Reciprocal of an expression
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1/ x
_invert(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
.
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)
For finite sets, 1/X
is the set
:
1/{a, b, c}
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 
Arithmetical expression or a set.
x