMPoly)

data CFmpzModMPoly

Constructors

CFmpzModMPoly

Instances

Storable CFmpzModMPoly

Defined in Data.Number.Flint.Fmpz.Mod.MPoly.FFI

Methods

sizeOf :: CFmpzModMPoly -> Int

alignment :: CFmpzModMPoly -> Int

peekElemOff :: Ptr CFmpzModMPoly -> Int -> IO CFmpzModMPoly

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

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

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

peek :: Ptr CFmpzModMPoly -> IO CFmpzModMPoly

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

newFmpzModMPoly :: FmpzModMPolyCtx -> IO FmpzModMPoly

Create a new FmpzModMPoly

withFmpzModMPoly :: FmpzModMPoly -> (Ptr CFmpzModMPoly -> IO a) -> IO (FmpzModMPoly, a)

Context object

data FmpzModMPolyCtx

Constructors

FmpzModMPolyCtx !(ForeignPtr CFmpzModMPolyCtx)

data CFmpzModMPolyCtx

Instances

Storable CFmpzModMPolyCtx

Defined in Data.Number.Flint.Fmpz.Mod.MPoly.FFI

Methods

sizeOf :: CFmpzModMPolyCtx -> Int

alignment :: CFmpzModMPolyCtx -> Int

peekElemOff :: Ptr CFmpzModMPolyCtx -> Int -> IO CFmpzModMPolyCtx

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

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

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

peek :: Ptr CFmpzModMPolyCtx -> IO CFmpzModMPolyCtx

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

newFmpzModMPolyCtx :: CLong -> Ptr COrdering -> Ptr CFmpz -> IO FmpzModMPolyCtx

Create a new FmpzModMPolyCtx

withFmpzModMPolyCtx :: FmpzModMPolyCtx -> (Ptr CFmpzModMPolyCtx -> IO a) -> IO (FmpzModMPolyCtx, a)

Use a FmpzModMPolyCtx

fmpz_mod_mpoly_ctx_init :: Ptr CFmpzModMPolyCtx -> CLong -> Ptr COrdering -> Ptr CFmpz -> IO ()

fmpz_mod_mpoly_ctx_init ctx nvars ord p

Initialise a context object for a polynomial ring modulo n with nvars variables and ordering ord. The possibilities for the ordering are ORD_LEX, ORD_DEGLEX and ORD_DEGREVLEX.

fmpz_mod_mpoly_ctx_nvars :: Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_mpoly_ctx_nvars ctx

Return the number of variables used to initialize the context.

fmpz_mod_mpoly_ctx_ord :: Ptr CFmpzModMPolyCtx -> IO (Ptr COrdering)

fmpz_mod_mpoly_ctx_ord ctx

Return the ordering used to initialize the context.

fmpz_mod_mpoly_ctx_get_modulus :: Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_ctx_get_modulus n ctx

Set n to the modulus used to initialize the context.

fmpz_mod_mpoly_ctx_clear :: Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_ctx_clear ctx

Release up any space allocated by an ctx.

Memory management

fmpz_mod_mpoly_init :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_init A ctx

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

fmpz_mod_mpoly_init2 :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_init2 A alloc ctx

Initialise A for use with the given an 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.

fmpz_mod_mpoly_init3 :: Ptr CFmpzModMPoly -> CLong -> CFBitCnt -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_init3 A alloc bits ctx

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

fmpz_mod_mpoly_clear :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_clear A ctx

Release any space allocated for A.

Input/Output

fmpz_mod_mpoly_get_str_pretty :: Ptr CFmpzModMPoly -> Ptr (Ptr CChar) -> Ptr CFmpzModMPolyCtx -> IO CString

fmpz_mod_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.

fmpz_mod_mpoly_fprint_pretty :: Ptr CFile -> Ptr CFmpzModMPoly -> Ptr (Ptr CChar) -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_fprint_pretty file A x ctx

Print a string representing A to file.

fmpz_mod_mpoly_print_pretty :: Ptr CFmpzModMPoly -> Ptr (Ptr CChar) -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_print_pretty A x ctx

Print a string representing A to stdout.

fmpz_mod_mpoly_set_str_pretty :: Ptr CFmpzModMPoly -> CString -> Ptr (Ptr CChar) -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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

fmpz_mod_mpoly_gen :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_is_gen :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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 \(0\).

fmpz_mod_mpoly_set :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set A B ctx

Set A to B.

fmpz_mod_mpoly_equal :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_equal A B ctx

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

fmpz_mod_mpoly_swap :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_swap poly1 poly2 ctx

Efficiently swap A and B.

Constants

fmpz_mod_mpoly_is_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_is_fmpz A ctx

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

fmpz_mod_mpoly_get_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_fmpz c A ctx

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

fmpz_mod_mpoly_set_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_fmpz A c ctx

fmpz_mod_mpoly_set_ui :: Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_ui A c ctx

fmpz_mod_mpoly_set_si :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_si A c ctx

Set A to the constant c.

fmpz_mod_mpoly_zero :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_zero A ctx

Set A to the constant \(0\).

fmpz_mod_mpoly_one :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_one A ctx

Set A to the constant \(1\).

fmpz_mod_mpoly_equal_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_equal_fmpz A c ctx

fmpz_mod_mpoly_equal_ui :: Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_equal_ui A c ctx

fmpz_mod_mpoly_equal_si :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_equal_si A c ctx

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

fmpz_mod_mpoly_is_zero :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_is_zero A ctx

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

fmpz_mod_mpoly_is_one :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_is_one A ctx

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

Degrees

fmpz_mod_mpoly_degrees_fit_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_degrees_fit_si A ctx

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

fmpz_mod_mpoly_degrees_fmpz :: Ptr (Ptr CFmpz) -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_degrees_fmpz degs A ctx

fmpz_mod_mpoly_degrees_si :: Ptr CLong -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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 \(-1\).

fmpz_mod_mpoly_degree_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_degree_fmpz deg A var ctx

fmpz_mod_mpoly_degree_si :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_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 \(-1\).

fmpz_mod_mpoly_total_degree_fits_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_total_degree_fits_si A ctx

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

fmpz_mod_mpoly_total_degree_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_total_degree_fmpz tdeg A ctx

fmpz_mod_mpoly_total_degree_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_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 \(-1\).

fmpz_mod_mpoly_used_vars :: Ptr CInt -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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

fmpz_mod_mpoly_get_coeff_fmpz_monomial :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_coeff_fmpz_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.

fmpz_mod_mpoly_set_coeff_fmpz_monomial :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_fmpz_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.

fmpz_mod_mpoly_get_coeff_fmpz_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_coeff_fmpz_fmpz c A exp ctx

fmpz_mod_mpoly_get_coeff_fmpz_ui :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_coeff_fmpz_ui c A exp ctx

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

fmpz_mod_mpoly_set_coeff_fmpz_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_fmpz_fmpz A c exp ctx

fmpz_mod_mpoly_set_coeff_ui_fmpz :: Ptr CFmpzModMPoly -> CULong -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_ui_fmpz A c exp ctx

fmpz_mod_mpoly_set_coeff_si_fmpz :: Ptr CFmpzModMPoly -> CLong -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_si_fmpz A c exp ctx

fmpz_mod_mpoly_set_coeff_fmpz_ui :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_fmpz_ui A c exp ctx

fmpz_mod_mpoly_set_coeff_ui_ui :: Ptr CFmpzModMPoly -> CULong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_ui_ui A c exp ctx

fmpz_mod_mpoly_set_coeff_si_ui :: Ptr CFmpzModMPoly -> CLong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_coeff_si_ui A c exp ctx

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

fmpz_mod_mpoly_get_coeff_vars_ui :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CLong -> Ptr CULong -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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

fmpz_mod_mpoly_cmp :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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

fmpz_mod_mpoly_is_canonical :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_is_canonical A ctx

Return \(1\) if A is in canonical form. Otherwise, return \(0\). To be in canonical form, all of the terms must have nonzero coefficient, and the terms must be sorted from greatest to least.

fmpz_mod_mpoly_length :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_mpoly_length A ctx

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

fmpz_mod_mpoly_resize :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_get_term_coeff_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_term_coeff_fmpz c A i ctx

Set c to the coefficient of the term of index i.

fmpz_mod_mpoly_set_term_coeff_fmpz :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_term_coeff_fmpz A i c ctx

fmpz_mod_mpoly_set_term_coeff_ui :: Ptr CFmpzModMPoly -> CLong -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_term_coeff_ui A i c ctx

fmpz_mod_mpoly_set_term_coeff_si :: Ptr CFmpzModMPoly -> CLong -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_term_coeff_si A i c ctx

Set the coefficient of the term of index i to c.

fmpz_mod_mpoly_term_exp_fits_si :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_term_exp_fits_si poly i ctx

fmpz_mod_mpoly_term_exp_fits_ui :: Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_term_exp_fits_ui poly 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 \(0\).

fmpz_mod_mpoly_get_term_exp_fmpz :: Ptr (Ptr CFmpz) -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_term_exp_fmpz exp A i ctx

fmpz_mod_mpoly_get_term_exp_ui :: Ptr CULong -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_term_exp_ui exp A i ctx

fmpz_mod_mpoly_get_term_exp_si :: Ptr CLong -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_term_exp_si exp 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).

fmpz_mod_mpoly_get_term_var_exp_ui :: Ptr CFmpzModMPoly -> CLong -> CLong -> Ptr CFmpzModMPolyCtx -> IO CULong

fmpz_mod_mpoly_get_term_var_exp_ui A i var ctx

fmpz_mod_mpoly_get_term_var_exp_si :: Ptr CFmpzModMPoly -> CLong -> CLong -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_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).

fmpz_mod_mpoly_set_term_exp_fmpz :: Ptr CFmpzModMPoly -> CLong -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_term_exp_fmpz A i exp ctx

fmpz_mod_mpoly_set_term_exp_ui :: Ptr CFmpzModMPoly -> CLong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_set_term_exp_ui A i exp ctx

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

fmpz_mod_mpoly_get_term :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_get_term M A i ctx

Set M to the term of index i in A.

fmpz_mod_mpoly_get_term_monomial :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_push_term_fmpz_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_fmpz_fmpz A c exp ctx

fmpz_mod_mpoly_push_term_ui_fmpz :: Ptr CFmpzModMPoly -> CULong -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_ui_fmpz A c exp ctx

fmpz_mod_mpoly_push_term_si_fmpz :: Ptr CFmpzModMPoly -> CLong -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_si_fmpz A c exp ctx

fmpz_mod_mpoly_push_term_fmpz_ui :: Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_fmpz_ui A c exp ctx

fmpz_mod_mpoly_push_term_ui_ui :: Ptr CFmpzModMPoly -> CULong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_ui_ui A c exp ctx

fmpz_mod_mpoly_push_term_si_ui :: Ptr CFmpzModMPoly -> CLong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_push_term_si_ui A c exp ctx

Append a term to A with coefficient c and exponent vector exp. This function runs in constant average time.

fmpz_mod_mpoly_sort_terms :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_sort_terms A ctx

Sort the terms of A into the canonical ordering dictated by the ordering in ctx. This function simply reorders the terms: It does not combine like terms, nor does it delete terms with coefficient zero. This function runs in linear time in the size of A.

fmpz_mod_mpoly_combine_like_terms :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_combine_like_terms A ctx

Combine adjacent like terms in A and delete terms with coefficient zero. If the terms of A were sorted to begin with, the result will be in canonical form. This function runs in linear time in the size of A.

Random generation

fmpz_mod_mpoly_randtest_bound :: Ptr CFmpzModMPoly -> Ptr CFRandState -> CLong -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_randtest_bound A state length 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).

fmpz_mod_mpoly_randtest_bounds :: Ptr CFmpzModMPoly -> Ptr CFRandState -> CLong -> Ptr CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_randtest_bounds A state length 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]).

fmpz_mod_mpoly_randtest_bits :: Ptr CFmpzModMPoly -> Ptr CFRandState -> CLong -> CMpLimb -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_randtest_bits A state length exp_bits ctx

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

Addition/Subtraction

fmpz_mod_mpoly_add_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_add_fmpz A B c ctx

fmpz_mod_mpoly_add_ui :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_add_ui A B c ctx

fmpz_mod_mpoly_add_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_add_si A B c ctx

Set A to \(B + c\).

fmpz_mod_mpoly_sub_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_sub_fmpz A B c ctx

fmpz_mod_mpoly_sub_ui :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_sub_ui A B c ctx

fmpz_mod_mpoly_sub_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_sub_si A B c ctx

Set A to \(B - c\).

fmpz_mod_mpoly_add :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_add A B C ctx

Set A to \(B + C\).

fmpz_mod_mpoly_sub :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_sub A B C ctx

Set A to \(B - C\).

Scalar operations

fmpz_mod_mpoly_neg :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_neg A B ctx

Set A to \(-B\).

fmpz_mod_mpoly_scalar_mul_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_scalar_mul_fmpz A B c ctx

fmpz_mod_mpoly_scalar_mul_ui :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_scalar_mul_ui A B c ctx

fmpz_mod_mpoly_scalar_mul_si :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_scalar_mul_si A B c ctx

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

fmpz_mod_mpoly_scalar_addmul_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_scalar_addmul_fmpz A B C d ctx

Sets A to \(B + C \times d\).

fmpz_mod_mpoly_make_monic :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_make_monic A B ctx

Set A to B divided by the leading coefficient of B. This throws if B is zero or the leading coefficient is not invertible.

Differentiation

fmpz_mod_mpoly_derivative :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_derivative A B var ctx

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

Evaluation

fmpz_mod_mpoly_evaluate_all_fmpz :: Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr (Ptr CFmpz) -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_evaluate_all_fmpz eval A vals ctx

Set ev to the evaluation of A where the variables are replaced by the corresponding elements of the array vals.

fmpz_mod_mpoly_evaluate_one_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_evaluate_one_fmpz 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.

fmpz_mod_mpoly_compose_fmpz_mod_mpoly_geobucket :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr (Ptr (Ptr CFmpzModMPoly)) -> Ptr CFmpzModMPolyCtx -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_compose_fmpz_mod_mpoly_geobucket A B C ctxB ctxAC

fmpz_mod_mpoly_compose_fmpz_mod_mpoly :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr (Ptr (Ptr CFmpzModMPoly)) -> Ptr CFmpzModMPolyCtx -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_compose_fmpz_mod_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. The length of the array C is the number of variables in ctxB. Neither A nor B is allowed to alias any other polynomial. Return \(1\) for success and \(0\) for failure. The main method attempts to perform the calculation using matrices and chooses heuristically between the geobucket and horner methods if needed.

Multiplication

fmpz_mod_mpoly_mul :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_mul A B C ctx

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

fmpz_mod_mpoly_mul_johnson :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_mul_johnson A B C ctx

Set A to \(B \times C\) using Johnson's heap-based method.

fmpz_mod_mpoly_mul_dense :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_mul_dense A B C ctx

Try to set A to \(B \times C\) using dense arithmetic. If the return is \(0\), the operation was unsuccessful. Otherwise, it was successful and the return is \(1\).

Powering

fmpz_mod_mpoly_pow_fmpz :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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.

fmpz_mod_mpoly_pow_ui :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CULong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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

fmpz_mod_mpoly_divides :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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 \(0\).

fmpz_mod_mpoly_div :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_div Q A B ctx

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

fmpz_mod_mpoly_divrem :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_divrem Q R A B ctx

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

fmpz_mod_mpoly_divrem_ideal :: Ptr (Ptr (Ptr CFmpzModMPoly)) -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr (Ptr (Ptr CFmpzModMPoly)) -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_divrem_ideal Q R A B len ctx

This function is as per fmpz_mod_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

fmpz_mod_mpoly_term_content :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_content_vars :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CLong -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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.

fmpz_mod_mpoly_gcd :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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.

fmpz_mod_mpoly_gcd_cofactors :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_cofactors G Abar Bbar A B ctx

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

fmpz_mod_mpoly_gcd_brown :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_brown G A B ctx

fmpz_mod_mpoly_gcd_hensel :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_hensel G A B ctx

fmpz_mod_mpoly_gcd_subresultant :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_subresultant G A B ctx

fmpz_mod_mpoly_gcd_zippel :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_zippel G A B ctx

fmpz_mod_mpoly_gcd_zippel2 :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_gcd_zippel2 G A B ctx

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

fmpz_mod_mpoly_resultant :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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.

fmpz_mod_mpoly_discriminant :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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

fmpz_mod_mpoly_sqrt :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_sqrt Q A ctx

If \(Q^2=A\) has a solution, set Q to a solution and return \(1\), otherwise return \(0\) and set Q to zero.

fmpz_mod_mpoly_is_square :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_is_square A ctx

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

fmpz_mod_mpoly_quadratic_root :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_quadratic_root Q A B ctx

If \(Q^2+AQ=B\) has a solution, set Q to a solution and return \(1\), otherwise return \(0\).

Univariate Functions

fmpz_mod_mpoly_univar_init :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_univar_init A ctx

Initialize A.

fmpz_mod_mpoly_univar_clear :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_univar_clear A ctx

Clear A.

fmpz_mod_mpoly_univar_swap :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_univar_swap A B ctx

Swap A and B.

fmpz_mod_mpoly_to_univar :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPoly -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_from_univar :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyUnivar -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_univar_degree_fits_si :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_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 \(0\).

fmpz_mod_mpoly_univar_length :: Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_mpoly_univar_length A ctx

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

fmpz_mod_mpoly_univar_get_term_exp_si :: Ptr CFmpzModMPolyUnivar -> CLong -> Ptr CFmpzModMPolyCtx -> IO CLong

fmpz_mod_mpoly_univar_get_term_exp_si A i ctx

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

fmpz_mod_mpoly_univar_get_term_coeff :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyUnivar -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_univar_get_term_coeff c A i ctx

fmpz_mod_mpoly_univar_swap_term_coeff :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyUnivar -> CLong -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_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.

fmpz_mod_mpoly_univar_set_coeff_ui :: Ptr CFmpzModMPolyUnivar -> CULong -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_univar_set_coeff_ui Ax e c ctx

Set the coefficient of \(X^e\) in Ax to c.

fmpz_mod_mpoly_univar_resultant :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_univar_resultant R Ax Bx ctx

Try to set R to the resultant of Ax and Bx.

fmpz_mod_mpoly_univar_discriminant :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyUnivar -> Ptr CFmpzModMPolyCtx -> IO CInt

fmpz_mod_mpoly_univar_discriminant D Ax ctx

Try to set D to the discriminant of Ax.

Internal Functions

fmpz_mod_mpoly_inflate :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_inflate A B shift stride ctx

Apply the function e -> shift[v] + stride[v]*e to each exponent e corresponding to the variable v. It is assumed that each shift and stride is not negative.

fmpz_mod_mpoly_deflate :: Ptr CFmpzModMPoly -> Ptr CFmpzModMPoly -> Ptr CFmpz -> Ptr CFmpz -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_deflate A B shift stride ctx

Apply the function e -> (e - shift[v])/stride[v] to each exponent e corresponding to the variable v. If any stride[v] is zero, the corresponding numerator e - shift[v] is assumed to be zero, and the quotient is defined as zero. This allows the function to undo the operation performed by fmpz_mod_mpoly_inflate when possible.

fmpz_mod_mpoly_deflation :: Ptr CFmpz -> Ptr CFmpz -> Ptr CFmpzModMPoly -> Ptr CFmpzModMPolyCtx -> IO ()

fmpz_mod_mpoly_deflation shift stride A ctx

For each variable \(v\) let \(S_v\) be the set of exponents appearing on \(v\). Set shift[v] to \(\operatorname{min}(S_v)\) and set stride[v] to \(\operatorname{gcd}(S-\operatorname{min}(S_v))\). If A is zero, all shifts and strides are set to zero.