120
edits
Add: Difference between revisions
Jump to navigation
Jump to search
m
9 revisions imported: Migrate from miraheze
Miraheze>Marshall |
m (9 revisions imported: Migrate from miraheze) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Built-in|Add|+}}, '''Plus''', '''Addition''', or '''Sum''', is a [[dyadic]] [[scalar function]] that [ | {{Built-in|Add|+}}, '''Plus''', '''Addition''', or '''Sum''', is a [[dyadic]] [[scalar function]] that [[wikipedia:Addition|adds]] numbers together. As a [[basic arithmetic]] operation, Add is subject to the language's [[number]] specification. Add shares the glyph <source lang=apl inline>+</source> with the [[monadic]] function [[Conjugate]], and is closely related to [[Subtract]] (<source lang=apl inline>-</source>). | ||
== Examples == | == Examples == | ||
| Line 20: | Line 20: | ||
== Scalar mapping == | == Scalar mapping == | ||
In mathematics, addition of two identical structures almost always follows the same rules as in APL: it maps over the structures element-wise. This is a fundamental property of a (finite-dimensional) [ | In mathematics, addition of two identical structures almost always follows the same rules as in APL: it maps over the structures element-wise. This is a fundamental property of a (finite-dimensional) [[wikipedia:vector space|vector space]], in which addition of two vectors is equivalent to adding the coefficients of basis vectors one by one. This property likely inspired APL's definition of a scalar function. | ||
Addition of [[Complex number|complex]] and [[hypercomplex numbers]] can also be considered an element-wise operation, since each of these types of numbers forms a vector space over the reals. Addition of scalars is always performed within a single domain: mixed-type addition such as adding a real to a complex number treats the real number as complex with imaginary part zero. | Addition of [[Complex number|complex]] and [[hypercomplex numbers]] can also be considered an element-wise operation, since each of these types of numbers forms a vector space over the reals. Addition of scalars is always performed within a single domain: mixed-type addition such as adding a real to a complex number treats the real number as complex with imaginary part zero. | ||
| Line 45: | Line 45: | ||
* [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Add.htm Dyalog] | * [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Add.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_020.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_020.htm APLX] | ||
* [https://www.jsoftware.com/help/dictionary/d100.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plus#dyadic J NuVoc] | * [https://www.jsoftware.com/help/dictionary/d100.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plus#dyadic J NuVoc] | ||
{{APL built-ins}} | {{APL built-ins}} | ||