g tddlmZddlmZGddeZGddeZGddeZGd d eZy ) ) Predicate) Dispatcherc(eZdZdZdZeddZy)PrimePredicatea Prime number predicate. Explanation =========== ``ask(Q.prime(x))`` is true iff ``x`` is a natural number greater than 1 that has no positive divisors other than ``1`` and the number itself. Examples ======== >>> from sympy import Q, ask >>> ask(Q.prime(0)) False >>> ask(Q.prime(1)) False >>> ask(Q.prime(2)) True >>> ask(Q.prime(20)) False >>> ask(Q.prime(-3)) False prime PrimeHandlerzHandler for key 'prime'. Test that an expression represents a prime number. When the expression is an exact number, the result (when True) is subject to the limitations of isprime() which is used to return the result.docN__name__ __module__ __qualname____doc__namerhandlerY/var/www/openai/venv/lib/python3.12/site-packages/sympy/assumptions/predicates/ntheory.pyrrs 4 DGrrc(eZdZdZdZeddZy)CompositePredicatea Composite number predicate. Explanation =========== ``ask(Q.composite(x))`` is true iff ``x`` is a positive integer and has at least one positive divisor other than ``1`` and the number itself. Examples ======== >>> from sympy import Q, ask >>> ask(Q.composite(0)) False >>> ask(Q.composite(1)) False >>> ask(Q.composite(2)) False >>> ask(Q.composite(20)) True compositeCompositeHandlerzHandler for key 'composite'.r Nr rrrrr*s. D+1OPGrrc(eZdZdZdZeddZy) EvenPredicateaY Even number predicate. Explanation =========== ``ask(Q.even(x))`` is true iff ``x`` belongs to the set of even integers. Examples ======== >>> from sympy import Q, ask, pi >>> ask(Q.even(0)) True >>> ask(Q.even(2)) True >>> ask(Q.even(3)) False >>> ask(Q.even(pi)) False even EvenHandlerzHandler for key 'even'.r Nr rrrrrFs. D,EFGrrc(eZdZdZdZeddZy) OddPredicateaN Odd number predicate. Explanation =========== ``ask(Q.odd(x))`` is true iff ``x`` belongs to the set of odd numbers. Examples ======== >>> from sympy import Q, ask, pi >>> ask(Q.odd(0)) False >>> ask(Q.odd(2)) False >>> ask(Q.odd(3)) True >>> ask(Q.odd(pi)) False odd OddHandlerzHHandler for key 'odd'. Test that an expression represents an odd number.r Nr rrrrrbs , DGrrN)sympy.assumptionsrsympy.multipledispatchrrrrrrrrr#s@'-"Y"JQQ8GIG89r