I want to verify certain inequalities involving real numbers and infinity. One case is showing certain expression is less than infinity. However, the following situation really puzzles me:
a = SR.var('a')
bool(a < infinity)
It returns 'False'. But when I do
assume(a < infinity)
It says
ValueError: Assumption is redundant
Why is this the case and how should I get 'True' for 'bool(a < infinity)'?
Thanks!
"When all else fails, RTFM..."
sage: x.is_infinity?
Docstring:
Return "True" if "self" is an infinite expression.
EXAMPLES:
sage: SR(oo).is_infinity()
True
sage: x.is_infinity()
False
Init docstring: Initialize self. See help(type(self)) for accurate signature.
File: /usr/local/sage-10/src/sage/symbolic/expression.pyx
Type: builtin_function_or_method
Illustration :
sage: foo=(1/x).limit(x=0)
sage: foo.is_infinity()
True
Note that :
sage: bool(foo>0)
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In[7], line 1
----> 1 bool(foo>Integer(0))
File /usr/local/sage-10/src/sage/symbolic/expression.pyx:3453, in sage.symbolic.expression.Expression.__bool__()
3451 pynac_result = decide_relational(self._gobj)
3452 if pynac_result == relational_undecidable:
-> 3453 raise ValueError('undecidable relation: ' + repr(self))
3454
3455 # pynac is guaranteed to give the correct answer for comparing infinities
ValueError: undecidable relation: Infinity > 0
HTH,
Why is this not contradicting to the ValueError in your example?
Multiple synonyms to the same quantity :
sage: infinity is Infinity
True
sage: Infinity is +Infinity
True
BTW :
sage: foo=(1/x).limit(x=0)
sage: foo is infinity
False
sage: foo is Infinity
False
sage: foo is +Infinity
False
and, furthermore
sage: bool(foo==infinity)
False
sage: bool(foo==Infinity)
False
sage: bool(foo==+Infinity)
False
HTH,
Asked: 2024-11-26 04:17:05 +0100
Seen: 108 times
Last updated: Nov 26
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