$Assumptions
is the default setting for the Assumptions option used in such functions as Simplify, Refine, and Integrate.
Details
- The value of $Assumptions can be modified using Assuming.
- The initial setting for $Assumptions is True.
Examples
open all close allBasic Examples (1)
$Assumptions = a > 0The assumptions are now used by Refine and Integrate:
Refine[Sqrt[a ^ 2b ^ 2]]Integrate[x ^ a, {x, 0, 1}]Assuming[b < 0, Refine[Sqrt[a ^ 2b ^ 2]]]$AssumptionsBlock[{$Assumptions = a < 0 && b < 0}, Refine[Sqrt[a ^ 2b ^ 2]]]Remove the global assumptions:
$Assumptions = TrueScope (3)
Specify assumptions for simplifiers:
operations := {Refine[Sin[n Pi]], Simplify[Mod[n ^ p, p]], FullSimplify[EulerPhi[p ^ n] - p ^ n], FunctionExpand[Factorial2[n]]};Block[{$Assumptions = n∈Integers && p∈Primes && n > 0}, operations]Specify assumptions for Integrate and in integral transforms:
Block[{$Assumptions = a > 0}, {Integrate[1 / (x + a), {x, 0, 1}], FourierTransform[1 / (x ^ 2 + a), x, w]}]Specify assumptions for Limit and Series:
Block[{$Assumptions = a > 0}, {Limit[x ^ a, x -> Infinity], Series[Min[x ^ 2, 1 + a]Cos[x] + Sin[x], {x, 0, 2}]}]Properties & Relations (1)
Assuming locally adds assumptions to $Assumptions:
Block[{$Assumptions = x > 0}, Assuming[y > 0, {$Assumptions, Refine[Sqrt[x ^ 2y ^ 2]]}]]Possible Issues (1)
When Assumptions option is set directly, assumptions given with $Assumptions are not used:
Block[{$Assumptions = x > 0}, Simplify[Sqrt[x ^ 2 y ^ 2], Assumptions -> y < 0]]Text
Wolfram Research (2003), $Assumptions, Wolfram Language function, https://reference.wolfram.com/language/ref/$Assumptions.html.
CMS
Wolfram Language. 2003. "$Assumptions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/$Assumptions.html.
APA
Wolfram Language. (2003). $Assumptions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/$Assumptions.html