def __cmp__(cls, other):
# If the other object is not a Basic subclass, then we are not equal to
# it.
if not isinstance(other, BasicType):
return -1
n1 = cls.__name__
n2 = other.__name__
c = cmp(n1,n2)
if not c: return 0
UNKNOWN = len(ordering_of_classes)+1
try:
i1 = ordering_of_classes.index(n1)
except ValueError:
#print 'Add',n1,'to basic.ordering_of_classes list'
#return c
i1 = UNKNOWN
try:
i2 = ordering_of_classes.index(n2)
except ValueError:
#print 'Add',n2,'to basic.ordering_of_classes list'
#return c
i2 = UNKNOWN
if i1 == UNKNOWN and i2 == UNKNOWN:
return c
return cmp(i1,i2)
def __cmp__(self, other):
"""Comparison of two GeometryEntities."""
n1 = self.__class__.__name__
n2 = other.__class__.__name__
c = cmp(n1, n2)
if not c:
return 0
i1 = -1
for cls in self.__class__.__mro__:
try:
i1 = ordering_of_classes.index(cls.__name__)
break
except ValueError:
i1 = -1
if i1 == -1:
return c
i2 = -1
for cls in other.__class__.__mro__:
try:
i2 = ordering_of_classes.index(cls.__name__)
break
except ValueError:
i2 = -1
if i2 == -1:
return c
return cmp(i1, i2)
def __cmp__(self, other):
"""Comparison of two GeometryEntities."""
n1 = self.__class__.__name__
n2 = other.__class__.__name__
c = cmp(n1, n2)
if not c:
return 0
i1 = -1
for cls in self.__class__.__mro__:
try:
i1 = ordering_of_classes.index(cls.__name__)
break
except ValueError:
i1 = -1
if i1 == -1:
return c
i2 = -1
for cls in other.__class__.__mro__:
try:
i2 = ordering_of_classes.index(cls.__name__)
break
except ValueError:
i2 = -1
if i2 == -1:
return c
return cmp(i1, i2)
def __cmp__(cls, other):
# If the other object is not a Basic subclass, then we are not equal to
# it.
if not isinstance(other, BasicType):
return -1
n1 = cls.__name__
n2 = other.__name__
c = cmp(n1, n2)
if not c: return 0
UNKNOWN = len(ordering_of_classes) + 1
try:
i1 = ordering_of_classes.index(n1)
except ValueError:
#print 'Add',n1,'to basic.ordering_of_classes list'
#return c
i1 = UNKNOWN
try:
i2 = ordering_of_classes.index(n2)
except ValueError:
#print 'Add',n2,'to basic.ordering_of_classes list'
#return c
i2 = UNKNOWN
if i1 == UNKNOWN and i2 == UNKNOWN:
return c
return cmp(i1, i2)
def compare_pretty(a, b):
"""
Is a > b in the sense of ordering in printing?
THIS FUNCTION IS DEPRECATED. Use ``default_sort_key`` instead.
::
yes ..... return 1
no ...... return -1
equal ... return 0
Strategy:
It uses Basic.compare as a fallback, but improves it in many cases,
like ``x**3``, ``x**4``, ``O(x**3)`` etc. In those simple cases, it just parses the
expression and returns the "sane" ordering such as::
1 < x < x**2 < x**3 < O(x**4) etc.
Examples
========
>>> from sympy.abc import x
>>> from sympy import Basic, Number
>>> Basic._compare_pretty(x, x**2)
-1
>>> Basic._compare_pretty(x**2, x**2)
0
>>> Basic._compare_pretty(x**3, x**2)
1
>>> Basic._compare_pretty(Number(1, 2), Number(1, 3))
1
>>> Basic._compare_pretty(Number(0), Number(-1))
1
"""
try:
a = _sympify(a)
except SympifyError:
pass
try:
b = _sympify(b)
except SympifyError:
pass
# both objects are non-SymPy
if (not isinstance(a, Basic)) and (not isinstance(b, Basic)):
return cmp(a, b)
if not isinstance(a, Basic):
return -1 # other < sympy
if not isinstance(b, Basic):
return +1 # sympy > other
# now both objects are from SymPy, so we can proceed to usual comparison
return cmp(a.sort_key(), b.sort_key())
def compare_pretty(a, b):
"""
Is a > b in the sense of ordering in printing?
THIS FUNCTION IS DEPRECATED. Use ``default_sort_key`` instead.
::
yes ..... return 1
no ...... return -1
equal ... return 0
Strategy:
It uses Basic.compare as a fallback, but improves it in many cases,
like ``x**3``, ``x**4``, ``O(x**3)`` etc. In those simple cases, it just parses the
expression and returns the "sane" ordering such as::
1 < x < x**2 < x**3 < O(x**4) etc.
Examples
========
>>> from sympy.abc import x
>>> from sympy import Basic, Number
>>> Basic._compare_pretty(x, x**2)
-1
>>> Basic._compare_pretty(x**2, x**2)
0
>>> Basic._compare_pretty(x**3, x**2)
1
>>> Basic._compare_pretty(Number(1, 2), Number(1, 3))
1
>>> Basic._compare_pretty(Number(0), Number(-1))
1
"""
try:
a = _sympify(a)
except SympifyError:
pass
try:
b = _sympify(b)
except SympifyError:
pass
# both objects are non-SymPy
if (not isinstance(a, Basic)) and (not isinstance(b, Basic)):
return cmp(a, b)
if not isinstance(a, Basic):
return -1 # other < sympy
if not isinstance(b, Basic):
return +1 # sympy > other
# now both objects are from SymPy, so we can proceed to usual comparison
return cmp(a.sort_key(), b.sort_key())
def compare(self, other):
"""
Return -1, 0, 1 if the object is smaller, equal, or greater than other.
Not in the mathematical sense. If the object is of a different type
from the "other" then their classes are ordered according to
the sorted_classes list.
Examples
========
>>> from sympy.abc import x, y
>>> x.compare(y)
-1
>>> x.compare(x)
0
>>> y.compare(x)
1
"""
# all redefinitions of __cmp__ method should start with the
# following three lines:
if self is other:
return 0
c = cmp(self.__class__, other.__class__)
if c:
return c
#
st = self._hashable_content()
ot = other._hashable_content()
c = cmp(len(st), len(ot))
if c:
return c
for l, r in zip(st, ot):
if isinstance(l, Basic):
c = l.compare(r)
elif isinstance(l, frozenset):
c = 0
else:
c = cmp(l, r)
if c:
return c
return 0
def compare(self, other):
"""
Return -1, 0, 1 if the object is smaller, equal, or greater than other.
Not in the mathematical sense. If the object is of a different type
from the "other" then their classes are ordered according to
the sorted_classes list.
Examples
========
>>> from sympy.abc import x, y
>>> x.compare(y)
-1
>>> x.compare(x)
0
>>> y.compare(x)
1
"""
# all redefinitions of __cmp__ method should start with the
# following three lines:
if self is other:
return 0
c = cmp(self.__class__, other.__class__)
if c:
return c
#
st = self._hashable_content()
ot = other._hashable_content()
c = cmp(len(st), len(ot))
if c:
return c
for l, r in zip(st, ot):
if isinstance(l, Basic):
c = l.compare(r)
elif isinstance(l, frozenset):
c = 0
else:
c = cmp(l, r)
if c:
return c
return 0
def test_logic_cmp():
l1 = And('a', Not('b'))
l2 = And('a', Not('b'))
assert hash(l1) == hash(l2)
assert (l1==l2) == T
assert (l1!=l2) == F
assert cmp(l1, l2) == 0
assert And('a','b','c') == And('b','a','c')
assert And('a','b','c') == And('c','b','a')
assert And('a','b','c') == And('c','a','b')
def sdp_add_term(f, term, u, O, K):
"""Add a single term using bisection method. """
M, c = term
if not c:
return f
if not f:
return [(M, c)]
monoms = sdp_monoms(f)
if cmp(O(M), O(monoms[ 0])) > 0:
return [(M, c)] + f
if cmp(O(M), O(monoms[-1])) < 0:
return f + [(M, c)]
lo, hi = 0, len(monoms)-1
while lo <= hi:
i = (lo + hi) // 2
j = cmp(O(M), O(monoms[i]))
if not j:
coeff = f[i][1] + c
if not coeff:
return f[:i] + f[i+1:]
else:
return f[:i] + [(M, coeff)] + f[i+1:]
else:
if j > 0:
hi = i - 1
else:
lo = i + 1
else:
return f[:i] + [(M, c)] + f[i+1:]
def sdp_sub_term(f, term, u, O, K):
"""Sub a single term using bisection method. """
M, c = term
if not c:
return f
if not f:
return [(M, -c)]
monoms = sdp_monoms(f)
if cmp(O(M), O(monoms[0])) > 0:
return [(M, -c)] + f
if cmp(O(M), O(monoms[-1])) < 0:
return f + [(M, -c)]
lo, hi = 0, len(monoms) - 1
while lo <= hi:
i = (lo + hi) // 2
j = cmp(O(M), O(monoms[i]))
if not j:
coeff = f[i][1] - c
if not coeff:
return f[:i] + f[i + 1:]
else:
return f[:i] + [(M, coeff)] + f[i + 1:]
else:
if j > 0:
hi = i - 1
else:
lo = i + 1
else:
return f[:i] + [(M, -c)] + f[i + 1:]
def _compare_pretty(a, b):
from sympy.series.order import Order
if isinstance(a, Order) and not isinstance(b, Order):
return 1
if not isinstance(a, Order) and isinstance(b, Order):
return -1
if a.is_Rational and b.is_Rational:
return cmp(a.p*b.q, b.p*a.q)
else:
from sympy.core.symbol import Wild
p1, p2, p3 = Wild("p1"), Wild("p2"), Wild("p3")
r_a = a.match(p1 * p2**p3)
if r_a and p3 in r_a:
a3 = r_a[p3]
r_b = b.match(p1 * p2**p3)
if r_b and p3 in r_b:
b3 = r_b[p3]
c = Basic.compare(a3, b3)
if c != 0:
return c
return Basic.compare(a,b)
def _compare_pretty(a, b):
from sympy.series.order import Order
if isinstance(a, Order) and not isinstance(b, Order):
return 1
if not isinstance(a, Order) and isinstance(b, Order):
return -1
if a.is_Rational and b.is_Rational:
return cmp(a.p * b.q, b.p * a.q)
else:
from sympy.core.symbol import Wild
p1, p2, p3 = Wild("p1"), Wild("p2"), Wild("p3")
r_a = a.match(p1 * p2**p3)
if r_a and p3 in r_a:
a3 = r_a[p3]
r_b = b.match(p1 * p2**p3)
if r_b and p3 in r_b:
b3 = r_b[p3]
c = Basic.compare(a3, b3)
if c != 0:
return c
return Basic.compare(a, b)
def monomial_grlex_cmp(a, b):
return cmp(sum(a), sum(b)) or cmp(a, b)
def monomial_lex_cmp(a, b):
return cmp(a, b)
def _what_known_about(self, k):
"""tries hard to give an answer to: what is known about fact `k`
NOTE: You should not use this directly -- see make__get_assumption
instead
This function is called when a request is made to see what a fact
value is.
If we are here, it means that the asked-for fact is not known, and
we should try to find a way to find its value.
For this we use several techniques:
1. _eval_is_<fact>
------------------
first fact-evaluation function is tried, for example
_eval_is_integer
2. relations
------------
if the first step did not succeeded (no such function, or its return
is None) then we try related facts. For example
means
rational --> integer
another example is joined rule:
integer & !odd --> even
so in the latter case if we are looking at what 'even' value is,
'integer' and 'odd' facts will be asked.
3. evalf() for comparable
-------------------------
as a last resort for comparable objects we get their numerical value
-- this helps to determine facts like 'positive' and 'negative'
In all cases when we settle on some fact value, it is given to
_learn_new_facts to deduce all its implications, and also the result
is cached in ._assumptions for later quick access.
"""
if k not in _assume_defined:
raise AttributeError('undefined assumption %r' % (k))
seen = self._a_inprogress
if k in seen:
raise CycleDetected
seen.append(k)
try:
# First try the assumption evaluation function if it exists
if hasattr(self, '_eval_is_' + k):
try:
a = getattr(self, '_eval_is_' + k)()
except CycleDetected:
pass
else:
if a is not None:
self._learn_new_facts(((k, a), ))
return a
# Try assumption's prerequisites
for pk in _assume_rules.prereq[k]:
if hasattr(self, '_eval_is_' + pk):
# cycle
if pk in seen:
continue
a = getattr(self, 'is_' + pk)
if a is not None:
self._learn_new_facts(((pk, a), ))
# it is possible that we either know or don't know k at
# this point
try:
return self._assumptions[k]
except KeyError:
pass
finally:
seen.pop()
# For positive/negative try to ask evalf
if k in _real_ordering and self.is_comparable:
e = self.evalf()
if e.is_Number:
a = _real_cmp0_table[k][cmp(e, 0)]
if a is not None:
self._learn_new_facts(((k, a), ))
return a
# No result -- unknown
# cache it (NB ._learn_new_facts(k, None) to learn other properties,
# and because assumptions may not be detached)
self._learn_new_facts(((k, None), ))
return None
def monomial_grevlex_cmp(a, b):
return cmp(sum(a), sum(b)) or cmp(tuple(reversed(b)), tuple(reversed(a)))
def __cmp__(a, b):
if type(a) is not type(b):
return cmp( str(type(a)), str(type(b)) )
else:
return cmp(a.args, b.args)
def __cmp__(a, b):
if type(a) is not type(b):
return cmp(str(type(a)), str(type(b)))
else:
return cmp(a.args, b.args)
def _compare_pretty(a, b):
return cmp(str(a), str(b))
def monomial_grevlex_cmp(a, b):
return cmp(sum(a), sum(b)) or cmp(tuple(reversed(b)), tuple(reversed(a)))
def _compare_pretty(a, b):
return cmp(str(a), str(b))
def monomial_lex_cmp(a, b):
return cmp(a, b)
def _what_known_about(self, k):
"""tries hard to give an answer to: what is known about fact `k`
NOTE: You should not use this directly -- see make__get_assumption
instead
This function is called when a request is made to see what a fact
value is.
If we are here, it means that the asked-for fact is not known, and
we should try to find a way to find its value.
For this we use several techniques:
1. _eval_is_<fact>
------------------
first fact-evaluation function is tried, for example
_eval_is_integer
2. relations
------------
if the first step did not succeeded (no such function, or its return
is None) then we try related facts. For example
means
rational --> integer
another example is joined rule:
integer & !odd --> even
so in the latter case if we are looking at what 'even' value is,
'integer' and 'odd' facts will be asked.
3. evalf() for comparable
-------------------------
as a last resort for comparable objects we get their numerical value
-- this helps to determine facts like 'positive' and 'negative'
In all cases when we settle on some fact value, it is given to
_learn_new_facts to deduce all its implications, and also the result
is cached in ._assumptions for later quick access.
"""
if k not in _assume_defined:
raise AttributeError('undefined assumption %r' % (k))
seen = self._a_inprogress
if k in seen:
raise CycleDetected
seen.append(k)
try:
# First try the assumption evaluation function if it exists
if hasattr(self, '_eval_is_' + k):
try:
a = getattr(self, '_eval_is_' + k)()
except CycleDetected:
pass
else:
if a is not None:
self._learn_new_facts( ((k, a),) )
return a
# Try assumption's prerequisites
for pk in _assume_rules.prereq[k]:
if hasattr(self, '_eval_is_' + pk):
# cycle
if pk in seen:
continue
a = getattr(self, 'is_' + pk)
if a is not None:
self._learn_new_facts( ((pk,a),) )
# it is possible that we either know or don't know k at
# this point
try:
return self._assumptions[k]
except KeyError:
pass
finally:
seen.pop()
# For positive/negative try to ask evalf
if k in _real_ordering and self.is_comparable:
e = self.evalf(1)
if e.is_Number:
a = _real_cmp0_table[k][cmp(e, 0)]
if a is not None:
self._learn_new_facts( ((k,a),) )
return a
# No result -- unknown
# cache it (NB ._learn_new_facts(k, None) to learn other properties,
# and because assumptions may not be detached)
self._learn_new_facts( ((k,None),) )
return None
def monomial_grlex_cmp(a, b):
return cmp(sum(a), sum(b)) or cmp(a, b)