
(/VERSIONCHECK 2) 

(DEFPARAMETER |FiniteRankAlgebra;CAT| 'NIL) 

(DEFPARAMETER |FiniteRankAlgebra;AL| 'NIL) 

(DEFUN |FiniteRankAlgebra| (&REST #0=#:G1816)
  (LET (#1=#:G1817)
    (COND
      ((SETQ #1#
             (|assoc| #2=(|devaluateList| #0#) |FiniteRankAlgebra;AL|))
       (CDR #1#))
      (T (SETQ |FiniteRankAlgebra;AL|
               (|cons5| (CONS #2#
                              (SETQ #1#
                                    (APPLY #'|FiniteRankAlgebra;| #0#)))
                        |FiniteRankAlgebra;AL|))
         #1#)))) 

(DEFUN |FiniteRankAlgebra;| (|t#1| |t#2|)
  (PROG (#0=#:G1815)
    (RETURN
      (PROG1 (LETT #0#
                   (|sublisV|
                       (PAIR '(|t#1| |t#2|)
                             (LIST (|devaluate| |t#1|)
                                   (|devaluate| |t#2|)))
                       (COND
                         (|FiniteRankAlgebra;CAT|)
                         ('T
                          (LETT |FiniteRankAlgebra;CAT|
                                (|Join| (|Algebra| '|t#1|)
                                        (|mkCategory| '|domain|
                                         '(((|rank|
                                             ((|PositiveInteger|)))
                                            T)
                                           ((|regularRepresentation|
                                             ((|Matrix| |t#1|) $
                                              (|Vector| $)))
                                            T)
                                           ((|trace| (|t#1| $)) T)
                                           ((|norm| (|t#1| $)) T)
                                           ((|coordinates|
                                             ((|Vector| |t#1|) $
                                              (|Vector| $)))
                                            T)
                                           ((|coordinates|
                                             ((|Matrix| |t#1|)
                                              (|Vector| $)
                                              (|Vector| $)))
                                            T)
                                           ((|represents|
                                             ($ (|Vector| |t#1|)
                                              (|Vector| $)))
                                            T)
                                           ((|discriminant|
                                             (|t#1| (|Vector| $)))
                                            T)
                                           ((|traceMatrix|
                                             ((|Matrix| |t#1|)
                                              (|Vector| $)))
                                            T)
                                           ((|characteristicPolynomial|
                                             (|t#2| $))
                                            T)
                                           ((|minimalPolynomial|
                                             (|t#2| $))
                                            (|has| |t#1| (|Field|))))
                                         '(((|CharacteristicZero|)
                                            (|has| |t#1|
                                             (|CharacteristicZero|)))
                                           ((|CharacteristicNonZero|)
                                            (|has| |t#1|
                                             (|CharacteristicNonZero|))))
                                         '((|Matrix| |t#1|)
                                           (|Vector| $)
                                           (|Vector| |t#1|)
                                           (|PositiveInteger|))
                                         NIL))
                                . #1=(|FiniteRankAlgebra|))))) . #1#)
        (SETELT #0# 0
                (LIST '|FiniteRankAlgebra| (|devaluate| |t#1|)
                      (|devaluate| |t#2|))))))) 
