Determinant

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

Determinant of a square matrix.

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

Determinant(matrix) -> numberas compute-engine declares it

SageMathmatrix(matrix).det()

Typed signatures

Type	Package	Applies
(matrix) -> number	compute-engine	always

Domain: Compute engine

Examples

Basic #

Equal columns make the determinant vanish, even symbolically

live ↗

In$\det\left(\bigl\lbrack\bigl\lbrack a_1, a_1\bigr\rbrack, \bigl\lbrack a_2, a_2\bigr\rbrack\bigr\rbrack\right)$Out$0$

A singular classic: rows in arithmetic progression give 0

live ↗

In$\det\left(\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack\bigr\rbrack\right)$Out$0$

Scope #

Complex and symbolic entries mix freely

live ↗

In$\det\left(\bigl\lbrack\bigl\lbrack1+i, 2, 3-2i\bigr\rbrack, \bigl\lbrack0, 4π, 5i\bigr\rbrack, \bigl\lbrack3, 0, 6\bigr\rbrack\bigr\rbrack\right)$Out$30i+(-12+48i)π$

An exact integer $3\times3$ determinant

live ↗

In$\det\left(\bigl\lbrack\bigl\lbrack1, 2, 4\bigr\rbrack, \bigl\lbrack5, 4, 5\bigr\rbrack, \bigl\lbrack9, 2, 7\bigr\rbrack\bigr\rbrack\right)$Out$-66$

live ↗

In$\det\left(\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, m, f\bigr\rbrack, \bigl\lbrack g, h, k\bigr\rbrack\bigr\rbrack\right)$Out$bfg+cdh-afh-bdk-cgm+akm$

live ↗

In$\det\left(\mathrm{IdentityMatrix}(22)\right)$Out$1$

Applications #

Swapping sign: $-\det A$ is $4$ here

live ↗

In$-\det\left(\bigl\lbrack\bigl\lbrack1, 3, 4\bigr\rbrack, \bigl\lbrack5, 7, 8\bigr\rbrack, \bigl\lbrack5, 2, 1\bigr\rbrack\bigr\rbrack\right)$Out$4$

About

Examples	7
Checked against	Wolfram Language 7 agreeSageMath 6 agree
Crosswalk	Wolfram LanguageSageMath

Implementation

mappedsagepackages/oracle/src/mappings.ts