Advanced Search

Question: How to force Maple to use basic math results?

Question:How to force Maple to use basic math results?

Harry Garst 239 Maple
linear-algebra abstract simplification kronecker
November 22 2024
1

Is there a way to force Maple to use basic linear algebra results?
Here is a result you can find in any linear algebra book (this one comes from Harville's Matrix Algebra From a Statistician's Perspective)
I'm using Maple to check my work and it would be helpful if some basic linear algebra results would be injected in Maple's algorithm.

> 

kernelopts(version); interface(version)

`Maple 2024.2, X86 64 WINDOWS, Oct 29 2024, Build ID 1872373`

  

`Standard Worksheet Interface, Maple 2024.2, Windows 11, October 29 2024 Build ID 1872373`

 (1)
> 

restart; with(LinearAlgebra)
> 

alias(`⨂` = LinearAlgebra:-KroneckerProduct)

`⨂`

 (2)

> 

for dim from 2 to 5 do A := Matrix(dim, dim, shape = symmetric, symbol = a); print(dim, Equal(1/`⨂`(A, A), `⨂`(1/A, 1/A)), simplify(1/`⨂`(A, A)-`⨂`(1/A, 1/A), symbolic)) end do; for dim from 2 to 5 do A := Matrix(dim, dim, shape = symmetric, symbol = a); print(dim, Equal(simplify(1/`⨂`(A, A)), simplify(`⨂`(1/A, 1/A))), simplify(1/`⨂`(A, A)-`⨂`(1/A, 1/A), symbolic)) end do

2, true, [`?`]

  

3, false, [`?`]

  

4, false, Matrix(16, 16, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (2, 15) = 0, (2, 16) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (3, 16) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (5, 16) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (6, 15) = 0, (6, 16) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (7, 16) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 0, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (8, 15) = 0, (8, 16) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (9, 16) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 0, (10, 13) = 0, (10, 14) = 0, (10, 15) = 0, (10, 16) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (11, 16) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 0, (12, 15) = 0, (12, 16) = 0, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (13, 16) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0, (14, 15) = 0, (14, 16) = 0, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (15, 16) = 0, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = 0, (16, 5) = 0, (16, 6) = 0, (16, 7) = 0, (16, 8) = 0, (16, 9) = 0, (16, 10) = 0, (16, 11) = 0, (16, 12) = 0, (16, 13) = 0, (16, 14) = 0, (16, 15) = 0, (16, 16) = 0})

  

5, false, Matrix(25, 25, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (1, 17) = 0, (1, 18) = 0, (1, 19) = 0, (1, 20) = 0, (1, 21) = 0, (1, 22) = 0, (1, 23) = 0, (1, 24) = 0, (1, 25) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (2, 15) = 0, (2, 16) = 0, (2, 17) = 0, (2, 18) = 0, (2, 19) = 0, (2, 20) = 0, (2, 21) = 0, (2, 22) = 0, (2, 23) = 0, (2, 24) = 0, (2, 25) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (3, 16) = 0, (3, 17) = 0, (3, 18) = 0, (3, 19) = 0, (3, 20) = 0, (3, 21) = 0, (3, 22) = 0, (3, 23) = 0, (3, 24) = 0, (3, 25) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 0, (4, 17) = 0, (4, 18) = 0, (4, 19) = 0, (4, 20) = 0, (4, 21) = 0, (4, 22) = 0, (4, 23) = 0, (4, 24) = 0, (4, 25) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (5, 16) = 0, (5, 17) = 0, (5, 18) = 0, (5, 19) = 0, (5, 20) = 0, (5, 21) = 0, (5, 22) = 0, (5, 23) = 0, (5, 24) = 0, (5, 25) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (6, 15) = 0, (6, 16) = 0, (6, 17) = 0, (6, 18) = 0, (6, 19) = 0, (6, 20) = 0, (6, 21) = 0, (6, 22) = 0, (6, 23) = 0, (6, 24) = 0, (6, 25) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (7, 16) = 0, (7, 17) = 0, (7, 18) = 0, (7, 19) = 0, (7, 20) = 0, (7, 21) = 0, (7, 22) = 0, (7, 23) = 0, (7, 24) = 0, (7, 25) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 0, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (8, 15) = 0, (8, 16) = 0, (8, 17) = 0, (8, 18) = 0, (8, 19) = 0, (8, 20) = 0, (8, 21) = 0, (8, 22) = 0, (8, 23) = 0, (8, 24) = 0, (8, 25) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (9, 16) = 0, (9, 17) = 0, (9, 18) = 0, (9, 19) = 0, (9, 20) = 0, (9, 21) = 0, (9, 22) = 0, (9, 23) = 0, (9, 24) = 0, (9, 25) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 0, (10, 13) = 0, (10, 14) = 0, (10, 15) = 0, (10, 16) = 0, (10, 17) = 0, (10, 18) = 0, (10, 19) = 0, (10, 20) = 0, (10, 21) = 0, (10, 22) = 0, (10, 23) = 0, (10, 24) = 0, (10, 25) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (11, 16) = 0, (11, 17) = 0, (11, 18) = 0, (11, 19) = 0, (11, 20) = 0, (11, 21) = 0, (11, 22) = 0, (11, 23) = 0, (11, 24) = 0, (11, 25) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 0, (12, 15) = 0, (12, 16) = 0, (12, 17) = 0, (12, 18) = 0, (12, 19) = 0, (12, 20) = 0, (12, 21) = 0, (12, 22) = 0, (12, 23) = 0, (12, 24) = 0, (12, 25) = 0, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (13, 16) = 0, (13, 17) = 0, (13, 18) = 0, (13, 19) = 0, (13, 20) = 0, (13, 21) = 0, (13, 22) = 0, (13, 23) = 0, (13, 24) = 0, (13, 25) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0, (14, 15) = 0, (14, 16) = 0, (14, 17) = 0, (14, 18) = 0, (14, 19) = 0, (14, 20) = 0, (14, 21) = 0, (14, 22) = 0, (14, 23) = 0, (14, 24) = 0, (14, 25) = 0, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (15, 16) = 0, (15, 17) = 0, (15, 18) = 0, (15, 19) = 0, (15, 20) = 0, (15, 21) = 0, (15, 22) = 0, (15, 23) = 0, (15, 24) = 0, (15, 25) = 0, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = 0, (16, 5) = 0, (16, 6) = 0, (16, 7) = 0, (16, 8) = 0, (16, 9) = 0, (16, 10) = 0, (16, 11) = 0, (16, 12) = 0, (16, 13) = 0, (16, 14) = 0, (16, 15) = 0, (16, 16) = 0, (16, 17) = 0, (16, 18) = 0, (16, 19) = 0, (16, 20) = 0, (16, 21) = 0, (16, 22) = 0, (16, 23) = 0, (16, 24) = 0, (16, 25) = 0, (17, 1) = 0, (17, 2) = 0, (17, 3) = 0, (17, 4) = 0, (17, 5) = 0, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0, (17, 16) = 0, (17, 17) = 0, (17, 18) = 0, (17, 19) = 0, (17, 20) = 0, (17, 21) = 0, (17, 22) = 0, (17, 23) = 0, (17, 24) = 0, (17, 25) = 0, (18, 1) = 0, (18, 2) = 0, (18, 3) = 0, (18, 4) = 0, (18, 5) = 0, (18, 6) = 0, (18, 7) = 0, (18, 8) = 0, (18, 9) = 0, (18, 10) = 0, (18, 11) = 0, (18, 12) = 0, (18, 13) = 0, (18, 14) = 0, (18, 15) = 0, (18, 16) = 0, (18, 17) = 0, (18, 18) = 0, (18, 19) = 0, (18, 20) = 0, (18, 21) = 0, (18, 22) = 0, (18, 23) = 0, (18, 24) = 0, (18, 25) = 0, (19, 1) = 0, (19, 2) = 0, (19, 3) = 0, (19, 4) = 0, (19, 5) = 0, (19, 6) = 0, (19, 7) = 0, (19, 8) = 0, (19, 9) = 0, (19, 10) = 0, (19, 11) = 0, (19, 12) = 0, (19, 13) = 0, (19, 14) = 0, (19, 15) = 0, (19, 16) = 0, (19, 17) = 0, (19, 18) = 0, (19, 19) = 0, (19, 20) = 0, (19, 21) = 0, (19, 22) = 0, (19, 23) = 0, (19, 24) = 0, (19, 25) = 0, (20, 1) = 0, (20, 2) = 0, (20, 3) = 0, (20, 4) = 0, (20, 5) = 0, (20, 6) = 0, (20, 7) = 0, (20, 8) = 0, (20, 9) = 0, (20, 10) = 0, (20, 11) = 0, (20, 12) = 0, (20, 13) = 0, (20, 14) = 0, (20, 15) = 0, (20, 16) = 0, (20, 17) = 0, (20, 18) = 0, (20, 19) = 0, (20, 20) = 0, (20, 21) = 0, (20, 22) = 0, (20, 23) = 0, (20, 24) = 0, (20, 25) = 0, (21, 1) = 0, (21, 2) = 0, (21, 3) = 0, (21, 4) = 0, (21, 5) = 0, (21, 6) = 0, (21, 7) = 0, (21, 8) = 0, (21, 9) = 0, (21, 10) = 0, (21, 11) = 0, (21, 12) = 0, (21, 13) = 0, (21, 14) = 0, (21, 15) = 0, (21, 16) = 0, (21, 17) = 0, (21, 18) = 0, (21, 19) = 0, (21, 20) = 0, (21, 21) = 0, (21, 22) = 0, (21, 23) = 0, (21, 24) = 0, (21, 25) = 0, (22, 1) = 0, (22, 2) = 0, (22, 3) = 0, (22, 4) = 0, (22, 5) = 0, (22, 6) = 0, (22, 7) = 0, (22, 8) = 0, (22, 9) = 0, (22, 10) = 0, (22, 11) = 0, (22, 12) = 0, (22, 13) = 0, (22, 14) = 0, (22, 15) = 0, (22, 16) = 0, (22, 17) = 0, (22, 18) = 0, (22, 19) = 0, (22, 20) = 0, (22, 21) = 0, (22, 22) = 0, (22, 23) = 0, (22, 24) = 0, (22, 25) = 0, (23, 1) = 0, (23, 2) = 0, (23, 3) = 0, (23, 4) = 0, (23, 5) = 0, (23, 6) = 0, (23, 7) = 0, (23, 8) = 0, (23, 9) = 0, (23, 10) = 0, (23, 11) = 0, (23, 12) = 0, (23, 13) = 0, (23, 14) = 0, (23, 15) = 0, (23, 16) = 0, (23, 17) = 0, (23, 18) = 0, (23, 19) = 0, (23, 20) = 0, (23, 21) = 0, (23, 22) = 0, (23, 23) = 0, (23, 24) = 0, (23, 25) = 0, (24, 1) = 0, (24, 2) = 0, (24, 3) = 0, (24, 4) = 0, (24, 5) = 0, (24, 6) = 0, (24, 7) = 0, (24, 8) = 0, (24, 9) = 0, (24, 10) = 0, (24, 11) = 0, (24, 12) = 0, (24, 13) = 0, (24, 14) = 0, (24, 15) = 0, (24, 16) = 0, (24, 17) = 0, (24, 18) = 0, (24, 19) = 0, (24, 20) = 0, (24, 21) = 0, (24, 22) = 0, (24, 23) = 0, (24, 24) = 0, (24, 25) = 0, (25, 1) = 0, (25, 2) = 0, (25, 3) = 0, (25, 4) = 0, (25, 5) = 0, (25, 6) = 0, (25, 7) = 0, (25, 8) = 0, (25, 9) = 0, (25, 10) = 0, (25, 11) = 0, (25, 12) = 0, (25, 13) = 0, (25, 14) = 0, (25, 15) = 0, (25, 16) = 0, (25, 17) = 0, (25, 18) = 0, (25, 19) = 0, (25, 20) = 0, (25, 21) = 0, (25, 22) = 0, (25, 23) = 0, (25, 24) = 0, (25, 25) = 0})

  

2, true, [`?`]

  

3, true, [`?`]

  

4, false, Matrix(16, 16, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (2, 15) = 0, (2, 16) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (3, 16) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (5, 16) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (6, 15) = 0, (6, 16) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (7, 16) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 0, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (8, 15) = 0, (8, 16) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (9, 16) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 0, (10, 13) = 0, (10, 14) = 0, (10, 15) = 0, (10, 16) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (11, 16) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 0, (12, 15) = 0, (12, 16) = 0, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (13, 16) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0, (14, 15) = 0, (14, 16) = 0, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (15, 16) = 0, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = 0, (16, 5) = 0, (16, 6) = 0, (16, 7) = 0, (16, 8) = 0, (16, 9) = 0, (16, 10) = 0, (16, 11) = 0, (16, 12) = 0, (16, 13) = 0, (16, 14) = 0, (16, 15) = 0, (16, 16) = 0})

  

5, false, Matrix(25, 25, {(1, 1) = 0, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (1, 12) = 0, (1, 13) = 0, (1, 14) = 0, (1, 15) = 0, (1, 16) = 0, (1, 17) = 0, (1, 18) = 0, (1, 19) = 0, (1, 20) = 0, (1, 21) = 0, (1, 22) = 0, (1, 23) = 0, (1, 24) = 0, (1, 25) = 0, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (2, 12) = 0, (2, 13) = 0, (2, 14) = 0, (2, 15) = 0, (2, 16) = 0, (2, 17) = 0, (2, 18) = 0, (2, 19) = 0, (2, 20) = 0, (2, 21) = 0, (2, 22) = 0, (2, 23) = 0, (2, 24) = 0, (2, 25) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (3, 12) = 0, (3, 13) = 0, (3, 14) = 0, (3, 15) = 0, (3, 16) = 0, (3, 17) = 0, (3, 18) = 0, (3, 19) = 0, (3, 20) = 0, (3, 21) = 0, (3, 22) = 0, (3, 23) = 0, (3, 24) = 0, (3, 25) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (4, 12) = 0, (4, 13) = 0, (4, 14) = 0, (4, 15) = 0, (4, 16) = 0, (4, 17) = 0, (4, 18) = 0, (4, 19) = 0, (4, 20) = 0, (4, 21) = 0, (4, 22) = 0, (4, 23) = 0, (4, 24) = 0, (4, 25) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 0, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = 0, (5, 12) = 0, (5, 13) = 0, (5, 14) = 0, (5, 15) = 0, (5, 16) = 0, (5, 17) = 0, (5, 18) = 0, (5, 19) = 0, (5, 20) = 0, (5, 21) = 0, (5, 22) = 0, (5, 23) = 0, (5, 24) = 0, (5, 25) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 0, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (6, 12) = 0, (6, 13) = 0, (6, 14) = 0, (6, 15) = 0, (6, 16) = 0, (6, 17) = 0, (6, 18) = 0, (6, 19) = 0, (6, 20) = 0, (6, 21) = 0, (6, 22) = 0, (6, 23) = 0, (6, 24) = 0, (6, 25) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 0, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 0, (7, 12) = 0, (7, 13) = 0, (7, 14) = 0, (7, 15) = 0, (7, 16) = 0, (7, 17) = 0, (7, 18) = 0, (7, 19) = 0, (7, 20) = 0, (7, 21) = 0, (7, 22) = 0, (7, 23) = 0, (7, 24) = 0, (7, 25) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 0, (8, 9) = 0, (8, 10) = 0, (8, 11) = 0, (8, 12) = 0, (8, 13) = 0, (8, 14) = 0, (8, 15) = 0, (8, 16) = 0, (8, 17) = 0, (8, 18) = 0, (8, 19) = 0, (8, 20) = 0, (8, 21) = 0, (8, 22) = 0, (8, 23) = 0, (8, 24) = 0, (8, 25) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 0, (9, 10) = 0, (9, 11) = 0, (9, 12) = 0, (9, 13) = 0, (9, 14) = 0, (9, 15) = 0, (9, 16) = 0, (9, 17) = 0, (9, 18) = 0, (9, 19) = 0, (9, 20) = 0, (9, 21) = 0, (9, 22) = 0, (9, 23) = 0, (9, 24) = 0, (9, 25) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 0, (10, 11) = 0, (10, 12) = 0, (10, 13) = 0, (10, 14) = 0, (10, 15) = 0, (10, 16) = 0, (10, 17) = 0, (10, 18) = 0, (10, 19) = 0, (10, 20) = 0, (10, 21) = 0, (10, 22) = 0, (10, 23) = 0, (10, 24) = 0, (10, 25) = 0, (11, 1) = 0, (11, 2) = 0, (11, 3) = 0, (11, 4) = 0, (11, 5) = 0, (11, 6) = 0, (11, 7) = 0, (11, 8) = 0, (11, 9) = 0, (11, 10) = 0, (11, 11) = 0, (11, 12) = 0, (11, 13) = 0, (11, 14) = 0, (11, 15) = 0, (11, 16) = 0, (11, 17) = 0, (11, 18) = 0, (11, 19) = 0, (11, 20) = 0, (11, 21) = 0, (11, 22) = 0, (11, 23) = 0, (11, 24) = 0, (11, 25) = 0, (12, 1) = 0, (12, 2) = 0, (12, 3) = 0, (12, 4) = 0, (12, 5) = 0, (12, 6) = 0, (12, 7) = 0, (12, 8) = 0, (12, 9) = 0, (12, 10) = 0, (12, 11) = 0, (12, 12) = 0, (12, 13) = 0, (12, 14) = 0, (12, 15) = 0, (12, 16) = 0, (12, 17) = 0, (12, 18) = 0, (12, 19) = 0, (12, 20) = 0, (12, 21) = 0, (12, 22) = 0, (12, 23) = 0, (12, 24) = 0, (12, 25) = 0, (13, 1) = 0, (13, 2) = 0, (13, 3) = 0, (13, 4) = 0, (13, 5) = 0, (13, 6) = 0, (13, 7) = 0, (13, 8) = 0, (13, 9) = 0, (13, 10) = 0, (13, 11) = 0, (13, 12) = 0, (13, 13) = 0, (13, 14) = 0, (13, 15) = 0, (13, 16) = 0, (13, 17) = 0, (13, 18) = 0, (13, 19) = 0, (13, 20) = 0, (13, 21) = 0, (13, 22) = 0, (13, 23) = 0, (13, 24) = 0, (13, 25) = 0, (14, 1) = 0, (14, 2) = 0, (14, 3) = 0, (14, 4) = 0, (14, 5) = 0, (14, 6) = 0, (14, 7) = 0, (14, 8) = 0, (14, 9) = 0, (14, 10) = 0, (14, 11) = 0, (14, 12) = 0, (14, 13) = 0, (14, 14) = 0, (14, 15) = 0, (14, 16) = 0, (14, 17) = 0, (14, 18) = 0, (14, 19) = 0, (14, 20) = 0, (14, 21) = 0, (14, 22) = 0, (14, 23) = 0, (14, 24) = 0, (14, 25) = 0, (15, 1) = 0, (15, 2) = 0, (15, 3) = 0, (15, 4) = 0, (15, 5) = 0, (15, 6) = 0, (15, 7) = 0, (15, 8) = 0, (15, 9) = 0, (15, 10) = 0, (15, 11) = 0, (15, 12) = 0, (15, 13) = 0, (15, 14) = 0, (15, 15) = 0, (15, 16) = 0, (15, 17) = 0, (15, 18) = 0, (15, 19) = 0, (15, 20) = 0, (15, 21) = 0, (15, 22) = 0, (15, 23) = 0, (15, 24) = 0, (15, 25) = 0, (16, 1) = 0, (16, 2) = 0, (16, 3) = 0, (16, 4) = 0, (16, 5) = 0, (16, 6) = 0, (16, 7) = 0, (16, 8) = 0, (16, 9) = 0, (16, 10) = 0, (16, 11) = 0, (16, 12) = 0, (16, 13) = 0, (16, 14) = 0, (16, 15) = 0, (16, 16) = 0, (16, 17) = 0, (16, 18) = 0, (16, 19) = 0, (16, 20) = 0, (16, 21) = 0, (16, 22) = 0, (16, 23) = 0, (16, 24) = 0, (16, 25) = 0, (17, 1) = 0, (17, 2) = 0, (17, 3) = 0, (17, 4) = 0, (17, 5) = 0, (17, 6) = 0, (17, 7) = 0, (17, 8) = 0, (17, 9) = 0, (17, 10) = 0, (17, 11) = 0, (17, 12) = 0, (17, 13) = 0, (17, 14) = 0, (17, 15) = 0, (17, 16) = 0, (17, 17) = 0, (17, 18) = 0, (17, 19) = 0, (17, 20) = 0, (17, 21) = 0, (17, 22) = 0, (17, 23) = 0, (17, 24) = 0, (17, 25) = 0, (18, 1) = 0, (18, 2) = 0, (18, 3) = 0, (18, 4) = 0, (18, 5) = 0, (18, 6) = 0, (18, 7) = 0, (18, 8) = 0, (18, 9) = 0, (18, 10) = 0, (18, 11) = 0, (18, 12) = 0, (18, 13) = 0, (18, 14) = 0, (18, 15) = 0, (18, 16) = 0, (18, 17) = 0, (18, 18) = 0, (18, 19) = 0, (18, 20) = 0, (18, 21) = 0, (18, 22) = 0, (18, 23) = 0, (18, 24) = 0, (18, 25) = 0, (19, 1) = 0, (19, 2) = 0, (19, 3) = 0, (19, 4) = 0, (19, 5) = 0, (19, 6) = 0, (19, 7) = 0, (19, 8) = 0, (19, 9) = 0, (19, 10) = 0, (19, 11) = 0, (19, 12) = 0, (19, 13) = 0, (19, 14) = 0, (19, 15) = 0, (19, 16) = 0, (19, 17) = 0, (19, 18) = 0, (19, 19) = 0, (19, 20) = 0, (19, 21) = 0, (19, 22) = 0, (19, 23) = 0, (19, 24) = 0, (19, 25) = 0, (20, 1) = 0, (20, 2) = 0, (20, 3) = 0, (20, 4) = 0, (20, 5) = 0, (20, 6) = 0, (20, 7) = 0, (20, 8) = 0, (20, 9) = 0, (20, 10) = 0, (20, 11) = 0, (20, 12) = 0, (20, 13) = 0, (20, 14) = 0, (20, 15) = 0, (20, 16) = 0, (20, 17) = 0, (20, 18) = 0, (20, 19) = 0, (20, 20) = 0, (20, 21) = 0, (20, 22) = 0, (20, 23) = 0, (20, 24) = 0, (20, 25) = 0, (21, 1) = 0, (21, 2) = 0, (21, 3) = 0, (21, 4) = 0, (21, 5) = 0, (21, 6) = 0, (21, 7) = 0, (21, 8) = 0, (21, 9) = 0, (21, 10) = 0, (21, 11) = 0, (21, 12) = 0, (21, 13) = 0, (21, 14) = 0, (21, 15) = 0, (21, 16) = 0, (21, 17) = 0, (21, 18) = 0, (21, 19) = 0, (21, 20) = 0, (21, 21) = 0, (21, 22) = 0, (21, 23) = 0, (21, 24) = 0, (21, 25) = 0, (22, 1) = 0, (22, 2) = 0, (22, 3) = 0, (22, 4) = 0, (22, 5) = 0, (22, 6) = 0, (22, 7) = 0, (22, 8) = 0, (22, 9) = 0, (22, 10) = 0, (22, 11) = 0, (22, 12) = 0, (22, 13) = 0, (22, 14) = 0, (22, 15) = 0, (22, 16) = 0, (22, 17) = 0, (22, 18) = 0, (22, 19) = 0, (22, 20) = 0, (22, 21) = 0, (22, 22) = 0, (22, 23) = 0, (22, 24) = 0, (22, 25) = 0, (23, 1) = 0, (23, 2) = 0, (23, 3) = 0, (23, 4) = 0, (23, 5) = 0, (23, 6) = 0, (23, 7) = 0, (23, 8) = 0, (23, 9) = 0, (23, 10) = 0, (23, 11) = 0, (23, 12) = 0, (23, 13) = 0, (23, 14) = 0, (23, 15) = 0, (23, 16) = 0, (23, 17) = 0, (23, 18) = 0, (23, 19) = 0, (23, 20) = 0, (23, 21) = 0, (23, 22) = 0, (23, 23) = 0, (23, 24) = 0, (23, 25) = 0, (24, 1) = 0, (24, 2) = 0, (24, 3) = 0, (24, 4) = 0, (24, 5) = 0, (24, 6) = 0, (24, 7) = 0, (24, 8) = 0, (24, 9) = 0, (24, 10) = 0, (24, 11) = 0, (24, 12) = 0, (24, 13) = 0, (24, 14) = 0, (24, 15) = 0, (24, 16) = 0, (24, 17) = 0, (24, 18) = 0, (24, 19) = 0, (24, 20) = 0, (24, 21) = 0, (24, 22) = 0, (24, 23) = 0, (24, 24) = 0, (24, 25) = 0, (25, 1) = 0, (25, 2) = 0, (25, 3) = 0, (25, 4) = 0, (25, 5) = 0, (25, 6) = 0, (25, 7) = 0, (25, 8) = 0, (25, 9) = 0, (25, 10) = 0, (25, 11) = 0, (25, 12) = 0, (25, 13) = 0, (25, 14) = 0, (25, 15) = 0, (25, 16) = 0, (25, 17) = 0, (25, 18) = 0, (25, 19) = 0, (25, 20) = 0, (25, 21) = 0, (25, 22) = 0, (25, 23) = 0, (25, 24) = 0, (25, 25) = 0})

 (3)

Download Using_basic_linear_algebra.mw
Please Wait...