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+⍝ WEYL-BRAUER MATRICES IN APL
+
+⍝ Weyl-Brauer matrices are higher dimensional versions of Pauli spin matrices.
+⍝ They can be built up using the Pauli spin matrices as blocks. The building up
+⍝ can be done by making a mega-array of Pauli matrices then collapsing it down
+⍝ by taking the outer/Kronecker product along one of its dimensions - perfect
+⍝ for APL!
+
+⎕IO←0⋄⎕PW←210                   ⍝ Set index origin, console width
+
+a←2 2⍴1 0 0 1                   ⍝ Identity matrix
+b←2 2⍴1 0 0 ¯1                  ⍝ Pauli matrices
+p←2 2⍴0 1 1 0
+q←2 2⍴0 0J1 0J¯1 0
+
+v←p q b                         ⍝ Vector of Pauli matrices
+e←v∘.(+.×)v                     ⍝ Products of Pauli matrices
+e+⍉e                            ⍝ Anticommutators of Pauli matrices
+
+n←3                             ⍝ Number of vector space dimensions is 2×n
+                                ⍝ Dimension of matrices is 2 2*n
+
+u←(⍳n)∘.>⍳n                     ⍝ Upper triangular matrix of ones
+
+k←{⊃⍪/,/⍺∘.×⊂⍵}                 ⍝ Kronecker product of matrices
+
+v←,k/((p q),2 2⍴a b)[;u+2×⍉u]   ⍝ Weyl-Brauer matrices
+e←v∘.(+.×)v                     ⍝ Products of Weyl-Brauer matrices
+0 0⍉e                           ⍝ Check matrices square to the identity
+e+⍉e                            ⍝ Anticommutators of Weyl-Brauer matrices
+
+I←+.×/v                         ⍝ Pseudo-scalar I
+m←2*n
+n m
+II←⊃I+.×I
+((⍳m)∘.=⍳m)≡II                  ⍝ I squares to identity for even n
+((⍳m)∘.=⍳m)≡-II                 ⍝ or -identity for odd n