Inequality Solvers¶
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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 Poly >>> from sympy.solvers.inequalities import solve_rational_inequalities
>>> 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
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sympy.solvers.inequalities.
solve_poly_inequality
(poly, rel)[source]¶ Solve a polynomial inequality with rational coefficients.
Examples
>>> from sympy import Poly >>> from sympy.abc import x >>> from sympy.solvers.inequalities import solve_poly_inequality
>>> 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
solve_poly_inequalities
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sympy.solvers.inequalities.
reduce_rational_inequalities
(exprs, gen, relational=True)[source]¶ Reduce a system of rational inequalities with rational coefficients.
Examples
>>> from sympy import Poly, 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) & (x < oo) >>> reduce_rational_inequalities([[(x + 2, ">")]], x) (-2 < x) & (x < oo) >>> reduce_rational_inequalities([[x + 2]], x) Eq(x, -2)
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sympy.solvers.inequalities.
reduce_abs_inequality
(expr, rel, gen)[source]¶ Reduce an inequality with nested absolute values.
Examples
>>> from sympy import Abs, Symbol >>> from sympy.solvers.inequalities import reduce_abs_inequality >>> 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
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sympy.solvers.inequalities.
reduce_abs_inequalities
(exprs, gen)[source]¶ Reduce a system of inequalities with nested absolute values.
Examples
>>> from sympy import Abs, Symbol >>> from sympy.abc import x >>> from sympy.solvers.inequalities import reduce_abs_inequalities >>> x = Symbol('x', 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 import sympify as S, Symbol >>> from sympy.abc import x, y >>> from sympy.solvers.inequalities 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)
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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 \(solvify\).
Notes
Currently, we cannot solve all the inequalities due to limitations in \(solvify\). Also, the solution returned for trigonometric inequalities are restricted in its periodic interval.
Examples
>>> from sympy.solvers.inequalities import solve_univariate_inequality >>> from sympy import Symbol, sin, Interval, S >>> x = Symbol('x')
>>> solve_univariate_inequality(x**2 >= 4, x) ((2 <= x) & (x < oo)) | ((x <= -2) & (-oo < x))
>>> 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
solvify
solver returning solveset solutions with solve’s output API