Assume

class sympy.assumptions.assume.AppliedPredicate(predicate, arg)

The class of expressions resulting from applying a Predicate.

Examples

>>> from sympy import Q, Symbol
>>> x = Symbol('x')
>>> Q.integer(x)
Q.integer(x)
>>> type(Q.integer(x))
<class 'sympy.assumptions.assume.AppliedPredicate'>

property arg

Return the expression used by this assumption.

Examples

>>> from sympy import Q, Symbol
>>> x = Symbol('x')
>>> a = Q.integer(x + 1)
>>> a.arg
x + 1

property args

Returns a tuple of arguments of ‘self’.

Notes

Never use self._args, always use self.args. Only use _args in __new__ when creating a new function. Don’t override .args() from Basic (so that it’s easy to change the interface in the future if needed).

Examples

>>> from sympy import cot
>>> from sympy.abc import x, y

>>> cot(x).args
(x,)

>>> cot(x).args[0]
x

>>> (x*y).args
(x, y)

>>> (x*y).args[1]
y

property func

The top-level function in an expression.

The following should hold for all objects:

>> x == x.func(*x.args)

Examples

>>> from sympy.abc import x
>>> a = 2*x
>>> a.func
<class 'sympy.core.mul.Mul'>
>>> a.args
(2, x)
>>> a.func(*a.args)
2*x
>>> a == a.func(*a.args)
True

sort_key(order=None)

Return a sort key.

Examples

>>> from sympy.core import S, I

>>> sorted([S(1)/2, I, -I], key=lambda x: x.sort_key())
[1/2, -I, I]

>>> S("[x, 1/x, 1/x**2, x**2, x**(1/2), x**(1/4), x**(3/2)]")
[x, 1/x, x**(-2), x**2, sqrt(x), x**(1/4), x**(3/2)]
>>> sorted(_, key=lambda x: x.sort_key())
[x**(-2), 1/x, x**(1/4), sqrt(x), x, x**(3/2), x**2]

class sympy.assumptions.assume.AssumptionsContext

Set representing assumptions.

This is used to represent global assumptions, but you can also use this class to create your own local assumptions contexts. It is basically a thin wrapper to Python’s set, so see its documentation for advanced usage.

Examples

>>> from sympy import AppliedPredicate, Q
>>> from sympy.assumptions.assume import global_assumptions
>>> global_assumptions
AssumptionsContext()
>>> from sympy.abc import x
>>> global_assumptions.add(Q.real(x))
>>> global_assumptions
AssumptionsContext({Q.real(x)})
>>> global_assumptions.remove(Q.real(x))
>>> global_assumptions
AssumptionsContext()
>>> global_assumptions.clear()

add(*assumptions)

Add an assumption.

class sympy.assumptions.assume.Predicate(name, handlers=None)

A predicate is a function that returns a boolean value.

Predicates merely wrap their argument and remain unevaluated:

>>> from sympy import Q, ask, Symbol, S
>>> x = Symbol('x')
>>> Q.prime(7)
Q.prime(7)

To obtain the truth value of an expression containing predicates, use the function \(ask\):

>>> ask(Q.prime(7))
True

The tautological predicate \(Q.is_true\) can be used to wrap other objects:

>>> Q.is_true(x > 1)
Q.is_true(x > 1)
>>> Q.is_true(S(1) < x)
Q.is_true(1 < x)

eval(expr, assumptions=True)

Evaluate self(expr) under the given assumptions.

This uses only direct resolution methods, not logical inference.

sort_key(order=None)

Return a sort key.

Examples

>>> from sympy.core import S, I

>>> sorted([S(1)/2, I, -I], key=lambda x: x.sort_key())
[1/2, -I, I]

>>> S("[x, 1/x, 1/x**2, x**2, x**(1/2), x**(1/4), x**(3/2)]")
[x, 1/x, x**(-2), x**2, sqrt(x), x**(1/4), x**(3/2)]
>>> sorted(_, key=lambda x: x.sort_key())
[x**(-2), 1/x, x**(1/4), sqrt(x), x, x**(3/2), x**2]

sympy.assumptions.assume.assuming(*assumptions)

Context manager for assumptions

Examples

>>> from sympy.assumptions import assuming, Q, ask
>>> from sympy.abc import x, y

>>> print(ask(Q.integer(x + y)))
None

>>> with assuming(Q.integer(x), Q.integer(y)):
...     print(ask(Q.integer(x + y)))
True