Create a new FqNModMPolyCtx

Use a FqNModMPolyCtx

fq_nmod_mpoly_ctx_init ctx nvars ord fqctx

Initialise a context object for a polynomial ring with the given number of variables and the given ordering. It will have coefficients in the finite field fqctx. The possibilities for the ordering are ORD_LEX, ORD_DEGLEX and ORD_DEGREVLEX.

fq_nmod_mpoly_ctx_nvars ctx

Return the number of variables used to initialize the context.

fq_nmod_mpoly_ctx_ord ctx

Return the ordering used to initialize the context.

fq_nmod_mpoly_ctx_clear ctx

Release any space allocated by an ctx.

fq_nmod_mpoly_init A ctx

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

fq_nmod_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.

fq_nmod_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.

fq_nmod_mpoly_fit_length A len ctx

Ensure that A has space for at least len terms.

fq_nmod_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.

fq_nmod_mpoly_clear A ctx

Release any space allocated for A.

fq_nmod_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.

fq_nmod_mpoly_fprint_pretty file A x ctx

Print a string representing A to file.

fq_nmod_mpoly_print_pretty A x ctx

Print a string representing A to stdout.

fq_nmod_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.

fq_nmod_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.

fq_nmod_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 \(0\).

fq_nmod_mpoly_set A B ctx

Set A to B.

fq_nmod_mpoly_equal A B ctx

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

fq_nmod_mpoly_swap A B ctx

Efficiently swap A and B.

fq_nmod_mpoly_is_fq_nmod A ctx

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

fq_nmod_mpoly_get_fq_nmod c A ctx

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

fq_nmod_mpoly_set_fq_nmod A c ctx

fq_nmod_mpoly_set_ui A c ctx

Set A to the constant c.

fq_nmod_mpoly_set_fq_nmod_gen A ctx

Set A to the constant given by fq_nmod_gen.

fq_nmod_mpoly_zero A ctx

Set A to the constant \(0\).

fq_nmod_mpoly_one A ctx

Set A to the constant \(1\).

fq_nmod_mpoly_equal_fq_nmod A c ctx

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

fq_nmod_mpoly_is_zero A ctx

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

fq_nmod_mpoly_is_one A ctx

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

fq_nmod_mpoly_degrees_fit_si A ctx

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

fq_nmod_mpoly_degrees_fmpz degs A ctx

fq_nmod_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 \(-1\).

fq_nmod_mpoly_degree_fmpz deg A var ctx

fq_nmod_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 \(-1\).

fq_nmod_mpoly_total_degree_fits_si A ctx

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

fq_nmod_mpoly_total_degree_fmpz tdeg A ctx

fq_nmod_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 \(-1\).

fq_nmod_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.

fq_nmod_mpoly_get_coeff_fq_nmod_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.

fq_nmod_mpoly_set_coeff_fq_nmod_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.

fq_nmod_mpoly_get_coeff_fq_nmod_fmpz c A exp ctx

fq_nmod_mpoly_get_coeff_fq_nmod_ui c A exp ctx

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

fq_nmod_mpoly_set_coeff_fq_nmod_fmpz A c exp ctx

fq_nmod_mpoly_set_coeff_fq_nmod_ui A c exp ctx

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

fq_nmod_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.

fq_nmod_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.

fq_nmod_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 coefficients, and the terms must be sorted from greatest to least.

fq_nmod_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.

fq_nmod_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.

fq_nmod_mpoly_get_term_coeff_fq_nmod c A i ctx

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

fq_nmod_mpoly_term_exp_fits_si A i ctx

fq_nmod_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 \(0\).

fq_nmod_mpoly_get_term_exp_fmpz exp A i ctx

fq_nmod_mpoly_get_term_exp_ui exp A i ctx

fq_nmod_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).

fq_nmod_mpoly_get_term_var_exp_ui A i var ctx

fq_nmod_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).

fq_nmod_mpoly_set_term_exp_fmpz A i exp ctx

fq_nmod_mpoly_set_term_exp_ui A i exp ctx

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

fq_nmod_mpoly_get_term M A i ctx

Set M to the term of index i in A.

fq_nmod_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.

fq_nmod_mpoly_push_term_fq_nmod_fmpz A c exp ctx

fq_nmod_mpoly_push_term_fq_nmod_ui A c exp ctx

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

fq_nmod_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 bit size of A.

fq_nmod_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 bit size of A.

fq_nmod_mpoly_reverse A B ctx

Set A to the reversal of B.

fq_nmod_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).

fq_nmod_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]).

fq_nmod_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.

fq_nmod_mpoly_add_fq_nmod A B C ctx

Set A to \(B + c\).

fq_nmod_mpoly_sub_fq_nmod A B C ctx

Set A to \(B - c\).

fq_nmod_mpoly_add A B C ctx

Set A to \(B + C\).

fq_nmod_mpoly_sub A B C ctx

Set A to \(B - C\).

fq_nmod_mpoly_neg A B ctx

Set A to \(-B\).

fq_nmod_mpoly_scalar_mul_fq_nmod A B c ctx

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

fq_nmod_mpoly_make_monic A B ctx

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

fq_nmod_mpoly_derivative A B var ctx

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

fq_nmod_mpoly_evaluate_all_fq_nmod ev A vals ctx

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

fq_nmod_mpoly_evaluate_one_fq_nmod A B var val ctx

Set A to the evaluation of B where the variable of index var is replaced by val.

fq_nmod_mpoly_compose_fq_nmod_poly A B C ctx

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.

fq_nmod_mpoly_compose_fq_nmod_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.

fq_nmod_mpoly_compose_fq_nmod_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.

fq_nmod_mpoly_mul A B C ctx

Set A to B times C.

fq_nmod_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.

fq_nmod_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.

fq_nmod_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 \(0\).

fq_nmod_mpoly_div Q A B ctx

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

fq_nmod_mpoly_divrem Q R A B ctx

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

fq_nmod_mpoly_divrem_ideal Q R A B len ctx

This function is as per fq_nmod_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.

fq_nmod_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.

fq_nmod_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.

fq_nmod_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.

fq_nmod_mpoly_gcd_cofactors G Abar Bbar A B ctx

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

fq_nmod_mpoly_gcd_brown G A B ctx

fq_nmod_mpoly_gcd_hensel G A B ctx

fq_nmod_mpoly_gcd_zippel G A B ctx

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

fq_nmod_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.

fq_nmod_mpoly_discriminant D A var ctx

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

fq_nmod_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.

fq_nmod_mpoly_is_square A ctx

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

fq_nmod_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 \(0\).

fq_nmod_mpoly_univar_init A ctx

Initialize A.

fq_nmod_mpoly_univar_clear A ctx

Clear A.

fq_nmod_mpoly_univar_swap A B ctx

Swap A and \(B\).

fq_nmod_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.

fq_nmod_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.

fq_nmod_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 \(0\).

fq_nmod_mpoly_univar_length A ctx

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

fq_nmod_mpoly_univar_get_term_exp_si A i ctx

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

fq_nmod_mpoly_univar_get_term_coeff c A i ctx

fq_nmod_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.