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Reciprocal of an expression

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1/ x


_invert(x) computes the reciprocal 1/x of x.

1/x is equivalent to the function call _invert(x). It represents the inverse of the element x with respect to multiplication, i.e., x * (1/x) = 1.

The reciprocal of a number of type Type::Numeric is returned as a number.

1/x is overloaded for matrix domains (matrix) and returns the inverse of the matrix x.

If x is not an element of a library domain with an "_invert" method, 1/x is internally represented as x^(-1) = _power(x, -1).

If x is an element of a domain with a slot"_invert", then this method is used to compute 1/x. Many library domains overload the / operator by an appropriate "_invert" slot. Note that a/x calls the overloading slot x::dom::_invert(x) only for a = 1.

If neither x nor y overload the binary operator / by a "_divide" method, the quotient x/y is equivalent to x * y^(-1) = _mult(x, _power(y, -1)).

For finite sets, 1/X is the set .


Example 1

The reciprocal of an expression is the inverse with respect to *:

_invert(x), x * (1/x) = x * _invert(x)

3 * y * x^2 / 27 / x

Internally, a symbolic expression 1/x is represented as x^(-1) = _power(x, -1):

type(1/x), op(1/x, 0), op(1/x, 1), op(1/x, 2)

Example 2

For finite sets, 1/X is the set :

1/{a, b, c}

Example 3

Various library domains such as matrix domains or residue class domains overload _invert:

x := Dom::Matrix(Dom::IntegerMod(7))([[2, 3], [3, 4]]):
x, 1/x, x * (1/x)

delete x:



An arithmetical expression or a set

Return Values

Arithmetical expression or a set.

Overloaded By


See Also

MuPAD Functions

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