# Assumptions module¶

## Contents¶

Queries are used to ask information about expressions. Main method for this is ask():

sympy.assumptions.ask.ask(proposition, assumptions=True, context=AssumptionsContext())[source]

Method for inferring properties about objects.

Syntax

• ask(proposition)

• ask(proposition, assumptions)

where proposition is any boolean expression

Examples

>>> from sympy import ask, Q, pi
>>> from sympy.abc import x, y
>>> ask(Q.rational(pi))
False
>>> ask(Q.even(x*y), Q.even(x) & Q.integer(y))
True
>>> ask(Q.prime(4*x), Q.integer(x))
False

Remarks

Relations in assumptions are not implemented (yet), so the following will not give a meaningful result.

>>> ask(Q.positive(x), Q.is_true(x > 0))


It is however a work in progress.

## Querying¶

ask’s optional second argument should be a boolean expression involving assumptions about objects in expr. Valid values include:

• Q.integer(x)
• Q.positive(x)
• Q.integer(x) & Q.positive(x)
• etc.

Q is an object holding known predicates.

See documentation for the logic module for a complete list of valid boolean expressions.

You can also define a context so you don’t have to pass that argument each time to function ask(). This is done by using the assuming context manager from module sympy.assumptions.

>>> from sympy import *
>>> x = Symbol('x')
>>> y = Symbol('y')
>>> facts = Q.positive(x), Q.positive(y)
>>> with assuming(*facts):
...     print(ask(Q.positive(2*x + y)))
True


## Design¶

Each time ask is called, the appropriate Handler for the current key is called. This is always a subclass of sympy.assumptions.AskHandler. Its classmethods have the names of the classes it supports. For example, a (simplified) AskHandler for the ask ‘positive’ would look like this:

class AskPositiveHandler(CommonHandler):

def Mul(self):
# return True if all argument's in self.expr.args are positive
...

def Add(self):
for arg in self.expr.args:
if not ask(arg, positive, self.assumptions):
break
else:
# if all argument's are positive
return True
...


The .Mul() method is called when self.expr is an instance of Mul, the Add method would be called when self.expr is an instance of Add and so on.

## Extensibility¶

You can define new queries or support new types by subclassing sympy.assumptions.AskHandler
and registering that handler for a particular key by calling register_handler:
sympy.assumptions.ask.register_handler(key, handler)[source]

Register a handler in the ask system. key must be a string and handler a class inheriting from AskHandler:

>>> from sympy.assumptions import register_handler, ask, Q
>>> from sympy.assumptions.handlers import AskHandler
>>> class MersenneHandler(AskHandler):
...     # Mersenne numbers are in the form 2**n + 1, n integer
...     @staticmethod
...     def Integer(expr, assumptions):
...         from sympy import log
...         return ask(Q.integer(log(expr + 1, 2)))
>>> register_handler('mersenne', MersenneHandler)
>>> ask(Q.mersenne(7))
True


You can undo this operation by calling remove_handler.

sympy.assumptions.ask.remove_handler(key, handler)[source]

Removes a handler from the ask system. Same syntax as register_handler

You can support new types [1] by adding a handler to an existing key. In the following example, we will create a new type MyType and extend the key ‘prime’ to accept this type (and return True)

>>> from sympy.core import Basic
>>> from sympy.assumptions import register_handler
>>> from sympy.assumptions.handlers import AskHandler
>>> class MyType(Basic):
...     pass
>>> class MyAskHandler(AskHandler):
...     @staticmethod
...     def MyType(expr, assumptions):
...         return True
>>> a = MyType()
>>> register_handler('prime', MyAskHandler)
>>> ask(Q.prime(a))
True


## Performance improvements¶

On queries that involve symbolic coefficients, logical inference is used. Work on improving satisfiable function (sympy.logic.inference.satisfiable) should result in notable speed improvements.

Logic inference used in one ask could be used to speed up further queries, and current system does not take advantage of this. For example, a truth maintenance system (http://en.wikipedia.org/wiki/Truth_maintenance_system) could be implemented.

## Misc¶

You can find more examples in the in the form of test under directory sympy/assumptions/tests/

 [1] New type must inherit from Basic, otherwise an exception will be raised. This is a bug and should be fixed.