
(DEFPARAMETER |SquareMatrixCategory;CAT| 'NIL) 

(DECLAIM (NOTINLINE |SquareMatrixCategory;|)) 

(DEFPARAMETER |SquareMatrixCategory;AL| 'NIL) 

(DEFUN |SquareMatrixCategory| (|t#1| |t#2| |t#3| |t#4|)
  (LET (#1=#:G703
        (#2=#:G704
         (LIST (|devaluate| |t#1|) (|devaluate| |t#2|) (|devaluate| |t#3|)
               (|devaluate| |t#4|))))
    (COND ((SETQ #1# (|assoc| #2# |SquareMatrixCategory;AL|)) (CDR #1#))
          (T
           (SETQ |SquareMatrixCategory;AL|
                   (|cons5|
                    (CONS #2# (SETQ #1# (APPLY #'|SquareMatrixCategory;| #2#)))
                    |SquareMatrixCategory;AL|))
           #1#)))) 

(DEFUN |SquareMatrixCategory;| (|t#1| |t#2| |t#3| |t#4|)
  (SPROG ((#1=#:G702 NIL))
         (PROG1
             (LETT #1#
                   (|sublisV|
                    (PAIR '(|t#1| |t#2| |t#3| |t#4|)
                          (LIST |t#1| |t#2| |t#3| |t#4|))
                    (COND (|SquareMatrixCategory;CAT|)
                          ('T
                           (LETT |SquareMatrixCategory;CAT|
                                 (|Join| (|SemiRng|) (|AbelianMonoid|)
                                         (|BiModule| '|t#2| '|t#2|)
                                         (|TwoSidedRecip|)
                                         (|RectangularMatrixCategory| |t#1|
                                                                      |t#1|
                                                                      '|t#2|
                                                                      '|t#3|
                                                                      '|t#4|)
                                         (|FullyRetractableTo| '|t#2|)
                                         (|mkCategory|
                                          '(((|scalarMatrix| ($ |t#2|)) T)
                                            ((|diagonalMatrix|
                                              ($ (|List| |t#2|)))
                                             T)
                                            ((|diagonal| (|t#3| $)) T)
                                            ((|trace| (|t#2| $)) T)
                                            ((|diagonalProduct| (|t#2| $)) T)
                                            ((* (|t#4| $ |t#4|)) T)
                                            ((* (|t#3| |t#3| $)) T)
                                            ((|determinant| (|t#2| $))
                                             (|has| |t#2| (|CommutativeRing|)))
                                            ((|minordet| (|t#2| $))
                                             (|has| |t#2| (|CommutativeRing|)))
                                            ((|Pfaffian| (|t#2| $))
                                             (|has| |t#2| (|CommutativeRing|)))
                                            ((|inverse|
                                              ((|Union| $ "failed") $))
                                             (|has| |t#2| (|Field|)))
                                            ((^ ($ $ (|Integer|)))
                                             (|has| |t#2| (|Field|))))
                                          '(((|SemiRing|)
                                             (|has| |t#2| (|SemiRing|)))
                                            ((|DifferentialExtension| |t#2|)
                                             (|has| |t#2| (|Ring|)))
                                            ((|FullyLinearlyExplicitOver|
                                              |t#2|)
                                             (|has| |t#2| (|Ring|)))
                                            ((|Algebra| |t#2|)
                                             (|has| |t#2|
                                                    (|CommutativeRing|))))
                                          NIL NIL)))))))
           (SETELT #1# 0
                   (LIST '|SquareMatrixCategory| |t#1| |t#2| |t#3| |t#4|))))) 
