|
| int | degree_of_extension (int level) |
| bool | down_level (int newlevel, int oldlevel, TowerPolynomial &f) |
| void | remove (int level, TowerPolynomial &f) |
| int | compare (int level, const TowerPolynomial f, const TowerPolynomial g) |
| TowerPolynomial | random (int level, int deg) |
| TowerPolynomial | random (int level) |
| TowerPolynomial | var (int level, int v) |
| void | add_term (int level, TowerPolynomial &result, long coeff, exponents_t exp) const |
| void | negate_in_place (int level, TowerPolynomial &f) |
| void | add_in_place (int level, TowerPolynomial &f, const TowerPolynomial g) |
| void | subtract_in_place (int level, TowerPolynomial &f, const TowerPolynomial g) |
| TowerPolynomial | mult_by_int (int level, long c, const TowerPolynomial f) |
| TowerPolynomial | mult (int level, const TowerPolynomial f, const TowerPolynomial g, bool reduce_by_extension) |
| void | remainder (int level, TowerPolynomial &f, const TowerPolynomial g) |
| TowerPolynomial | division_in_place_monic (int level, TowerPolynomial &f, const TowerPolynomial g) |
| bool | division_in_place (int level, TowerPolynomial &f, const TowerPolynomial g, TowerPolynomial &result_quot) |
| void | pseudo_remainder (int level, TowerPolynomial &f, const TowerPolynomial g) |
| TowerPolynomial | pseudo_division (int level, TowerPolynomial &f, const TowerPolynomial g) |
| TowerPolynomial | gcd (int level, const TowerPolynomial f, const TowerPolynomial g) |
| TowerPolynomial | gcd_coefficients (int level, const TowerPolynomial f, const TowerPolynomial g, TowerPolynomial &result_u, TowerPolynomial &result_v) |
| TowerPolynomial | resultant (int level, TowerPolynomial f, TowerPolynomial g) |
| void | make_monic (int level, TowerPolynomial &f) |
| TowerPolynomial | invert (int level, const TowerPolynomial a) |
| void | normal_form (int level, TowerPolynomial &f) |
| void | subtract_multiple_to (int level, TowerPolynomial &f, long a, int i, TowerPolynomial g) |
| void | elem_text_out (buffer &o, int level, const TowerPolynomial f, bool p_one, bool p_plus, bool p_parens, M2_ArrayString names) const |
| void | extensions_text_out (buffer &o, M2_ArrayString names) const |
| int | degree (int level, int var, const TowerPolynomial f) const |
| TowerPolynomial | diff (int level, int var, const TowerPolynomial f) |
| TowerPolynomial | power_mod (int level, const TowerPolynomial f, mpz_srcptr n, const TowerPolynomial g) |
| TowerPolynomial | lowerP (int level, const TowerPolynomial f) |
| int | index_of_var (int level, const TowerPolynomial f) const |
| void | degrees_of_vars (int level, const TowerPolynomial f, std::vector< int > &result_max_degs) const |
| | ~DPoly () |
| | DPoly (long p, int nvars0, const TowerPolynomial *extensions=nullptr) |
|
| static void | increase_size_0 (int newdeg, TowerPolynomial &f) |
| static void | increase_size_n (int newdeg, TowerPolynomial &f) |
| static TowerPolynomial | alloc_poly_n (int deg, TowerPolynomial *elems=nullptr) |
| static TowerPolynomial | alloc_poly_0 (int deg, long *elems=nullptr) |
| static void | dealloc_poly (TowerPolynomial &f) |
| static void | display_poly (FILE *fil, int level, const TowerPolynomial f) |
| static TowerPolynomial | read_poly (char *&str, int level) |
| static std::ostream & | append_to_stream (std::ostream &o, int level, const TowerPolynomial f) |
| static char * | to_string (int level, const TowerPolynomial f) |
| static bool | is_equal (int level, const TowerPolynomial f, const TowerPolynomial g) |
| static TowerPolynomial | copy (int level, const TowerPolynomial f) |
| static TowerPolynomial | from_long (int level, long c) |
| static bool | is_zero (TowerPolynomial f) |
| static bool | is_one (int level, const TowerPolynomial f) |
|
| void | initialize (long p, int nvars0, const TowerPolynomial *ext0) |
| void | reset_degree_0 (TowerPolynomial &f) |
| void | reset_degree_n (int level, TowerPolynomial &f) |
| void | mult_by_coeff_0 (TowerPolynomial &f, long b) |
| void | mult_by_coeff_n (int level, TowerPolynomial &f, TowerPolynomial b) |
| void | make_monic_0 (TowerPolynomial &f, long &result_multiplier) |
| void | make_monic_n (int level, TowerPolynomial &f, TowerPolynomial &result_multiplier) |
| bool | make_monic3 (int level, TowerPolynomial &u1, TowerPolynomial &u2, TowerPolynomial &u3) |
| void | add_in_place_0 (TowerPolynomial &f, const TowerPolynomial g) |
| void | add_in_place_n (int level, TowerPolynomial &f, const TowerPolynomial g) |
| void | subtract_in_place_0 (TowerPolynomial &f, const TowerPolynomial g) |
| void | subtract_in_place_n (int level, TowerPolynomial &f, const TowerPolynomial g) |
| TowerPolynomial | mult_0 (const TowerPolynomial f, const TowerPolynomial g, bool reduce_by_extension) |
| TowerPolynomial | mult_n (int level, const TowerPolynomial f, const TowerPolynomial g, bool reduce_by_extension) |
| TowerPolynomial | random_0 (int deg) |
| TowerPolynomial | random_n (int level, int deg) |
| TowerPolynomial | diff_0 (const TowerPolynomial f) |
| TowerPolynomial | diff_n (int level, int whichvar, const TowerPolynomial f) |
| TowerPolynomial | mult_by_int_0 (long c, const TowerPolynomial f) |
| TowerPolynomial | mult_by_int_n (int level, long c, const TowerPolynomial f) |
Arithmetic engine for tower-polynomial rings: (Z/p)[x_0][x_1]...[x_{nvars-1}] modulo a chain of extensions.
- Note
- AI-generated documentation. Verify against the source before relying on it.
Holds the characteristic p, the number of variables, and an extensions array — one tower-polynomial per algebraic level giving the relation that defines the next variable over the previous (nullptr means transcendental, captured by degree_of_extension < 0). Almost every public operation (mult, add_in_place, gcd, resultant, pseudo_division, ...) takes an explicit level argument that dispatches the recursive descent down the tower. Used by DRing, which fixes a particular working level on top of a shared DPoly.
Definition at line 109 of file dpoly.hpp.
1.15.0