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# Calculus¶

This module contains query handlers responsible for calculus queries: infinitesimal, bounded, etc.

Handler for key ‘bounded’.

Test that an expression is bounded respect to all its variables.

Examples of usage:

>>> from sympy import Symbol, Q
>>> from sympy.abc import x
>>> a.Symbol(x, Q.positive(x)) == None
True
>>> a.Symbol(x, Q.bounded(x))
True


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.

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
static Pow(expr, assumptions)[source]

Unbounded ** NonZero -> Unbounded Bounded ** Bounded -> Bounded Abs()<=1 ** Positive -> Bounded Abs()>=1 ** Negative -> Bounded Otherwise unknown

static Symbol(expr, assumptions)[source]

Handles Symbol.

Examples:

>>> from sympy import Symbol, Q
>>> from sympy.abc import x
>>> a.Symbol(x, Q.positive(x)) == None
True
>>> a.Symbol(x, Q.bounded(x))
True


Handler for key ‘infinitesimal’ Test that a given expression is equivalent to an infinitesimal number

Infinitesimal*Bounded -> Infinitesimal

static Mul(expr, assumptions)[source]

Infinitesimal*Bounded -> Infinitesimal

static Pow(expr, assumptions)

Infinitesimal*Bounded -> Infinitesimal

Handlers

nTheory