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solve.h
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1
7#ifndef SYMENGINE_SOLVE_H
8#define SYMENGINE_SOLVE_H
9
10#include <symengine/sets.h>
13#include <symengine/polys/uexprpoly.h>
16#include <symengine/matrix.h>
17
18namespace SymEngine
19{
20/*
21 * Solves the given equation `f` and returns all possible values of `sym` as a
22 * Set, given
23 * they satisfy the `domain` constraint.
24 */
25RCP<const Set> solve(const RCP<const Basic> &f, const RCP<const Symbol> &sym,
26 const RCP<const Set> &domain = universalset());
27
28// Solves rational equations.
29RCP<const Set> solve_rational(const RCP<const Basic> &f,
30 const RCP<const Symbol> &sym,
31 const RCP<const Set> &domain = universalset());
32
33// Solves Trigonometric equations.
34RCP<const Set> solve_trig(const RCP<const Basic> &f,
35 const RCP<const Symbol> &sym,
36 const RCP<const Set> &domain = universalset());
37
38// Solves Polynomial equations.
39// Use this method, If you know for sure that `f` is a Polynomial.
40RCP<const Set> solve_poly(const RCP<const Basic> &f,
41 const RCP<const Symbol> &sym,
42 const RCP<const Set> &domain = universalset());
43
44// Helper method for solving lower order polynomials using known formulae.
45RCP<const Set> solve_poly_heuristics(const vec_basic &coeffs,
46 const RCP<const Set> &domain
47 = universalset());
48
49// Helper method for solving linear equations.
50RCP<const Set> solve_poly_linear(const vec_basic &coeffs,
51 const RCP<const Set> &domain = universalset());
52
53// Helper method for solving quadratic equations.
54RCP<const Set> solve_poly_quadratic(const vec_basic &coeffs,
55 const RCP<const Set> &domain
56 = universalset());
57
58// Helper method for solving cubic equations.
59RCP<const Set> solve_poly_cubic(const vec_basic &coeffs,
60 const RCP<const Set> &domain = universalset());
61
62// Helper method for solving quartic(degree-4) equations.
63RCP<const Set> solve_poly_quartic(const vec_basic &coeffs,
64 const RCP<const Set> &domain
65 = universalset());
66
67/*
68 * Helper method to decide if solve_trig can solve a particular equation.
69 * Checks the argument of Trigonometric part, and returns false if it is
70 * non-linear;
71 * true otherwise.
72 */
73bool is_a_LinearArgTrigEquation(const Basic &b, const Symbol &x);
74
75/* returns Inverse of a complex equation `fX = gY` wrt symbol `sym`.
76 * It is like a solver developed specifically to solve equations of the
77 * form `exp(f(x)) = gY`(required for trig solvers).
78 * For example : invertComplex(exp(x), {1}, x) would give you
79 * `{2*I*pi*n | n in (-oo, oo)}` aka values of `x` when `exp(x) = 1`.
80 * Dummy `nD` is used as the symbol for `ImageSet` while returning the solution
81 * set.
82 */
83RCP<const Set> invertComplex(const RCP<const Basic> &fX,
84 const RCP<const Set> &gY,
85 const RCP<const Symbol> &sym,
86 const RCP<const Dummy> &nD = dummy("n"),
87 const RCP<const Set> &domain = universalset());
88
89// Solver for System of Equations
90// TODO : solve systems that have infinitely many solutions or no solution.
91// Input as an Augmented Matrix. (A|b) to solve `Ax=b`.
92vec_basic linsolve(const DenseMatrix &system, const vec_sym &syms);
93
94// Input as a vector of linear equations.
95vec_basic linsolve(const vec_basic &system, const vec_sym &syms);
96
97// converts system of linear equations into Matrix form.
98// first Matrix is for `A` and second one is for `b`.
100linear_eqns_to_matrix(const vec_basic &equations, const vec_sym &syms);
101} // namespace SymEngine
102
103#endif // SYMENGINE_SOLVE_H
Main namespace for SymEngine package.
Definition: add.cpp:19
RCP< const UniversalSet > universalset()
Definition: sets.h:568
RCP< const Dummy > dummy()
inline version to return Dummy
Definition: symbol.h:88