Escalonando Matrizes em APL: Código

escalona.apl

∇R←IDENTITY N
  R←(N N)⍴(1,N⍴0)
∇

∇R←EXTENDBOTTOM MAT
  R←(((↑⍴MAT)⍴1),0)\[1]MAT
∇

∇R←EXTENDRIGHT MAT
  R←(((2⌷⍴MAT)⍴1),0)\MAT
∇

∇R←N PIVOT MAT;LST;IDX
  LST←N⌷[1]MAT
  IDX←(0≠LST)⍳1
  →(IDX>⍴LST)/0
  R←IDX⌷LST
∇

∇R←A GCD B
  →(B=0)/END
  (A B)←(B (|B | A))
  →1
END: R←A
∇

∇R←SIMPVEC VEC;SIMPL
  SIMPL←VEC÷GCD/⌊|VEC[⍒|VEC]
  →(×+/0<SIMPL-⌊SIMPL)/DONTSIMPL
  R←SIMPL
  →0
  DONTSIMPL:R←VEC
∇

∇R←L GAUSSELIM A;ZEROLNS
  →(0=+/|A[L;])/END
  A[L;]←(×L PIVOT A)×SIMPVEC A[L;]
  ZEROLNS←(~L=ZEROLNS)/ZEROLNS←⍳↑⍴A
  R←{A[⍵;]←((L PIVOT A)×A[⍵;])-(A[⍵;L]×A[L;])}¨ZEROLNS
END:R←A
∇

∇R←GAUSSJORDAN MAT
  R←{MAT←⍵ GAUSSELIM MAT}¨⍳↑⍴MAT
  R←{MAT[⍵;]←SIMPVEC MAT[⍵;]}¨⍳↑⍴MAT
  R←MAT
∇