On Jul 26, 2009, at 8:36 AM, Vinzent Steinberg wrote:
>
> I assume every 'query' got renamed to 'ask'.
>
> 2009/7/21 Fabian Pedregosa <fab...@fseoane.net>:
>>
>> ---
>> doc/src/modules.txt | 5 +-
>> doc/src/modules/queries.txt | 375 ++++++++++++++++++++++++++++++++
>> +++++++++++
>> 2 files changed, 378 insertions(+), 2 deletions(-)
>> create mode 100644 doc/src/modules/queries.txt
>>
>> diff --git a/doc/src/modules.txt b/doc/src/modules.txt
>> index 0816df0..ae5bbdb 100644
>> --- a/doc/src/modules.txt
>> +++ b/doc/src/modules.txt
>> @@ -17,6 +17,7 @@ access any SymPy module, or use this contens:
>> :maxdepth: 2
>>
>> modules/core.txt
>> + modules/concrete.txt
>> modules/evalf.txt
>> modules/functions.txt
>> modules/geometry.txt
>> @@ -26,14 +27,14 @@ access any SymPy module, or use this contens:
>> modules/logic.txt
>> modules/matrices.txt
>> modules/mpmath/index.txt
>> - modules/rewriting.txt
>> modules/polynomials.txt
>> modules/printing.txt
>> modules/plotting.txt
>> + modules/queries.txt
>> + modules/rewriting.txt
>> modules/series.txt
>> modules/simplify.txt
>> modules/statistics.txt
>> - modules/concrete.txt
>> modules/solvers.txt
>> modules/utilities/index.txt
>>
>> diff --git a/doc/src/modules/queries.txt b/doc/src/modules/
>> queries.txt
>> new file mode 100644
>> index 0000000..0d665cb
>> --- /dev/null
>> +++ b/doc/src/modules/queries.txt
>> @@ -0,0 +1,375 @@
>> +Query module
>> +============
>> +
>> +.. module:: sympy.queries
>> +
>> +Queries are used to ask information about expression. Main method
>> in this
>> +module is function query:
>
> 2 colons?
>
>> +
>> +.. automethod:: sympy.queries.query
>> +
>> +Assumptions
>> +===========
>> +
>> +query has a keyword argument assumptions. It's value should be a
>> boolean
>> +expression involving assumptions about objects in expr. Valid
>> values include:
>> +
>> + * Assume(x, integer=True)
>> + * Assume(x, integer=False)
>> + * Assume(x, integer=True) & Assume(x, positive=True)
>> + * etc.
>> +
>> +See documentation for the logic module for a complete list of
>> valid boolean
>> +expressions.
>> +
>
> What about lowercase 'assume'? For the use there is no difference
> between ask() and assume(), and integrate() (at some point also
> solve()) could also return a class, so this is maybe more consistent.
>
>> +
>> +Supported queries
>> +=================
>> +
>> +bounded
>> +-------
>> +
>> +Test that a function is bounded with respect to it's variables.
>> For example,
>> +sin(x) is a bounded functions, but exp(x) is not.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> x = Symbol('x')
>> + >>> query(exp(x), bounded=True)
>> + False
>> + >>> query(exp(x), bounded=True , assumptions=Assume(x,
>> bounded=True))
>> + True
>> + >>> query(sin(x), bounded=True)
>> + True
>> +
>> +
>> +commutative
>> +-----------
>> +
>> +Test that objects are commutative. By default, symbols in SymPy
>> are considered
>> +commutative except otherwise stated
>> +
>
> Dot?
>
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> x, y = symbols('x y')
>> + >>> query(x, commutative=True)
>> + True
>> + >>> query(x, commutative=True, assumptions=Assume(x,
>> commutative=False))
>> + False
>> + >>> query(x*y, commutative=True, assumptions=Assume(x,
>> commutative=False))
>> + False
>> +
>> +
>> +complex
>> +-------
>> +
>> +Test that expression belongs to the field of complex numbers.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(2, complex=True)
>> + True
>> + >>> query(I, complex=True)
>> + True
>> + >>> x, y = symbols('x y')
>> + >>> query(x+I*y, complex=True, assumptions=Assume(x,
>> real=True) & Assume(y, real=True))
>> + True
>> +
>> +
>> +even
>> +----
>> +
>> +Test that expression represents an even number, that is, an number
>> that
>> +can be written in the form 2*n, n integer.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(2, even=True)
>> + True
>> + >>> n = Symbol('n')
>> + >>> query(2*n, even=True, assumptions=Assume(n, integer=True))
>> + True
>> +
>> +
>> +extended_real
>> +-------------
>> +
>> +Test that an expression belongs to the field of extended real
>> numbers, that is, real
>> +numbers union {Infinity, -Infinity}
>
> Dot?
>
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(oo, extended_real=True)
>> + True
>> + >>> query(2, extended_real=True)
>> + True
>> + >>> query(x, extended_real=True, assumptions=Assume(x,
>> real=True))
>> + True
>> +
>> +
>> +imaginary
>> +---------
>> +
>> +Test that an expression belongs to the field of imaginary numbers,
>> that is,
>> + it can be written as x*I, where x is real and I is the imaginary
>> unit.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(2*I, imaginary=True)
>> + True
>> + >>> x = Symbol('x')
>> + >>> query(x*I, imaginary=True, assumptions=Assume(x, real=True))
>> + True
>> +
>> +
>> +infinitesimal
>> +-------------
>> +
>> +Test that an expression is equivalent to an infinitesimal number.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(1/oo, infinitesimal=True)
>> + True
>> + >>> x, y = symbols('x y')
>> + >>> query(2*x, infinitesimal=True, assumptions=Assume(x,
>> infinitesimal=True))
>> + True
>> + >>> query(x*y, infinitesimal=True, assumptions=Assume(x,
>> infinitesimal=True) & Assume(y, bounded=True))
>> + True
>> +
>> +
>> +integer
>> +-------
>> +
>> +Test that an expression belongs to the field of integer numbers
>> +
>
> Dot?
>
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(2, integer=True)
>> + True
>> + >>> query(sqrt(2), integer=True)
>> + False
>> + >>> x = Symbol('x')
>> + >>> query(x/2, integer=True, assumptions=Assume(x, even=True))
>> + True
>> +
>> +
>> +irrational
>> +----------
>> +
>> +Test that an expression represents an irrational number.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(pi, irrational=True)
>> + True
>> + >>> query(sqrt(2), irrational=True)
>> + True
>> + >>> query(x*sqrt(2), irrational=True, assumptions=Assume(x,
>> rational=True))
>> + True
>> +
>> +
>> +rational
>> +--------
>> +
>> +Test that an expression represents a rational number.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(Rational(3, 4), rational=True)
>> + True
>> + >>> x, y = symbols('x y')
>> + >>> query(x/2, rational=True, assumptions=Assume(x,
>> integer=True))
>> + True
>> + >>> query(x/y, rational=True, assumptions=Assume(x,
>> integer=True) & Assume(y, integer=True))
>> + True
>> +
>> +
>> +negative
>> +--------
>> +
>> +Test that an expression is less (strict) than zero.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(0.3, negative=True)
>> + False
>> + >>> x = Symbol('x')
>> + >>> query(-x, negative=True, assumptions=Assume(x,
>> positive=True))
>> + True
>> +
>> +Remarks
>> +^^^^^^^
>> +negative numbers are defined as real numbers that are not zero nor
>> positive, so
>> +complex numbers (with nontrivial imaginary coefficients) will
>> return False
>> +in this query. The same applies to query positive.
>> +
>> +
>> +positive
>> +--------
>> +
>> +Test that a given expression is greater (strict) than zero.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(0.3, positive=True)
>> + True
>> + >>> x = Symbol('x')
>> + >>> query(-x, positive=True, assumptions=Assume(x,
>> negative=True))
>> + True
>> +
>> +Remarks
>> +^^^^^^^
>> +see Remarks for negative
>> +
>
> So positive=True and negative=True is equivalent to nonzero=True?
>
>> +
>> +prime
>> +-----
>> +
>> +Test that an expression represents a prime number.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(13, prime=True)
>> + True
>> +
>> +Remarks: Use sympy.ntheory.isprime for efficiently test numeric
>> values
>> +
>
> Dot?
>
>> +
>> +real
>> +----
>> +
>> +Test that an expression belongs to the field of real numbers.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(sqrt(2), real=True)
>> + True
>> + >>> x, y = symbols('x y')
>> + >>> query(x*y, real=True, assumptions=Assume(x, real=True) &
>> Assume(y, real=True))
>> + True
>> +
>> +
>> +odd
>> +---
>> +
>> +Test that an expression represents an odd number.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> query(3, odd=True)
>> + True
>> + >>> n = Symbol('n')
>> + >>> query(2*n + 1, odd=True, assumptions=Assume(n,
>> integer=True))
>> + True
>> +
>> +
>> +zero
>> +----
>> +
>> +Test that an expression is zero. This is mostly used for
>> assumptions.
>> +
>> +Examples::
>> +
>> + >>> from sympy import *
>> + >>> x = Symbol('x')
>> + >>> query(x, negative=True, assumptions=Assume(x, real=True)
>> & Assume(x, positive=False) & Assume(x, zero=False))
>> + True
>> +
>> +Note: To solve equations, use solve() instead
>> +
>
> I think contradictory arguments should also be covered. (Things like
> Assume(integer=False, odd=True).)
It looks like they are:
>>> Assume(integer=False, odd=True)
Traceback (most recent call last):
File "<console>", line 1, in <module>
File "./sympy/core/basic.py", line 305, in __new__
obj._learn_new_facts(assumptions)
File "./sympy/core/assumptions.py", line 336, in _learn_new_facts
self._assume_rules.deduce_all_facts(facts, base)
File "./sympy/core/facts.py", line 882, in deduce_all_facts
assert new_facts[k] == v, ('inconsitency between
facts',new_facts,k,v)
AssertionError: ('inconsitency between facts', {'nonzero': True,
'even': False, 'composite': False, 'prime': False, 'zero': False,
'integer': False, 'odd': False}, 'odd', True)
Aaron Meurer
>
>> +
>> +Design
>> +======
>> +
>> +Each time query is called, the appropriate Handler for the current
>> key is called. This is
>> +always a subclass of sympy.queries.QueryHandler. It's classmethods
>> have the name's of the classes
>> +it supports. For example, a (simplified) QueryHandler for the
>> query 'positive' would
>> +look like this::
>> +
>> + class QueryPositiveHandler(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 query(arg, positive=True, 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.queries.QueryHandler
>> + and registering that handler for a particular key by calling
>> register_handler:
>
> Are 2 colons necessary? I'm not sure...
>
>> +
>> +.. automethod:: sympy.queries.register_handler
>> +
>> +You can undo this operation by calling remove_handler.
>> +
>> +.. automethod:: sympy.queries.remove_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)
>
> A dot?
>
>> +
>> +.. parsed-literal::
>> +
>> + >>> from sympy.core import Basic
>> + >>> from sympy.queries import register_handler
>> + >>> from sympy.queries.handlers import QueryHandler
>> + >>> class MyType(Basic):
>> + ... pass
>> + >>> class MyQueryHandler(QueryHandler):
>> + ... @staticmethod
>> + ... def MyType(expr, assumptions):
>> + ... return True
>> + >>> a = MyType()
>> + >>> register_handler('prime', MyQueryHandler)
>> + None
>> + >>> query(a, prime=True)
>> + 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 query 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/query/tests/
>> +
>> +.. [1] New type must inherit from Basic, otherwise an exception
>> will be raised.
>> + This is a bug and should be fixed.
>> --
>> 1.6.2.2
>
> Thank you.
>
> Vinzent
>
> >
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