Element

Element[x,dom]
or asserts that x is an element of the domain dom.

Element[x,reg]
or asserts that x is an element of the region reg.

Element[x1|x2|,dom]
asserts that all the are elements of dom.

Element[patt,dom]
asserts that any expression matching the pattern patt is an element of dom.

DetailsDetails

  • can be entered as x EscelEsc dom or .
  • Element can be used to set up assumptions in Simplify and related functions.
  • dom may be a numeric domain or a region in .
  • Possible domains dom are:
  • Algebraicsalgebraic numbers
    BooleansTrue or False
    Complexescomplex numbers
    Integersintegers
    Primesprime numbers
    Rationalsrational numbers
    Realsreal numbers
  • Possible regions reg are defined by RegionQ.
  • if possible evaluates immediately when x is numeric.
  • For a domain dom, is equivalent to .
  • For a region reg, asserts that the point with coordinates belongs to reg.
  • is equivalent to .
  • evaluates to if its truth or falsity cannot immediately be determined.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Test whether is an element of the reals:

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Test whether the point belongs to the unit disk:

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Express domain membership for an expression:

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Assert that the point belongs to the unit ball:

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Use element assertions to integrate over a region:

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Or to optimize over a region:

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Enter using EscelemEsc:

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Introduced in 1999
(4.0)
| Updated in 2014
(10.0)