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| {{Built-in|Root|√}} (<source lang=j inline>%:</syntaxhighlight> in [[J]]) is a [[dyadic]] [[scalar function]] that computes the [[wikipedia:nth root|nth root]]; <source lang=apl inline>X√Y</syntaxhighlight> is equal to <source lang=apl inline>Y*÷X</syntaxhighlight>, the right [[argument]] raised to the [[power]] of the [[reciprocal]] of the left argument. The positioning of arguments resembles the [[Comparison with traditional mathematics#Explicitness|mathematical notation]] <math>\sqrt[x]{y}</math>. Root shares the [[glyph]] <source lang=apl inline>√</syntaxhighlight> with the monadic function [[Square Root]], which is the same as Root with the default left argument of 2. Root is defined in [[J]], [[NARS2000]], [[dzaima/APL]], and [[Extended Dyalog APL]]. | | {{Built-in|Root|√}} (<syntaxhighlight lang=j inline>%:</syntaxhighlight> in [[J]]) is a [[dyadic]] [[scalar function]] that computes the [[wikipedia:nth root|nth root]]; <syntaxhighlight lang=apl inline>X√Y</syntaxhighlight> is equal to <syntaxhighlight lang=apl inline>Y*÷X</syntaxhighlight>, the right [[argument]] raised to the [[power]] of the [[reciprocal]] of the left argument. The positioning of arguments resembles the [[Comparison with traditional mathematics#Explicitness|mathematical notation]] <math>\sqrt[x]{y}</math>. Root shares the [[glyph]] <syntaxhighlight lang=apl inline>√</syntaxhighlight> with the monadic function [[Square Root]], which is the same as Root with the default left argument of 2. Root is defined in [[J]], [[NARS2000]], [[dzaima/APL]], and [[Extended Dyalog APL]]. |
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| == See also == | | == See also == |
Latest revision as of 22:10, 10 September 2022
Root (√) (%: in J) is a dyadic scalar function that computes the nth root; X√Y is equal to Y*÷X, the right argument raised to the power of the reciprocal of the left argument. The positioning of arguments resembles the mathematical notation ![{\displaystyle {\sqrt[{x}]{y}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/58c28156258e3c4cf15e8af14abcc0163150e3e6)
. Root shares the glyph √ with the monadic function Square Root, which is the same as Root with the default left argument of 2. Root is defined in J, NARS2000, dzaima/APL, and Extended Dyalog APL.
See also
External links
Documentation
| APL built-ins [edit]
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| Primitives (Timeline) |
Functions
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| Scalar
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| Monadic
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Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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| Dyadic
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Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
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| Non-Scalar
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| Structural
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Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
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| Selection
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First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
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| Selector
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Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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| Computational
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Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
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| Operators |
Monadic
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Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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| Dyadic
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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)
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| Quad names
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Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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