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Outer Product: Difference between revisions
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However, it does not allow for creating a Cartesian pairing involving cells of the left argument specified with negative left rank L (except trivially, in cases in which Table's application has no effect, e.g. <syntaxhighlight lang=j inline>u"2 _"_ 1/</syntaxhighlight>). This is because negative assigned rank in J is encoded as infinite rank; in J's terminology, negative rank is "internal rank" only. | However, it does not allow for creating a Cartesian pairing involving cells of the left argument specified with negative left rank L (except trivially, in cases in which Table's application has no effect, e.g. <syntaxhighlight lang=j inline>u"2 _"_ 1/</syntaxhighlight>). This is because negative assigned rank in J is encoded as infinite rank; in J's terminology, negative rank is "internal rank" only. | ||
<syntaxhighlight lang=j> | <syntaxhighlight lang=j> | ||
+b.0 | }.+b.0 NB. dyadic ranks of + | ||
0 0 0 | 0 0 0 | ||
}.+"_1 _2 b.0 NB. | }.+"_1 _2 b.0 NB. dyadic ranks of derived verb +"_1 _2 as seen by Table | ||
_ _ | _ _ | ||
</syntaxhighlight> | </syntaxhighlight> | ||
{{Works in|[[J]]}} | |||
Given the <syntaxhighlight lang=j inline>u"(lu, _)</syntaxhighlight> definition of Table, even in a hypothetical J dialect in which assignment of negative rank is visible as such to modifiers, a left negative rank L used with Table would be applied twice (once by the ranks added by Table, and once by the operand itself). This would result in the L-cells ''of each of the left argument's L-cells'' being paired ''1-to-1'' with the specified cells of the right argument—not a Cartesian pairing. If a J dialect both allowed externally visible negative rank and defined Table to instead be <syntaxhighlight lang=j inline>u"lu _"_ ru</syntaxhighlight>, one could express e.g. the Cartesian pairing of the [[major cells]] of the left and right arguments as <syntaxhighlight lang=j inline>u"_1/</syntaxhighlight>. | Given the <syntaxhighlight lang=j inline>u"(lu, _)</syntaxhighlight> definition of Table, even in a hypothetical J dialect in which assignment of negative rank is visible as such to modifiers, a left negative rank L used with Table would be applied twice (once by the ranks added by Table, and once by the operand itself). This would result in the L-cells ''of each of the left argument's L-cells'' being paired ''1-to-1'' with the specified cells of the right argument—not a Cartesian pairing. If a J dialect both allowed externally visible negative rank and defined Table to instead be <syntaxhighlight lang=j inline>u"lu _"_ ru</syntaxhighlight>, one could express e.g. the Cartesian pairing of the [[major cells]] of the left and right arguments as <syntaxhighlight lang=j inline>u"_1/</syntaxhighlight>. | ||