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Type and property representing even integers

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testtype(obj, Type::Even)
assume(x, Type::Even)
is(ex, Type::Even)


Type::Even represents even integers. This type can also be used as a property to mark identifiers as even integers.

The call testtype(obj, Type::Even) checks, whether obj is an even number and returns TRUE, if it holds, otherwise FALSE.

testtype only performs a syntactical test identifying MuPAD® objects of type DOM_INT and checks, if bool(domtype(x/2) = DOM_INT) holds.

The call assume(x, Type::Even) marks the identifier x as an even number.

The call is(ex, Type::Even) derives, whether the expression ex is an even number (or this property can be derived).

This type represents a property that can be used in assume and is.


Example 1

The following numbers are of type Type::Even:

testtype(2, Type::Even),
testtype(-4, Type::Even),
testtype(8, Type::Even),
testtype(-11114, Type::Even),
testtype(4185296581467695598, Type::Even)

Example 2

We use this type as a property:

assume(x, Type::Even):

The following calls to is derive the properties of a composite expression from the properties of its indeterminates:

is(3*x^2, Type::Even), is(x + 1, Type::Even)

is(x, Type::Integer), is(2*x, Type::Integer),
is(x/2, Type::Integer), is(x/3, Type::Integer)

assume(y, Type::Odd): is(x + y, Type::Even)

is(2*(x + y), Type::Even)

delete x, y:



Any MuPAD object


An identifier or a mathematical expression containing identifiers


An arithmetical expression

Return Values

See assume, is and testtype

See Also

MuPAD Functions

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