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.