(def varpars [ {:symbol "x", :quantity "length"}
               {:symbol "v", :quantity "velocity"}
               {:symbol "t", :quantity "time"}
               {:symbol "a", :quantity "acceleration"} ])

=> (generate-dimmat varpars)
[[1N 1N 0 1N] [0 -1N 1N -2N]]

Contains function

 - `generate-dimmat`

Given
```
(def varpars [ {:symbol "x", :quantity "length"}
               {:symbol "v", :quantity "velocity"}
               {:symbol "t", :quantity "time"}
               {:symbol "a", :quantity "acceleration"} ])
```
to get the [dimensional matrix](https://neuralgraphs.com/lectures/diman/lectp8.html#p4_thispage) of the system containing (only) the above dimensional quantities
```
=> (generate-dimmat varpars)
[[1N 1N 0 1N] [0 -1N 1N -2N]]
```

(def varpars [ {:symbol "x", :quantity "length"}
               {:symbol "v", :quantity "velocity"}
               {:symbol "t", :quantity "time"}
               {:symbol "a", :quantity "acceleration"} ])
(def soln_matrix [ [1 -11 5 8]
                   [0 9 -4 -7] ])

=> (get-dimensionless-products soln_matrix varpars)
[{:symbol "pi0", :expression "x^(1)*v^(-11)*t^(5)*a^(8)"} {:symbol "pi1", :expression "v^(9)*t^(-4)*a^(-7)"}]

=> (get-pi-expression (get-dimensionless-products soln_matrix varpars) "pi0")
"x^(1)*v^(-11)*t^(5)*a^(8)"

Contains function

 - `get-dimensionless-products`
 - `get-pi-expression`

Given
```
(def varpars [ {:symbol "x", :quantity "length"}
               {:symbol "v", :quantity "velocity"}
               {:symbol "t", :quantity "time"}
               {:symbol "a", :quantity "acceleration"} ])
(def soln_matrix [ [1 -11 5 8]
                   [0 9 -4 -7] ])
```
to get the [set of dimensionless products](https://neuralgraphs.com/lectures/diman/lectp8.html#p4_thispage)
```
=> (get-dimensionless-products soln_matrix varpars)
[{:symbol "pi0", :expression "x^(1)*v^(-11)*t^(5)*a^(8)"} {:symbol "pi1", :expression "v^(9)*t^(-4)*a^(-7)"}]
```
and to extract a particular dimensionless product from the set
```
=> (get-pi-expression (get-dimensionless-products soln_matrix varpars) "pi0")
"x^(1)*v^(-11)*t^(5)*a^(8)"
```

(def dimat [ [2 -1 3 0 0 -2 1]
             [1 0 -1 0 2 1 2]
             [0 1 0 3 1 -1 2] ])

=> (get-augmented-matrix dimat)
[[0 -2 1 -2 1 -3 0] [2 1 2 -1 0 1 0] [1 -1 2 0 -1 0 -3]]

=> (solve (get-augmented-matrix dimat))
[[1 0N 0N -11N 9N -9N 15N] [0 1 0N 5N -4N 5N -6N] [0 0N 1N 8N -7N 7N -12N]]

=> (get-solution-matrix (solve (get-augmented-matrix dimat)))
[[1 0 0 0 -11N 5N 8N] [0 1 0 0 9N -4N -7N] [0 0 1 0 -9N 5N 7N] [0 0 0 1 15N -6N -12N]]

Contains function

 - `get-augmented-matrix`
 - `solve`
 - `get-solution-matrix`

Given the dimensional matrix of a system
```
(def dimat [ [2 -1 3 0 0 -2 1]
             [1 0 -1 0 2 1 2]
             [0 1 0 3 1 -1 2] ])
```
to get the augmented matrix
```
=> (get-augmented-matrix dimat)
[[0 -2 1 -2 1 -3 0] [2 1 2 -1 0 1 0] [1 -1 2 0 -1 0 -3]]
```
and solve
```
=> (solve (get-augmented-matrix dimat))
[[1 0N 0N -11N 9N -9N 15N] [0 1 0N 5N -4N 5N -6N] [0 0N 1N 8N -7N 7N -12N]]
```
To get the solution matrix
```
=> (get-solution-matrix (solve (get-augmented-matrix dimat)))
[[1 0 0 0 -11N 5N 8N] [0 1 0 0 9N -4N -7N] [0 0 1 0 -9N 5N 7N] [0 0 0 1 15N -6N -12N]]
```