def assume(self):
"""
Make this assumption.
TEST::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: decl = GenericDeclaration(x, 'even')
sage: decl.assume()
sage: cos(x*pi).simplify()
1
sage: decl2 = GenericDeclaration(x, 'odd')
sage: decl2.assume()
Traceback (most recent call last):
...
ValueError: Assumption is inconsistent
sage: decl.forget()
"""
from sage.calculus.calculus import maxima
if self._context is None:
# We get the list here because features may be added with time.
valid_features = list(maxima("features"))
if self._assumption not in [
repr(x).strip() for x in list(valid_features)
]:
raise ValueError(
"%s not a valid assumption, must be one of %s" %
(self._assumption, valid_features))
cur = maxima.get("context")
self._context = maxima.newcontext('context' +
maxima._next_var_name())
try:
maxima.eval("declare(%s, %s)" %
(self._var._maxima_init_(), self._assumption))
# except TypeError, mess:
# if 'inconsistent' in str(mess): # note Maxima doesn't tell you if declarations are redundant
# raise ValueError, "Assumption is inconsistent"
except RuntimeError as mess:
if 'inconsistent' in str(
mess
): # note Maxima doesn't tell you if declarations are redundant
raise ValueError("Assumption is inconsistent")
else:
raise
maxima.set("context", cur)
if not self in _assumptions:
maxima.activate(self._context)
_assumptions.append(self)
def assume(self):
"""
Make this assumption.
TEST::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: decl = GenericDeclaration(x, 'even')
sage: decl.assume()
sage: cos(x*pi).simplify()
1
sage: decl2 = GenericDeclaration(x, 'odd')
sage: decl2.assume()
Traceback (most recent call last):
...
ValueError: Assumption is inconsistent
sage: decl.forget()
"""
from sage.calculus.calculus import maxima
if self._context is None:
# We get the list here because features may be added with time.
valid_features = list(maxima("features"))
if self._assumption not in [repr(x).strip() for x in list(valid_features)]:
raise ValueError("%s not a valid assumption, must be one of %s" % (self._assumption, valid_features))
cur = maxima.get("context")
self._context = maxima.newcontext('context' + maxima._next_var_name())
try:
maxima.eval("declare(%s, %s)" % (self._var._maxima_init_(), self._assumption))
# except TypeError, mess:
# if 'inconsistent' in str(mess): # note Maxima doesn't tell you if declarations are redundant
# raise ValueError, "Assumption is inconsistent"
except RuntimeError as mess:
if 'inconsistent' in str(mess): # note Maxima doesn't tell you if declarations are redundant
raise ValueError("Assumption is inconsistent")
else:
raise
maxima.set("context", cur)
if not self in _assumptions:
maxima.activate(self._context)
_assumptions.append(self)
def assume(self):
"""
Make this assumption.
TESTS::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: decl = GenericDeclaration(x, 'even')
sage: decl.assume()
sage: cos(x*pi).simplify()
1
sage: decl2 = GenericDeclaration(x, 'odd')
sage: decl2.assume()
Traceback (most recent call last):
...
ValueError: Assumption is inconsistent
sage: decl.forget()
"""
if self in _assumptions:
return
from sage.calculus.calculus import maxima
cur = None
context = None
if self._context is None:
self._validate_feature()
cur = maxima.get("context")
# newcontext makes a fresh context that only has $global as
# a subcontext, and makes it the current $context,
# but does not deactivate other current contexts.
context = maxima.newcontext('context' + maxima._next_var_name())
must_declare = True
elif not maxima.featurep(self._var, self._assumption):
# Reactivating a previously active context.
# Run $declare again with the assumption
# to catch possible inconsistency
# with the active contexts.
cur = maxima.get("context")
# Redeclaring on the existing context does not seem to trigger
# inconsistency checking.
## maxima.set("context", self._context._maxima_init_())
# Instead, use a temporary context for this purpose
context = maxima.newcontext('context' + maxima._next_var_name())
must_declare = True
else:
must_declare = False
if must_declare:
try:
maxima.eval("declare(%s, %s)" %
(self._var._maxima_init_(), self._assumption))
except RuntimeError as mess:
if 'inconsistent' in str(
mess
): # note Maxima doesn't tell you if declarations are redundant
# Inconsistency with one of the active contexts.
raise ValueError("Assumption is inconsistent")
else:
raise
else:
if self._context is None:
self._context = context
context = None
finally:
assert cur is not None
maxima.set("context", cur)
if context is not None:
maxima.killcontext(context)
maxima.activate(self._context)
self._var.decl_assume(self._assumption)
_assumptions[self] = True
class GenericDeclaration(SageObject):
def __init__(self, var, assumption):
"""
This class represents generic assumptions, such as a variable being
an integer or a function being increasing. It passes such
information to maxima's declare (wrapped in a context so it is able
to forget).
INPUT:
- ``var`` - the variable about which assumptions are
being made
- ``assumption`` - a Maxima feature, either user
defined or in the list given by maxima('features')
EXAMPLES::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: decl = GenericDeclaration(x, 'integer')
sage: decl.assume()
sage: sin(x*pi)
sin(pi*x)
sage: sin(x*pi).simplify()
0
sage: decl.forget()
sage: sin(x*pi)
sin(pi*x)
Here is the list of acceptable features.
::
sage: maxima('features')
[integer,noninteger,even,odd,rational,irrational,real,imaginary,complex,analytic,increasing,decreasing,oddfun,evenfun,posfun,constant,commutative,lassociative,rassociative,symmetric,antisymmetric,integervalued]
"""
self._var = var
self._assumption = assumption
self._context = None
def __repr__(self):
"""
EXAMPLES::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: GenericDeclaration(x, 'foo')
x is foo
"""
return "%s is %s" % (self._var, self._assumption)
def __cmp__(self, other):
"""
TESTS::
sage: from sage.symbolic.assumptions import GenericDeclaration as GDecl
sage: var('y')
y
sage: GDecl(x, 'integer') == GDecl(x, 'integer')
True
sage: GDecl(x, 'integer') == GDecl(x, 'rational')
False
sage: GDecl(x, 'integer') == GDecl(y, 'integer')
False
"""
if isinstance(self, GenericDeclaration) and isinstance(other, GenericDeclaration):
return cmp( (self._var, self._assumption),
(other._var, other._assumption) )
else:
return cmp(type(self), type(other))
def has(self, arg):
"""
Check if this assumption contains the argument ``arg``.
EXAMPLES::
sage: from sage.symbolic.assumptions import GenericDeclaration as GDecl
sage: var('y')
y
sage: d = GDecl(x, 'integer')
sage: d.has(x)
True
sage: d.has(y)
False
"""
return (arg - self._var).is_trivial_zero()
def assume(self):
"""
TEST::
sage: from sage.symbolic.assumptions import GenericDeclaration
sage: decl = GenericDeclaration(x, 'even')
sage: decl.assume()
sage: cos(x*pi).simplify()
1
sage: decl2 = GenericDeclaration(x, 'odd')
sage: decl2.assume()
Traceback (most recent call last):
...
ValueError: Assumption is inconsistent
sage: decl.forget()
"""
from sage.calculus.calculus import maxima
if self._context is None:
# We get the list here because features may be added with time.
valid_features = list(maxima("features"))
if self._assumption not in [repr(x).strip() for x in list(valid_features)]:
raise ValueError, "%s not a valid assumption, must be one of %s" % (self._assumption, valid_features)
cur = maxima.get("context")
self._context = maxima.newcontext('context' + maxima._next_var_name())
try:
maxima.eval("declare(%s, %s)" % (repr(self._var), self._assumption))
# except TypeError, mess:
# if 'inconsistent' in str(mess): # note Maxima doesn't tell you if declarations are redundant
# raise ValueError, "Assumption is inconsistent"
except RuntimeError, mess:
if 'inconsistent' in str(mess): # note Maxima doesn't tell you if declarations are redundant
raise ValueError, "Assumption is inconsistent"
else:
raise
maxima.set("context", cur)
if not self in _assumptions:
maxima.activate(self._context)
_assumptions.append(self)