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Miraheze>Marshall (Created page with ":''This page describes the dyadic arithmetic function. For negation of a single argument, see Negate. For subtraction of sets, see Without.'' {{Built-in|Subtract|-}},...") |
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:''This page describes the dyadic arithmetic function. For negation of a single argument, see [[Negate]]. For subtraction of sets, see [[Without]].'' | :''This page describes the dyadic arithmetic function. For negation of a single argument, see [[Negate]]. For subtraction of sets, see [[Without]].'' | ||
{{Built-in|Subtract|-}}, '''Minus''', '''Subtraction''', or '''Difference''' is a [[dyadic]] [[scalar function]] which gives the arithmetic [[wikipedia:Subtraction|difference]] of its [[argument]]s. Subtract shares the [[glyph]] <source lang=apl inline>-</source> with the arithmetic | {{Built-in|Subtract|-}}, '''Minus''', '''Subtraction''', or '''Difference''' is a [[dyadic]] [[scalar function]] which gives the arithmetic [[wikipedia:Subtraction|difference]] of its [[argument]]s. Subtract shares the [[glyph]] <source lang=apl inline>-</source> with the arithmetic function [[Negate]], and its result is the left argument [[plus]] the negation of the right. | ||
== Examples == | == Examples == | ||
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== Properties == | == Properties == | ||
See also [[ | See also [[Add#Properties]]. | ||
Subtraction is anti-commutative: swapping the arguments negates the result, or using [[Commute]], <source lang=apl inline>-⍨</source> {{←→}} <source lang=apl inline>--</source>. | Subtraction is anti-commutative: swapping the arguments negates the result, or using [[Commute]], <source lang=apl inline>-⍨</source> {{←→}} <source lang=apl inline>--</source>. | ||
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7 | 7 | ||
</source> | </source> | ||
In the absense of rounding error we have <source lang=apl inline>-/v {{←→}} <source lang=apl inline>+/v×(⍴v)⍴1 ¯1</source> for a [[vector]] <source lang=apl inline>v</source>. | In the absense of rounding error we have <source lang=apl inline>-/v</source> {{←→}} <source lang=apl inline>+/v×(⍴v)⍴1 ¯1</source> for a [[vector]] <source lang=apl inline>v</source>. | ||
An interesting property of the alternating difference is that it can be used as a [[wikipedia:Divisibility rule|divisibility test]] for division by 11, a counterpart to the better-known test for divisibility by 9. A number is divisible by 11 if and only if the sum of its digits is divisible by 11, so repeatedly taking the alternating sum of the digits determines divisibility by 11. | An interesting property of the alternating difference is that it can be used as a [[wikipedia:Divisibility rule|divisibility test]] for division by 11, a counterpart to the better-known test for divisibility by 9. A number is divisible by 11 if and only if the sum of its digits is divisible by 11, so repeatedly taking the alternating sum of the digits determines divisibility by 11. | ||
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[[Scan]] with subtraction produces a prefix of an [[wikipedia:Alternating series|alternating series]]. This property is one of the reasons why scan was designed to reduce [[prefix]]es rather than [[suffix]]es of the argument array. As an example, we can see that an alternating series using the [[power]]s of two begins to converge to a third: | [[Scan]] with subtraction produces a prefix of an [[wikipedia:Alternating series|alternating series]]. This property is one of the reasons why scan was designed to reduce [[prefix]]es rather than [[suffix]]es of the argument array. As an example, we can see that an alternating series using the [[power]]s of two begins to converge to a third: | ||
<source lang=apl | <source lang=apl> | ||
-\ ÷2*⍳6 | -\ ÷2*⍳6 | ||
0.5 0.25 0.375 0.3125 0.34375 0.328125 | 0.5 0.25 0.375 0.3125 0.34375 0.328125 | ||
</source> | </source> | ||
== See also == | |||
* [[Divide]] | |||
* [[Without]] | |||
== External links == | == External links == | ||
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=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Subtract.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_040.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_040.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d120.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minus#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d120.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minus#dyadic NuVoc] | ||
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#basic-arithmetic BQN] | |||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] | |||