
(DEFPARAMETER |FiniteRankAlgebra;CAT| 'NIL) 

(DECLAIM (NOTINLINE |FiniteRankAlgebra;|)) 

(DEFPARAMETER |FiniteRankAlgebra;AL| 'NIL) 

(DEFUN |FiniteRankAlgebra| (|t#1| |t#2|)
  (LET (#1=#:G691 (#2=#:G692 (LIST (|devaluate| |t#1|) (|devaluate| |t#2|))))
    (COND ((SETQ #1# (|assoc| #2# |FiniteRankAlgebra;AL|)) (CDR #1#))
          (T
           (SETQ |FiniteRankAlgebra;AL|
                   (|cons5|
                    (CONS #2# (SETQ #1# (APPLY #'|FiniteRankAlgebra;| #2#)))
                    |FiniteRankAlgebra;AL|))
           #1#)))) 

(DEFUN |FiniteRankAlgebra;| (|t#1| |t#2|)
  (SPROG ((#1=#:G690 NIL))
         (PROG1
             (LETT #1#
                   (|sublisV| (PAIR '(|t#1| |t#2|) (LIST |t#1| |t#2|))
                              (COND (|FiniteRankAlgebra;CAT|)
                                    ('T
                                     (LETT |FiniteRankAlgebra;CAT|
                                           (|Join| (|Algebra| '|t#1|)
                                                   (|TwoSidedRecip|)
                                                   (|mkCategory|
                                                    '(((|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|))))
                                                    NIL NIL)))))))
           (SETELT #1# 0 (LIST '|FiniteRankAlgebra| |t#1| |t#2|))))) 
