Trace

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Trace of a matrix or pair of tensor axes.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001919via PlanePartition✓↗Wolfram LanguageTr!↗

Trace(list<number> | number, axis1: integer?, axis2: integer?) -> list<number> | numberTrace of a matrix or pair of tensor axes.

Typed signatures

Type	Package	Applies
((plane_partition) -> number) & ((number | tensor, axis1: integer?, axis2: integer?) -> number | tensor)	combinatoricsreplaces compute-engine	always
(number | tensor, axis1: integer?, axis2: integer?) -> number | tensor	compute-engine	always

Domain: Compute engine

Definition

Epsil, as the implementation runs it.

on PlanePartition, over _x

0 if Length(Flatten(_x)) < 1 else Apply((reading: list<integer>) => Apply(
                                                                           (lengths: list<integer>) => Apply(
                                                                                                              (rowIds: list<integer>) => Apply(
                                                                                                                                                (columnIds: list<integer>) => Max(Sum(Map(Function(reading[u] if rowIds[u] == columnIds[u] else 0, u), Range(1, Length(reading), 1))), 0),
                                                                                                                                                Flatten(Map(Function(Range(1, lengths[i], 1), i), Range(1, Length(_x)))),
                                                                                                                                              ),
                                                                                                              Flatten(Map(
                                                                                                                           Function(Map(Function(i, j), Range(1, lengths[i], 1)), i),
                                                                                                                           Range(1, Length(_x)),
                                                                                                                         )),
                                                                                                            ),
                                                                           Map(
                                                                                Function(Length(r), r),
                                                                                _x,
                                                                              ),
                                                                         ), Flatten(_x))

Examples

Basic #

The sum of the diagonal

live ↗

In$\operatorname{tr}\left(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack\right)$Out$5$

live ↗

In$\operatorname{tr}\left(\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack\bigr\rbrack\right)$Out$15$

The plane partition with rows $32 \mid 21 \mid 1$: the diagonal entries $3$ and $1$

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{PlanePartition}}([[3, 2], [2, 1], [1]]), \text{Trace})$Out$4$

Scope #

live ↗

live ↗

In$\operatorname{tr}\left(\mathrm{Array}(a, \bigl\lbrack4, 3, 2\bigr\rbrack)\right)$Out$\operatorname{tr}\left(\bigl\lbrack\bigl\lbrack\bigl\lbrack a(1, 1, 1), a(1, 1, 2)\bigr\rbrack, \bigl\lbrack a(1, 2, 1), a(1, 2, 2)\bigr\rbrack, \bigl\lbrack a(1, 3, 1), a(1, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(2, 1, 1), a(2, 1, 2)\bigr\rbrack, \bigl\lbrack a(2, 2, 1), a(2, 2, 2)\bigr\rbrack, \bigl\lbrack a(2, 3, 1), a(2, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(3, 1, 1), a(3, 1, 2)\bigr\rbrack, \bigl\lbrack a(3, 2, 1), a(3, 2, 2)\bigr\rbrack, \bigl\lbrack a(3, 3, 1), a(3, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(4, 1, 1), a(4, 1, 2)\bigr\rbrack, \bigl\lbrack a(4, 2, 1), a(4, 2, 2)\bigr\rbrack, \bigl\lbrack a(4, 3, 1), a(4, 3, 2)\bigr\rbrack\bigr\rbrack\bigr\rbrack\right)$

live ↗

In$\operatorname{tr}(\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack\bigr\rbrack, f)$Out$15$

live ↗

In$\operatorname{tr}(\mathrm{Array}(a, \bigl\lbrack4, 3, 2\bigr\rbrack), f, 2)$Out$\operatorname{tr}(\bigl\lbrack\bigl\lbrack\bigl\lbrack a(1, 1, 1), a(1, 1, 2)\bigr\rbrack, \bigl\lbrack a(1, 2, 1), a(1, 2, 2)\bigr\rbrack, \bigl\lbrack a(1, 3, 1), a(1, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(2, 1, 1), a(2, 1, 2)\bigr\rbrack, \bigl\lbrack a(2, 2, 1), a(2, 2, 2)\bigr\rbrack, \bigl\lbrack a(2, 3, 1), a(2, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(3, 1, 1), a(3, 1, 2)\bigr\rbrack, \bigl\lbrack a(3, 2, 1), a(3, 2, 2)\bigr\rbrack, \bigl\lbrack a(3, 3, 1), a(3, 3, 2)\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack a(4, 1, 1), a(4, 1, 2)\bigr\rbrack, \bigl\lbrack a(4, 2, 1), a(4, 2, 2)\bigr\rbrack, \bigl\lbrack a(4, 3, 1), a(4, 3, 2)\bigr\rbrack\bigr\rbrack\bigr\rbrack, f, 2)$

About

Examples	7
Checked against	Wolfram Language 4 agree1 differSageMath 2 agree
Crosswalk	FindStatWolfram LanguageSageMath

Implementation

mappedsagepackages/oracle/src/mappings.ts