Calculus¶
This module contains query handlers responsible for calculus queries: infinitesimal, finite, etc.
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class
sympy.assumptions.handlers.calculus.
AskFiniteHandler
[source]¶ Handler for key ‘finite’.
Test that an expression is bounded respect to all its variables.
Examples of usage:
>>> from sympy import Symbol, Q >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler >>> from sympy.abc import x >>> a = AskFiniteHandler() >>> a.Symbol(x, Q.positive(x)) == None True >>> a.Symbol(x, Q.finite(x)) True
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static
Add
(expr, assumptions)[source]¶ Return True if expr is bounded, False if not and None if unknown.
Truth Table:
B
U
?
‘+’
‘-‘
‘x’
‘+’
‘-‘
‘x’
B
B
U
?
U
‘+’
U
?
?
U
?
?
‘-‘
?
U
?
?
U
?
‘x’
?
?
?
?
‘B’ = Bounded
‘U’ = Unbounded
‘?’ = unknown boundedness
‘+’ = positive sign
‘-‘ = negative sign
‘x’ = sign unknown
All Bounded -> True
1 Unbounded and the rest Bounded -> False
>1 Unbounded, all with same known sign -> False
Any Unknown and unknown sign -> None
Else -> None
When the signs are not the same you can have an undefined result as in oo - oo, hence ‘bounded’ is also undefined.
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static
Mul
(expr, assumptions)[source]¶ Return True if expr is bounded, False if not and None if unknown.
Truth Table:
B
U
?
s
/s
B
B
U
?
U
U
U
?
?
?
B = Bounded
U = Unbounded
? = unknown boundedness
s = signed (hence nonzero)
/s = not signed
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static
Pow
(expr, assumptions)[source]¶ Unbounded ** NonZero -> Unbounded Bounded ** Bounded -> Bounded Abs()<=1 ** Positive -> Bounded Abs()>=1 ** Negative -> Bounded Otherwise unknown
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static
Symbol
(expr, assumptions)[source]¶ Handles Symbol.
Examples
>>> from sympy import Symbol, Q >>> from sympy.assumptions.handlers.calculus import AskFiniteHandler >>> from sympy.abc import x >>> a = AskFiniteHandler() >>> a.Symbol(x, Q.positive(x)) == None True >>> a.Symbol(x, Q.finite(x)) True
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static