fq_zech_mpoly.h

Initialises ctx for polynomials in nvars variables with the ordering ord over \mathbb{F}_{p^{\mathit{deg}}}, defined by a Conway polynomial if the database has one and a random primitive polynomial otherwise (see fq_zech_ctx_init_ui); the generator is printed as #. This is the only way to create a context.

Replaces the field of ctx by \mathbb{F}_{p^{\mathit{deg}}} with the same characteristic. Polynomials of the context become invalid.

Return the number of variables and the ordering, and free the context.

Returns the nmod_t of the characteristic p of the field.

Initialise A as zero (allocating nothing, space for alloc terms, or space for alloc terms with bits-bit exponent fields), and free it.

Ensure space for length terms; ensure exponent fields of at least bits bits, repacking the exponents; ensure space for len terms with exactly bits bits, discarding the exponent data.

Keep only the newlen leading terms, and repack the exponents into Abits bits (returning 0 if they do not fit).

Print A to file or stdout with the variable names x (or x1, x2, ... if x is NULL).

The variable of index var, assignment, swap and equality test.

Test whether A is constant, set it to the constant c (an integer is reduced modulo p), to 0 or to 1, and test for 0 and 1.

Returns a pointer to the leading coefficient of the nonzero A.

Degrees in each variable, in one variable, and the total degree; -1 for the zero polynomial.

Sets C to the coefficient of \prod_i x_{v_i}^{e_i} in A viewed as a polynomial in the variables vars[i] with coefficients in the others.

Return the number of terms, whether A is canonical, or throw if it is not.

Return whether the exponents of the term of index i fit a ulong or slong.

Sort the terms into the order of the context, and combine equal adjacent monomials and remove zero coefficients.

Set A to B + C, B - C, B - c or -B.

Set A to c B, to B + d C, or to B divided by its leading coefficient (throwing if B is zero).

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

Sets A to B with the variable of index var replaced by val.

Set A to B C by Johnson's heap algorithm [Joh1974].

Set A to B^k; fq_zech_mpoly_pow_ui returns 1 for success.

If B divides A, set Q (poly1) to the quotient and return 1; otherwise return 0. Uses the heap algorithm of Monagan and Pearce [MonPea2011].

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

Set G to the monic GCD of A and B (and the cofactors A/G, B/G), computed by converting to fq_nmod_mpoly and calling fq_nmod_mpoly_gcd or fq_nmod_mpoly_gcd_cofactors. Return 1 for success.

Memory management, printing and consistency check of the univariate representation.

Convert B to a polynomial in the variable of index var, and back (with Abits-bit exponents in the last version).

Access the terms of the univariate representation.

Ensure room for len coefficients and exponent vectors of N words (the common allocation is alloc), and set the length.

Radix sort of terms, merge-addition and heap multiplication of term arrays, and evaluation at a point.

_fq_zech_mpoly_get_nmod_mpoly sets s to t if all coefficients of t lie in the prime field \mathbb{F}_p and returns 1, and returns 0 otherwise. _fq_zech_mpoly_set_nmod_mpoly maps a polynomial over \mathbb{F}_p into \mathbb{F}_q. The two contexts must have the same variables and ordering.

Convert between Zech logarithm and polynomial representation of the same field (the fq_nmod_ctx of the Zech context) with the same variables and ordering.

Sets c to the leading coefficient of A viewed as a polynomial in its first num_vars variables.

Memory management and basic operations of fq_zech_mpolyu_t.