From 6f480d3706c9f01f2f9044f4f016853a1e8239e6 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Fri, 8 Jan 2021 19:09:35 -0500 Subject: =?UTF-8?q?There's=20no=20identity=20element=20for=20=E2=88=BE?= =?UTF-8?q?=CB=9D=20on=20an=20empty=20list?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/spec/inferred.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'docs/spec/inferred.html') diff --git a/docs/spec/inferred.html b/docs/spec/inferred.html index d4d22610..e1d08a02 100644 --- a/docs/spec/inferred.html +++ b/docs/spec/inferred.html @@ -66,7 +66,7 @@ -

Additionally, the identity of ∾˝ must be recognized: if 0=≠𝕩, then ∾˝𝕩 is (0∾2↓≢𝕩)⥊𝕩.

+

Additionally, the identity of ∾˝ must be recognized: if 0=≠𝕩 and 1<=𝕩, then ∾˝𝕩 is (0∾2↓≢𝕩)⥊𝕩. If 1==𝕩, then there is no identity element, as the result of ∾ always has rank at least 1, but the cell rank is 0.

Undo

The Undo 1-modifier ⁼, given an operand 𝔽 and argument 𝕩, and possibly a left argument 𝕨, finds a value y such that 𝕩≡𝕨𝔽y, that is, an element of the pre-image of 𝕩 under 𝔽 or 𝕨𝔽⊢. Thus it satisfies the constraint 𝕩 ≡ 𝕨𝔽𝕨𝔽⁼𝕩 (𝕨𝔽⁼⊢ is a right inverse of 𝕨𝔽⊢) provided 𝔽⁼ and 𝔽 both complete without error. 𝔽⁼ should of course give an error if no inverse element exists, and can also fail if no inverse can be found. It is also preferred for 𝔽⁼ to give an error if there are many choices of inverse with no clear way to choose one of them: for example, 0‿0⍉m returns the diagonal of matrix m; 0‿0⍉⁼2‿3 requires values to be chosen for the off-diagonal elements in its result. It is better to give an error, encouraging the programmer to use a fully-specified approach like 2‿3⌾(0‿0⊸⍉) applied to a matrix of initial elements, than to return a result that could be very different from other implementations.

When working with limited-precision numbers, it may be difficult or impossible to exactly invert the operand function. Instead, it is generally acceptable to perform a computation that, if done with unlimited precision, would exactly invert 𝔽 computed with unlimited precision. This principle is the basis for the numeric inverses specified below. It is also acceptable to find an inverse by numeric methods, provided that the error in the inverse value found relative to an unlimited-precision inverse can be kept close to the inherent error in the implementation's number format.

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