Absolute value #
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This file defines a notational class has_abs which adds the unary operator abs and the notation
|.|. The concept of an absolute value occurs in lattice ordered groups and in GL and GM spaces.
Mathematical structures possessing an absolute value often also possess a unique decomposition of
elements into "positive" and "negative" parts which are in some sense "disjoint" (e.g. the Jordan
decomposition of a measure). This file also defines has_pos_part and has_neg_part classes
which add unary operators pos and neg, representing the maps taking an element to its positive
and negative part respectively along with the notation ⁺ and ⁻.
Notations #
The following notation is introduced:
|.|for the absolute value;.⁺for the positive part;.⁻for the negative part.
Tags #
absolute
- abs : α → α
Absolute value is a unary operator with properties similar to the absolute value of a real number.
Instances of this typeclass
Instances of other typeclasses for has_abs
- has_abs.has_sizeof_inst
- pos : α → α
The positive part of an element admiting a decomposition into positive and negative parts.
Instances for has_pos_part
- has_pos_part.has_sizeof_inst
- neg : α → α
The negative part of an element admiting a decomposition into positive and negative parts.
Instances for has_neg_part
- has_neg_part.has_sizeof_inst