Inequality Solvers¶
- sympy.solvers.inequalities.solve_rational_inequalities(eqs)[source]¶
Solve a system of rational inequalities with rational coefficients.
Examples
>>> from sympy.abc import x >>> from sympy import solve_rational_inequalities, Poly
>>> solve_rational_inequalities([[ ... ((Poly(-x + 1), Poly(1, x)), '>='), ... ((Poly(-x + 1), Poly(1, x)), '<=')]]) {1}
>>> solve_rational_inequalities([[ ... ((Poly(x), Poly(1, x)), '!='), ... ((Poly(-x + 1), Poly(1, x)), '>=')]]) Union(Interval.open(-oo, 0), Interval.Lopen(0, 1))
See also
- sympy.solvers.inequalities.solve_poly_inequality(poly, rel)[source]¶
Solve a polynomial inequality with rational coefficients.
Examples
>>> from sympy import solve_poly_inequality, Poly >>> from sympy.abc import x
>>> solve_poly_inequality(Poly(x, x, domain='ZZ'), '==') [{0}]
>>> solve_poly_inequality(Poly(x**2 - 1, x, domain='ZZ'), '!=') [Interval.open(-oo, -1), Interval.open(-1, 1), Interval.open(1, oo)]
>>> solve_poly_inequality(Poly(x**2 - 1, x, domain='ZZ'), '==') [{-1}, {1}]
See also
- sympy.solvers.inequalities.solve_poly_inequalities(polys)[source]¶
Solve polynomial inequalities with rational coefficients.
Examples
>>> from sympy import Poly >>> from sympy.solvers.inequalities import solve_poly_inequalities >>> from sympy.abc import x >>> solve_poly_inequalities((( ... Poly(x**2 - 3), ">"), ( ... Poly(-x**2 + 1), ">"))) Union(Interval.open(-oo, -sqrt(3)), Interval.open(-1, 1), Interval.open(sqrt(3), oo))
- sympy.solvers.inequalities.reduce_rational_inequalities(exprs, gen, relational=True)[source]¶
Reduce a system of rational inequalities with rational coefficients.
Examples
>>> from sympy import Symbol >>> from sympy.solvers.inequalities import reduce_rational_inequalities
>>> x = Symbol('x', real=True)
>>> reduce_rational_inequalities([[x**2 <= 0]], x) Eq(x, 0)
>>> reduce_rational_inequalities([[x + 2 > 0]], x) -2 < x >>> reduce_rational_inequalities([[(x + 2, ">")]], x) -2 < x >>> reduce_rational_inequalities([[x + 2]], x) Eq(x, -2)
This function find the non-infinite solution set so if the unknown symbol is declared as extended real rather than real then the result may include finiteness conditions:
>>> y = Symbol('y', extended_real=True) >>> reduce_rational_inequalities([[y + 2 > 0]], y) (-2 < y) & (y < oo)
- sympy.solvers.inequalities.reduce_abs_inequality(expr, rel, gen)[source]¶
Reduce an inequality with nested absolute values.
Examples
>>> from sympy import reduce_abs_inequality, Abs, Symbol >>> x = Symbol('x', real=True)
>>> reduce_abs_inequality(Abs(x - 5) - 3, '<', x) (2 < x) & (x < 8)
>>> reduce_abs_inequality(Abs(x + 2)*3 - 13, '<', x) (-19/3 < x) & (x < 7/3)
See also
- sympy.solvers.inequalities.reduce_abs_inequalities(exprs, gen)[source]¶
Reduce a system of inequalities with nested absolute values.
Examples
>>> from sympy import reduce_abs_inequalities, Abs, Symbol >>> x = Symbol('x', extended_real=True)
>>> reduce_abs_inequalities([(Abs(3*x - 5) - 7, '<'), ... (Abs(x + 25) - 13, '>')], x) (-2/3 < x) & (x < 4) & (((-oo < x) & (x < -38)) | ((-12 < x) & (x < oo)))
>>> reduce_abs_inequalities([(Abs(x - 4) + Abs(3*x - 5) - 7, '<')], x) (1/2 < x) & (x < 4)
See also
- sympy.solvers.inequalities.reduce_inequalities(inequalities, symbols=[])[source]¶
Reduce a system of inequalities with rational coefficients.
Examples
>>> from sympy.abc import x, y >>> from sympy import reduce_inequalities
>>> reduce_inequalities(0 <= x + 3, []) (-3 <= x) & (x < oo)
>>> reduce_inequalities(0 <= x + y*2 - 1, [x]) (x < oo) & (x >= 1 - 2*y)
- sympy.solvers.inequalities.solve_univariate_inequality(expr, gen, relational=True, domain=Reals, continuous=False)[source]¶
Solves a real univariate inequality.
- Parameters
expr : Relational
The target inequality
gen : Symbol
The variable for which the inequality is solved
relational : bool
A Relational type output is expected or not
domain : Set
The domain over which the equation is solved
continuous: bool
True if expr is known to be continuous over the given domain (and so continuous_domain() doesn’t need to be called on it)
- Raises
NotImplementedError
The solution of the inequality cannot be determined due to limitation in
sympy.solvers.solveset.solvify()
.
Notes
Currently, we cannot solve all the inequalities due to limitations in
sympy.solvers.solveset.solvify()
. Also, the solution returned for trigonometric inequalities are restricted in its periodic interval.Examples
>>> from sympy import solve_univariate_inequality, Symbol, sin, Interval, S >>> x = Symbol('x')
>>> solve_univariate_inequality(x**2 >= 4, x) ((2 <= x) & (x < oo)) | ((-oo < x) & (x <= -2))
>>> solve_univariate_inequality(x**2 >= 4, x, relational=False) Union(Interval(-oo, -2), Interval(2, oo))
>>> domain = Interval(0, S.Infinity) >>> solve_univariate_inequality(x**2 >= 4, x, False, domain) Interval(2, oo)
>>> solve_univariate_inequality(sin(x) > 0, x, relational=False) Interval.open(0, pi)
See also
sympy.solvers.solveset.solvify
solver returning solveset solutions with solve’s output API