\hSrSSKJr SSKJrJrJrJrJrJ r SSK J r /SQr "SS\ 5r "S S \ 5r"S S \ 5r"S S\ 5r"SS\ 5r"SS\ 5rg)a4 Module for mathematical equality [1] and inequalities [2]. The purpose of this module is to provide the instances which represent the binary predicates in order to combine the relationals into logical inference system. Objects such as ``Q.eq``, ``Q.lt`` should remain internal to assumptions module, and user must use the classes such as :obj:`~.Eq()`, :obj:`~.Lt()` instead to construct the relational expressions. References ========== .. [1] https://en.wikipedia.org/wiki/Equality_(mathematics) .. [2] https://en.wikipedia.org/wiki/Inequality_(mathematics) )Q)is_eqis_neqis_gtis_geis_ltis_le)BinaryRelation)EqualityPredicateUnequalityPredicateStrictGreaterThanPredicateGreaterThanPredicateStrictLessThanPredicateLessThanPredicatecB\rSrSrSrSrSrSrSr\ S5r S Sjr Sr g) r a  Binary predicate for $=$. The purpose of this class is to provide the instance which represent the equality predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Eq()` instead to construct the equality expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_eq` Examples ======== >>> from sympy import ask, Q >>> Q.eq(0, 0) Q.eq(0, 0) >>> ask(_) True See Also ======== sympy.core.relational.Eq TeqNc"[R$N)rneselfs [/var/www/auris/envauris/lib/python3.13/site-packages/sympy/assumptions/relation/equality.pynegatedEqualityPredicate.negated: tt c,US:XaSn[/UQUP76$NT)rrargs assumptionss revalEqualityPredicate.eval>" $ K(d(K((rT __name__ __module__ __qualname____firstlineno____doc__ is_reflexive is_symmetricnamehandlerpropertyrr$__static_attributes__r'rrr r s44LL DG )rr cB\rSrSrSrSrSrSrSr\ S5r S Sjr S r g) r Ea Binary predicate for $\neq$. The purpose of this class is to provide the instance which represent the inequation predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Ne()` instead to construct the inequation expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_neq` Examples ======== >>> from sympy import ask, Q >>> Q.ne(0, 0) Q.ne(0, 0) >>> ask(_) False See Also ======== sympy.core.relational.Ne FTrNc"[R$r)rrrs rrUnequalityPredicate.negatedfrrc,US:XaSn[/UQUP76$r )rr!s rr$UnequalityPredicate.evaljs" $ K)t)[))rr'r(r)r'rrr r Es44LL DG *rr cR\rSrSrSrSrSrSrSr\ S5r \ S5r S Sjr S r g) rqa  Binary predicate for $>$. The purpose of this class is to provide the instance which represent the ">" predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Gt()` instead to construct the equality expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_gt` Examples ======== >>> from sympy import ask, Q >>> Q.gt(0, 0) Q.gt(0, 0) >>> ask(_) False See Also ======== sympy.core.relational.Gt FgtNc"[R$rrltrs rreversed#StrictGreaterThanPredicate.reversedrrc"[R$rrlers rr"StrictGreaterThanPredicate.negatedrrc,US:XaSn[/UQUP76$r )rr!s rr$StrictGreaterThanPredicate.evalr&rr'r(r*r+r,r-r.r/r0r1r2r3rArr$r4r'rrrrqH4LL DG )rrcR\rSrSrSrSrSrSrSr\ S5r \ S5r S S jr S r g) ra  Binary predicate for $>=$. The purpose of this class is to provide the instance which represent the ">=" predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Ge()` instead to construct the equality expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_ge` Examples ======== >>> from sympy import ask, Q >>> Q.ge(0, 0) Q.ge(0, 0) >>> ask(_) True See Also ======== sympy.core.relational.Ge TFgeNc"[R$rrDrs rrAGreaterThanPredicate.reversedrrc"[R$rr?rs rrGreaterThanPredicate.negatedrrc,US:XaSn[/UQUP76$r )rr!s rr$GreaterThanPredicate.evalr&rr'r(rIr'rrrrH4LL DG )rrcR\rSrSrSrSrSrSrSr\ S5r \ S5r S Sjr S r g) ra  Binary predicate for $<$. The purpose of this class is to provide the instance which represent the "<" predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Lt()` instead to construct the equality expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_lt` Examples ======== >>> from sympy import ask, Q >>> Q.lt(0, 0) Q.lt(0, 0) >>> ask(_) False See Also ======== sympy.core.relational.Lt Fr@Nc"[R$rrr=rs rrA StrictLessThanPredicate.reversedrrc"[R$rrrMrs rrStrictLessThanPredicate.negatedrrc,US:XaSn[/UQUP76$r )rr!s rr$StrictLessThanPredicate.evalr&rr'r(rIr'rrrrrJrrcR\rSrSrSrSrSrSrSr\ S5r \ S5r S S jr S r g) ria  Binary predicate for $<=$. The purpose of this class is to provide the instance which represent the "<=" predicate in order to allow the logical inference. This class must remain internal to assumptions module and user must use :obj:`~.Le()` instead to construct the equality expression. Evaluating this predicate to ``True`` or ``False`` is done by :func:`~.core.relational.is_le` Examples ======== >>> from sympy import ask, Q >>> Q.le(0, 0) Q.le(0, 0) >>> ask(_) True See Also ======== sympy.core.relational.Le TFrENc"[R$rr[rs rrALessThanPredicate.reversed"rrc"[R$rrXrs rrLessThanPredicate.negated&rrc,US:XaSn[/UQUP76$r )r r!s rr$LessThanPredicate.eval*r&rr'r(rIr'rrrrrTrrN)r.sympy.assumptionsrsympy.core.relationalrrrrrr binrelr __all__r r rrrrr'rrrjsm KK" L))))X)*.)*X-)-)`-)>-)`-)n-)`-)-)r