Property representing a residue class

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assume(x, (rem, class, <sub_set>))
is(ex, (rem, class, <sub_set>))
testtype(ex, (rem, class, <sub_set>))


Type::Residue(rem, class) represents the integers n for which n - rem is divisible by class.

The call assume(x, Type::Residue(rem, class)) marks the identifier x as an integer divisible by class with remainder rem.

The call is(ex, Type::Residue(rem, class)) derives, whether the expression ex is an integer divisible by class with remainder rem (or this property can be derived).

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

Type::Even and Type::Odd are objects created by Type::Residue.

The call testtype(obj, Type::Residue(rem, class)) checks, whether obj is an integer and is divisible by class with remainder rem. If the optional argument sub_set is given, testtype checks additionally testtype(obj, sub_set).


Example 1

Type::Residue can be used in testtype:

testtype(6, Type::Residue(2, 4)),
testtype(13, Type::Residue(1, 20))

Example 2

x is assumed to be divisible by 3 with remainder 1:

assume(x, Type::Residue(1, 3))

Which properties has x + 2 got?

getprop(x + 2)

x is an integer, but it may be odd or not:

is(x, Type::Integer), is(x, Type::Odd)

This example restricts possible values of x to odd integers:

assume(x, Type::Residue(1, 4));
is(x, Type::Odd),
is((-1)^x < 0)



An identifier or a mathematical expression containing identifiers


Remainder as integer number between 0 and class - 1; an integer larger than class - 1 will be divided by class and rem gets the remainder of this division


The divider as positive integer


A subset of the integers (e.g., Type::PosInt); otherwise Type::Integer is used


An arithmetical expression


Any MuPAD® object

Return Values

See assume, is and testtype

See Also

MuPAD Functions