Or: Difference between revisions

From APL Wiki
Jump to navigation Jump to search
(→‎Extended definition: Split the description for integers and non-integers)
(Move GCD into a dedicated page)
Line 1: Line 1:
{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic.
{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic. In many APLs, Or is a special case of the [[GCD]] function.


{|class=wikitable
{|class=wikitable
Line 28: Line 28:
0
0
</source>
</source>
== Extended definition ==
Many APL implementations extend this function to non-Boolean arguments. In this case, this function behaves as '''[[wikipedia:Greatest common divisor|Greatest Common Divisor]]''' or '''GCD'''. For positive integer arguments, it is defined as the largest positive number which divides both numbers. If one of the arguments is zero, the GCD function returns the other number.
<source lang=apl>
      ∘.∨⍨ 0,⍳10
0 1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1  1
2 1 2 1 2 1 2 1 2 1  2
3 1 1 3 1 1 3 1 1 3  1
4 1 2 1 4 1 2 1 4 1  2
5 1 1 1 1 5 1 1 1 1  5
6 1 2 3 2 1 6 1 2 3  2
7 1 1 1 1 1 1 7 1 1  1
8 1 2 1 4 1 2 1 8 1  2
9 1 1 3 1 1 3 1 1 9  1
10 1 2 1 2 5 2 1 2 1 10
</source>{{Works in|[[Dyalog APL]]}}
While the mathematical definition of GCD does not cover non-integers, some implementations accept them as arguments. In this case, the return value of <source lang=apl inline>R←X∨Y</source> is chosen so that both <source lang=apl inline>X÷R</source> and <source lang=apl inline>Y÷R</source> are integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers).
<source lang=apl>
      0.6∨13÷3
0.06666666667
      0.6(13÷3)÷0.6∨13÷3
9 65
      2J2∨3J1
1J1
      2J2 3J1÷1J1
2 2J¯1
</source>{{Works in|[[Dyalog APL]]}}


== External links ==
== External links ==

Revision as of 14:47, 1 June 2020

∨

Or (∨) is a dyadic scalar boolean function which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the logical disjunction in Boolean logic. In many APLs, Or is a special case of the GCD function.

∨ 0 1
0 0 1
1 1 1

Examples

The following shows all possible combinations of inputs as a Boolean function. 

      0 0 1 1 ∨ 0 1 0 1
0 1 1 1

When combined with Reduce, Or can be used to test if some value in a Boolean vector is true. 

      ∨/ 0 0 1 0 1
1
      ∨/ 0 0 0 0 0
0

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
Retrieved from ‘https://aplwiki.com/index.php?title=Or&oldid=4621’