
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;  Purpose:  Generate Presentation MathML code from MAXIMA
;;;  File: PrMathML.lsp
;;;  Author: Paul S. Wang
;;;  Date: March 1999
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
;=============================================================================
;    (c) copyright 1999  Kent State University
;               all rights reserved.
;=============================================================================
(in-package :maxima)
(macsyma-module mathml)

;; special variables used in TeXetting
(declaim (special *row* *indent* ccol mPrport $mPrautolabel $mPrworksheet $lamPrworksheet
             $mPrlabelleft $lamPrautolabel $mPrdisplaytype $mPrevaluate
             macmPr-lib lop rop $labels casep))

;;****************************************************************************
;;      Program : prmathml
;;****************************************************************************
;;Generatig MathML presenation codes for the expr 
;;This is a maxima top-level function used  the form
;;              prmathml(expr, [,(filename|stream)[,t (d)]])  on the C-line

(defmfun $prmathml (&rest margs)
         (prog (ccol *row* *indent* filename mexplabel mexpress mPrport x y)
           (setq mexpress (car margs))
           (setq ccol 1 *indent* 0 *row* t)
           (cond
             ((null mexpress) (princ " NO EXPRESSION GIVEN ")
              (return nil))
             ((null (cdr margs)) (setq filename nil) (setq mPrport t))
             ((null (cddr margs))
              (setq mPrport
                    (if (stringp (cadr margs))
                      (progn
                        (setq filename (cadr margs))
                        (open (cadr margs)
                            :direction :output 
                            :if-exists :append
                            :if-does-not-exist :create))
                      ;; otherwise, assume (cadr margs) is a stream.
                      (cadr margs))))
             (t (princ " wrong No. of Arguments given ")))
           (cond
             ((member mexpress $labels :test #'eq)
              (setq mexplabel
                    (intern (concatenate 'string "("
                                (princ-to-string (fullstrip1 mexpress))
                                ")")))
              (setq mexpress (eval mexpress)))
             (t (setq mexplabel nil)
                (when $mPrevaluate (setq mexpress (meval mexpress)))))
           (when $mPrautolabel (setq mexplabel (updateautolabel)))
           (when (symbolp (setq x mexpress))
             (setq x ($verbify x))
             (cond
               ((setq y (mget x 'mexprer))
                (setq mexpress
                      (list '(mdefine) (cons (list x) (cdadr y))
                            (caddr y))))
               ((setq y (mget x 'mmacro))
                (setq mexpress
                      (list '(mdefmacro) (cons (list x) (cdadr y))
                            (caddr y))))
               ((setq y (mget x 'aexpr))
                (setq mexpress
                      (list '(mdefine)
                            (cons (list x 'array)
                                  (cdadr y))
                            (caddr y))))))
           (when (and (consp mexpress) (consp (car mexpress))
                      (eq 'mlabel (caar mexpress)))
             (setq mexpress (cadr mexpress)))
           (cond
             ((and $lamPrworksheet
                   (when mexplabel
                     (member 'c (explode mexplabel) :test #'eq)))
              (format mPrport "\\begin{verbatim}~%~a " mexplabel)
              (mgrind mexpress mPrport)
              (format mPrport ";~%\\end{verbatim}~%"))
             ((and $mPrworksheet
                   (when mexplabel
                     (member 'c (explode mexplabel) :test
                             #'eq)))
              (format mPrport "|~a " mexplabel)
              (mgrind mexpress mPrport) (format mPrport ";|~%"))
             (t (cond
                  ($lamPrautolabel
                      (format mPrport "\\begin{equation}~%"))
                  ($mPrdisplaytype 
		    (tprinc "<math  xmlns='http://www.w3.org/1998/Math/MathML'>") )
                  (t (tprinc "<math  xmlns='http://www.w3.org/1998/Math/MathML'>")))
                (mPr_engine mexpress 'mparen 'mparen)
                (cond
                  ($lamPrautolabel
                      (format mPrport "~%\\end{equation}~%"))
                  ($mPrdisplaytype
                      (when mexplabel
                        (if $mPrlabelleft
                            (format mPrport "\\leqno{\\tt ~a}" mexplabel)
                            (format mPrport "\\eqno{\\tt ~a}" mexplabel)))
                        (tprinc "</math>") (myterpri))
                  (t (tprinc "</math>")))))
           (when filename (terpri mPrport) (close mPrport))
           (return 'done)))



;;      mPr_engine is a kernel fuction for this program. It checks whether
;;an argument "mexpress" is an atom or expression. Then it will assign
;;a proper function to the expression or just print if it is an atom.
;;This is an applied object-oriented programming technique.

;;      arg: mexpress - macsyma internal representaton
;;           lop , rop - left and right handside operator of mexpress

;;special check if expression is an array
;;check whether or not to put parenthesis 
;;if not a keyword,it is a function

;;;;;; This is the work house routine ;;;;;;;;

(defun mPr_engine (mexpress lop rop)
  (setq mexpress (nformat mexpress))
  (if (atom mexpress) (mPr-atom mexpress)
      (when (listp (car mexpress))
        (cond
          ((member 'array (car mexpress) :test #'eq)
           (mPr-array mexpress))
          ((or (<= (mPr-lbp (caar mexpress)) (mPr-rbp lop))
               (> (mPr-lbp rop) (mPr-rbp (caar mexpress))))
           (mPr-paren mexpress))
          (t (if (get (caar mexpress) 'mPrprocess)
                 (funcall (get (caar mexpress) 'mPrprocess) mexpress)
                 (mPr-function mexpress)))))))



;*************************************************************************
;;
;;                              Utilities Section
;;
;*************************************************************************

;;; tprinc is an intelligent low level printing routine.  it keeps track of 
;;; the size of the output for purposes of allowing the TeX file to
;;; have a reasonable line-length. tprinc will break it at a space 
;;; once it crosses a threshold.
;;; this has nothign to do with breaking the resulting equations.
 
;-      arg:    chstr -  string or number to princ
;-      scheme: This function keeps track of the current location
;-              on the line of the cursor and makes sure
;-              that a value is all printed on one line (and not divided
;-              by the crazy top level os routines)
 
(defun row-begin(str)
  (myterpri)
  (princ str  mPrport)
  (incf *indent*)
  (setq *row* t))

(defun myindent()
  (do ((i *indent*))
      ((equal i 0) nil)
    (princ "   " mPrport)
    (decf i)))

(defun row-end(str)
  (decf *indent*)
  (myterpri)
  (princ str mPrport)
  (setq *row* t))

(defun tpchar (c)
  (incf ccol)
  (princ c mPrport))

;would have exceeded the line length
; lead off with a space for safety
;so we split it up.
(defun tprinc (chstr)
  (prog (chlst linebreak)
    (cond ((> (+ (length (setq chlst (exploden chstr))) ccol) 80)
        (setq linebreak t)))
    (cond (*row* (setq *row* nil) (myterpri))) ;; *row* calls for new row
    (do ((ch chlst (cdr ch)) (colc ccol (1+ colc)))
        ((null ch) (setq ccol colc))
      (write-char (car ch) mPrport)
      (if (and linebreak (eq (car ch) '>))  ;; line break only after >
	  (myterpri))
)))

;;   myterpri is terpri with port and indent control

(defun myterpri ()
  (if mPrport (terpri mPrport) (mterpri))
  (setq ccol 1)
  (myindent)
)

;;      lastlementp is a predicate function to check a list l
;;that is there only one element left in the list.

(defun lastelementp (l) (equal (length l) 1))

;;      getsymbol is a function tool. It'll  get the information
;;from the database which is a symbol for an argument (atom)

(defun getsymbol (atom) (get atom 'chchr))

;;      get_process is a function tool. It'll  get the information
;;from the database about the process to handle the operator (atom)
;; (defun get_process (atom) (get atom 'mPrprocess))

;;      setup is a function to build the database (put properties) for 
;;each key word

; check if property exists already
(defun setup (arg)
  (mapc #'(lambda (ls) (setf (get (car arg) (car ls)) (cadr ls)))
        (cdr arg)))

;;      mPr-lbp and mPr-rbp are the functions to get information
;;      about size of the particular operator
;;      this is from the latex version of this prog
;;      not sure how well it works for MathML

(defun mPr-lbp (x) (cond ((get x 'mPr-lbp)) (t (lbp x))))

(defun mPr-rbp (x) (cond ((get x 'mPr-rbp)) (t (rbp x))))

;; reduce lbp and rbp value for mtimes to get less parentesis
(defun $lessparen ()
  (setf (get 'mtimes 'mPr-lbp) '110)
  (setf (get 'mtimes 'mPr-rbp) '110)
  '$done)
;; get back to normal case for paren
(defun $parenback ()
  (setf (get 'mtimes 'mPr-lbp) '120)
  (setf (get 'mtimes 'mPr-rbp) '120)
  '$done)

;;      mPr-abs is a function to handle abs()

(defun mPr-abs (mexpress)
  (tprinc "<mo>|</mo>")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (tprinc "<mo>|</mo>"))

(defun mPr-conjugate (mexpress)
  (tprinc "<mover>")
  (tprinc "<mrow>")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (tprinc "</mrow>")
  (tprinc "<mo>&#xaf;</mo>") ;; macron
  (tprinc "</mover>"))

;; a[1]^2 or a[x,y]^z
(defun mPr-arr-power(b e)
  (tprinc "<msubsup>")
  (mPr_engine (caar b) lop 'mfunction)
  (cond
   ((equal (length b) 2) 
     (mPr_engine (cadr b) lop rop)
   )
   (t (row-begin "<mrow>") ;;(tprinc "<mrow>")
     (do ((l (cdr b) (cdr l))) ((null l)(row-end "</mrow>"))
       (mPr_engine (car l) lop rop)
       (when (not (lastelementp l)) (tprinc "<mo>,</mo>")))
  ))
  (mPr_engine e 'mparen 'mparen) (tprinc "</msubsup>")
)

;;      when the operator is array ,this function will be called
;;      ex. a[x1,..] is a top level representation

(defun mPr-array (mexpress)
  (tprinc "<msub>")
  (mPr_engine (caar mexpress) lop 'mfunction)
  (row-begin "<mrow>") 
  (do ((l (cdr mexpress) (cdr l))) ((null l) (row-end "</mrow>")(tprinc "</msub>"))
    (mPr_engine (car l) lop rop)
    (when (not (lastelementp l)) (tprinc "<mo>,</mo>"))))

;;      mPr-at is a function to handel at(..) function 
;;
(defun mPr-at (mexpress)
  (row-begin "<mrow>") ;;(tprinc "<mrow>")
  (mPr_engine (cadr mexpress) lop rop)
  (tprinc "<msub><mo>|</mo>")
  (mPr_engine (caddr mexpress) 'mparen 'mparen)
  (tprinc "</msub>") (row-end "</mrow>")
)
;;      in mPr_engine ,whennever mexpress is an atom this function taking care 
;;of it by getting a TeX symbol if it exists. Also it handles some word which
;;has a reserved character for TeX

;; prints instead of returning value now
(defun mPr-atom (chr)
  (cond
    ((numberp chr) (mPr-num chr))
    ;; pwang 1/2005
    ;; ((atom chr) (tprinc "<mi>") (tprinc (fullstrip1 chr)) (tprinc "</mi>"))
    ((safe-get chr 'chchr) (tprinc "<mi>") 
     (tprinc (safe-get chr 'chchr)) (tprinc "</mi>"))
    (t
      (let ((my-atom (if (symbolp chr) (print-invert-case (stripdollar chr)) chr)))
        (tprinc "<mi>")
        (tprinc (coerce (mapcar #'handle_rsw (exploden my-atom)) 'string))
        (tprinc "</mi>")))))

(defun rm (a list)
  (do ((l list (cdr l)) (l2 nil)) ((null l) (reverse l2))
    (when (not (equal a (car l))) (setq l2 (cons (car l) l2)))))


;;      this fn is called by mPr-atom ,it checks for a reserved char.
(defun handle_rsw (c)
  (cond
    ((equal c #\<) "&lt;")
    ((equal c #\>) "&gt;")
    ((equal c #\&) "&amp;")
    (t c)))

;;      mPr-binomial :-
;;       top level:  binomail(x,y);

(defun mPr-binomial (mexpress)
  (row-begin "<mrow>") (tprinc "<mo>(</mo><mfrac linethickness=\"0\">")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (tprinc "  ")
  (mPr_engine (caddr mexpress) 'mparen 'mparen)
  (tprinc "</mfrac><mo>)</mo>") (row-end "</mrow>"))



;;      mPr-det is a function to handle determinant()

(defun mPr-det (mexpress)
  (let ((operand (cadr mexpress)))
    (tprinc "<mi>det</mi>")
    (mPr_engine operand 'mparen 'mparen)))

;;      mPr-dif is a function to handle diferentiation function. 
;;It calls to subfunctions powerof_d and denopart.
;;
(defun mPr-diff (mexpress)
  (cond
    ((powerof_d (cddr mexpress)) (denopart (cddr mexpress))
     (tprinc "</mfrac><mo>&InvisibleTimes;</mo>") 
     (mPr_engine (cadr mexpress) 'mtimes rop)
     (row-end "</mrow>"))
    (t (mPr_engine (cadr mexpress) lop rop))))

;;if there is no repeating differentiation
;; just diff(exp,x)
;; if diff(exp,x,no,..)
(defun powerof_d (l)
  (cond
    ((lastelementp l) 
     (row-begin "<mrow>")(tprinc "<mfrac><mo> &dd; </mo>") t)
    (t (do ((l1 l (cddr l1)) (l2 nil (cons (cadr l1) l2))
            (power_of_d nil))
           ((null l1) (setq power_of_d (addn l2 nil))
            (cond
              ((numberp power_of_d)
               (cond
                 ((equal 0 power_of_d) nil)
                 ((equal 1 power_of_d)(row-begin "<mrow>")(tprinc "<mfrac><mo> &dd; </mo>") t)
                 (t (row-begin "<mrow>")(tprinc "<mfrac><msup><mo> &dd;</mo><mn>")
		    (tprinc power_of_d) (tprinc "</mn></msup>") t)))
              (t (row-begin "<mrow>")(tprinc "<mfrac><msup><mo> &dd;</mo>")
                 (mPr_engine power_of_d 'mparen 'mparen)
                 (tprinc "</msup>") t))))))
)

;;if just diff(exp,x)
;;if diff(exp,x,nox,y,noy,...)
(defun denopart (l)
  (prog (result)
    (cond
      ((lastelementp l) (row-begin "<mrow>") (tprinc "<mo> &dd; </mo>")
       (p-op (getsymbol 'mtimes)) (mPr_engine (car l) 'mtimes rop)
      (row-end "</mrow>"))
      (t (do ((l1 l (cddr l1)) (l2 nil)) ((null l1) (setq result l2))
           (setq l2
                 (cons (append '((mexpt)) (list (car l1))
                               (list (cadr l1)))
                       l2)))
         (setq result (muln result nil))
         (cond
           ((atom result) (row-begin "<mrow>")(tprinc "<mo> &dd; </mo>")
	    (p-op (getsymbol 'mtimes))
            (mPr_engine result 'mparen 'mparen) (row-end "</mrow>"))
           ((listp result)
            (cond
              ((eq (caar result) 'mexpt) 
	       (row-begin "<mrow>")(tprinc "<mo> &dd; </mo>")
               (p-op (getsymbol 'mtimes))
               (mPr_engine result 'mtimes 'mparen) (row-end "</mrow>"))
              (t (row-begin "<mrow>") 
                 (do ((l1 (cdr result) (cdr l1)) (l2 nil)
                      (power_of_d nil))
                     ((null l1) (row-end "</mrow>"))
                   (tprinc "<mo> &dd; </mo>")
                   (p-op (getsymbol 'mtimes))
                   (mPr_engine (car l1) 'mtimes 'mtimes)
                   (when (not (lastelementp l1)) (tprinc "<mo>,</mo>"))
		 )
		 ))))))))
        
;; this fuction is adopted the main idea form macTeX from Prof. Richard
;; Fateman in the mPr-mexpt
;;
;; insert left-angle-brackets for mncexpt. a^<n> is how a^^n looks.
;; here is where we have to check for f(x)^b to be displayed
;; as f^b(x), as is the case for sin(x)^2 .
;; which should be sin^2 x rather than (sin x)^2 or (sin(x))^2. 
;; yet we must not display (a+b)^2 as +^2(a,b)...
;; or (sin(x))^(-1) as sin^(-1)x, which would be arcsine x
; this is f(x)
; this is f [or nil]
;this is (x) [maybe (x,y..), or nil]
;; this is the exponent
; there is such a function
;; insist it is a % or $ function
;     x
;;this case like sin(x)^x --> sin x
;; if for example exp = (x+2)^4
;;      in case x^^y
(defun mPr-expt (mexpress)
 (cond
  ((eq (caar mexpress) 'mexpt)
   (if (and (not (atom (cadr mexpress)))
	     (member 'array (caadr mexpress) :test #'eq) ;; array
       )
       (mPr-arr-power (cadr mexpress) (caddr mexpress))
       (let* ((fx (cadr mexpress))
            (f (and (not (atom fx)) (atom (caar fx)) (caar fx)))
            (bascdr (and f (cdr fx))) (expon (caddr mexpress))
            (doit (and f (member (char (string f) 0) (list #\% #\$) :test #'eq)
                       (not (member f '(%sum %product) :test #'eq)))))
        (cond
           (doit (cond     ;;;; sin^2 x case
                 ((atom expon) 
		  (row-begin "<mrow>")(tprinc "<msup>") (mPr-fname f)
                  (mPr-atom expon)(tprinc "</msup>") 
                  (tprinc "<mo>&ApplyFunction;</mo>")
                  (if (cdr bascdr) (mPr-listparen bascdr)
                      (mPr_engine (car bascdr) 'mtimes 'mtimes))
		  (row-end "</mrow>")
		 )
                 (t (tprinc "<msup>")
		    (mPr_engine fx 'mparen 'mparen)
                    (mPr_engine expon 'mparen 'mparen)
                    (tprinc "</msup>"))))
          (t (tprinc "<msup>")
            (mPr_engine (cadr mexpress) lop (caar mexpress))
            (mPr_engine (caddr mexpress) 'mparen 'mparen)
            (tprinc "</msup>")))))
  )
  (t (tprinc "<msup>") ;;;  mnexpt case
       (mPr_engine (cadr mexpress) lop (caar mexpress))
       (row-begin "<mrow>")(tprinc "<mo>&LeftAngleBracket;</mo>")
       (mPr_engine (caddr mexpress) 'mparen 'mparen)
       (tprinc "<mo>&RightAngleBracket;</mo>")(row-end "</mrow>")
       (tprinc "</msup>")))
)
;;      this function will check that whether or not an arg has a symbol
;;in data base or not, if not it 'll be treated to be function which 'll
;;be printed in rm font
(defun mPr-fname (f)
     (tprinc "<mi>")
     (tprinc (if (getsymbol f) (getsymbol f) f))
     (tprinc "</mi>")
)
;;      to handle if an operator is a function which will be printed
(defun mPr-function (mexpress)
  (mPr_engine (caar mexpress) 'mparen 'mparen)
  (tprinc "<mo>&ApplyFunction;</mo>")
  (mPr-listparen (cdr mexpress)))

(defun mPr-gamma (mexpress)
  (mPr_engine '|$Gamma| 'mparen 'mparen) ;; ensure big gamma instead of little gamma (CHCHR property)
  (tprinc "<mo>&ApplyFunction;</mo>")
  (mPr-listparen (cdr mexpress)))

;;      for infix operator , and also handle when there is a truncation
;;in macsyma expression (see mPr-infix1)
;;      mPr-infix calling
;;              1)mPr-infix1 calling 
;;                      1.1) p-op-oprd
;;              2)p-op-oprd
;;
;if -x or +x so call mPr-function
(defun mPr-infix (mexpress)
  (let ((moperator (car mexpress)) (moperands (cdr mexpress)))
    (cond
      ((equal (length moperands) 1) (mPr-function mexpress))
      (t (row-begin "<mrow>")
	 (mPr_engine (car moperands) lop (car moperator))
         (p-op-oprd moperator (cadr moperands))
         (mPr-infix1 moperator (cddr moperands))
	 (row-end "</mrow>")
))))

(defun mPr-infix1 (moperator moperands)
  (cond
    ((null moperands)
     (when (member 'trunc moperator :test #'equal)
       (p-op (getsymbol (car moperator)))
       (tprinc "<mo>&TripleDot;</mo>")))
    (t (p-op-oprd moperator (car moperands))
       (mPr-infix1 moperator (cdr moperands)))))

;;      p-op-oprd is a function printing operator and operand consecutively
;;      ex      + x     when + is a infix op and x is oprd

(defun p-op-oprd (moperator moperand)
  (let ((op (car moperator)))
    (cond
      ((equal op 'mplus)
       (cond
         ((listp moperand)
          (cond
            ((equal (caar moperand) 'mminus) (tprinc "<mo>-</mo>")
             (mPr_engine (cadr moperand) 'mminus rop))
            (t (tprinc "<mo>+</mo>") (mPr_engine moperand 'mplus rop))))
         (t (tprinc "<mo>+</mo>") (mPr-atom moperand))))
      (t (p-op (getsymbol op)) 
         (mPr_engine moperand op op))))
)

(defun p-op(symbol)
    (tprinc "<mo>") 
    (tprinc symbol) 
    (tprinc "</mo>") 
)

;;      mPr-intgrate handles an integration expression
;;      It will detect that integrate function is called in short form
;; or long form example: integrate(x^4,x,0,inf) is a long form.

;;short form
;;long form
(defun mPr-integrate (mexpress)
  (setq mexpress (meval 
    (list '($substitute) '((mminus) $inf) '$minf mexpress)))
  (cond
    ((equal (length mexpress) 3)
     (row-begin "<mrow>")(tprinc "<mo>&Integral;</mo>"))
    ((equal (length mexpress) 5)
     (row-begin "<mrow>")(tprinc "<msubsup><mo>&Integral;</mo>")
     (row-begin "<mrow>")
     (mPr_engine (cadddr mexpress) 'mparen 'mparen)
     (row-end "</mrow>")
     (tprinc "  ")
     (row-begin "<mrow>")
     (mPr_engine (car (cddddr mexpress)) 'mparen 'mparen)
     (row-end "</mrow>")
     (tprinc "</msubsup>"))
    (t (merror "Wrong NO. of Arguments")))
  (row-begin "<mrow>")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (row-end "</mrow>")(tprinc "<mo>&InvisibleTimes;</mo><mo> &dd; </mo>")
  (mPr_engine (caddr mexpress) 'mparen rop)
  (row-end "</mrow>"))

                      
;;      mPr-limit takes care the "limit(exp,var,val,dir)"
(defun mPr-limit (mexpress)
  (setq mexpress (meval 
    (list '($substitute) '((mminus) $inf) '$minf mexpress)))
  (row-begin "<mrow>")(tprinc "<munder><mo>lim</mo>")(row-begin "<mrow>")
  (mPr_engine (caddr mexpress) 'mparen 'mparen)
  (tprinc "<mo>&RightArrow;</mo>")
  (mPr_engine (cadddr mexpress) 'mparen 'mapren)
  (when (car (cddddr mexpress))
    (if (member (car (cddddr mexpress)) '($minus $plus) :test #'equal)
        (p-op (getsymbol (car (cddddr mexpress))))
        (merror "THE 4TH ARG MUST BE PLUS OR MINUS")))
  (row-end "</mrow>")(tprinc "</munder>")
  ;; (tprinc "<mo>&InvisibleTimes;</mo>")
  (mPr_engine (cadr mexpress) 'mparen rop)
  (row-end "</mrow>"))
;;      This function handles a macsyma list expression 
;; 
(defun mPr-list (mexpress)
  (tprinc "<mo>[</mo>")
  (do ((l (cdr mexpress) (cdr l))) ((null l) (tprinc "<mo>]</mo>"))
    (mPr_engine (car l) 'mparen 'mparen)
    (when (not (lastelementp l)) (tprinc "<mo>,</mo>"))))


;;      This function is a subfunction of mPr-expt , mPr-function and
;; mPr-mqapply
(defun mPr-listparen (mexpress)
  (row-begin "<mrow>")(tprinc "<mo>(</mo>")
  (do ((l mexpress (cdr l))) ((null l) (tprinc "<mo>)</mo>") (row-end "</mrow>"))
    (mPr_engine (car l) 'mparen 'mparen)
    (when (not (lastelementp l)) (tprinc "<mo>,</mo>"))))

;;      mPr-matrix handles matrix function
(defun mPr-matrix (mexpress)
  (row-begin "<mfenced open='(' close=')'><mtable>")
  (mapc #'(lambda (arg)
	    (row-begin "<mtr>")
            (do ((l (cdr arg) (cdr l))) ((null l) (row-end "</mtr>"))
	      (row-begin "<mtd>")
	      (mPr_engine (car l) 'mparen 'mparen)
	      (row-end "</mtd>")
	      ))
        (cdr mexpress))
  (row-end "</mtable></mfenced>")
)

(defun mPr-mqapply (mexpress)
  (mPr_engine (cadr mexpress) lop 'mfunction)
  (mPr-listparen (cddr mexpress)))

;; this function handles the floating point number.
;; convert 1.2e20 to 1.2 \\cdot 10^{20}
;; is it ddd.ddde+EE
;; it is not. go with it as given
(defun mPr-num (atom)
  (let (r firstpart exponent)
    (cond
      ((integerp atom) (tprinc "<mn>") (tprinc atom) (tprinc "</mn>"))
      (t (setq r (exploden atom))
         ;; Hmm. What if the exponent marker is something other than 'e' or 'E' ??
         (setq exponent (or (member #\e r :test #'eq) (member #\E r :test #'eq)))
         (cond
           ((null exponent) (tprinc "<mn>") (tprinc atom) (tprinc "</mn>"))
           (t (setq firstpart
                    (nreverse (cdr (or (member #\e (reverse r) :test #'eq) (member #\E (reverse r) :test #'eq)))))
              (tprinc "<mn>") 
	      (mapc #'tpchar firstpart) (tprinc "</mn>") 
	      (tprinc "<mo>&CenterDot;</mo><msup><mn>10</mn> <mn>")
              (mapc #'tpchar (cdr exponent))
	      (tprinc "</mn></msup>")))))))

;;      this function puts parenthesis for the expression
(defun mPr-paren (mexpress)
  (row-begin "<mrow>")(tprinc "<mo>(</mo>")
  (mPr_engine mexpress 'mparen 'mparen)
  (tprinc "<mo>)</mo>") (row-end "</mrow>"))
;;      this function handles "+" operator which is infix form
;;
;if -x or +x so call mPr-function
(defun mPr-plus (mexpress)
  (let ((moperands (cdr mexpress))
        (flag_trunc (member 'trunc (car mexpress) :test #'eq)))
    (cond
      ((equal (length moperands) 1) (mPr-prefix mexpress))
      (t (row-begin "<mrow>")
	 (mPr_engine (car moperands) lop 'mplus)
         (print_op_oprd (cadr moperands))
         (mPr-plus1 (cddr moperands) flag_trunc)
         (row-end "</mrow>")
      )
)))

(defun mPr-plus1 (moperands flag_trunc)
  (cond
    ((null moperands) (when flag_trunc (tprinc "<mo>+</mo><mo>&TripleDot;</mo>")))
    (t (print_op_oprd (car moperands))
       (mPr-plus1 (cdr moperands) flag_trunc))))


(defun print_op_oprd (moperand)
  (cond
    ((listp moperand)
     (cond
       ((equal (caar moperand) 'mminus) (tprinc "<mo>-</mo>")
        (mPr_engine (cadr moperand) 'mplus rop))
       (t (tprinc "<mo>+</mo>") (mPr_engine moperand 'mplus 'mparen))))
    (t (tprinc "<mo>+</mo>") (mPr-atom moperand))))
;;      mPr-postfix handles for postfix notation expression like factorial
;;
(defun mPr-postfix (mexpress)
  (row-begin "<mrow>")
  (mPr_engine (cadr mexpress) lop (caar mexpress))
  (row-end "</mrow>") 
  (p-op (getsymbol (caar mexpress))))

;;      mPr-prefix is a function to handle a prefix notation form
;;
(defun mPr-prefix (mexpress)
  (let ((op (caar mexpress)) (oprnd (cadr mexpress)))
    (row-begin "<mrow>")
    (p-op (getsymbol op))
    (mPr_engine oprnd op rop)
    (row-end "</mrow>")))
;;      this function takes care the quotient function or "/" sign
;;
(defun mPr-quotient (mexpress)
  (row-begin "<mfrac><mrow>")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (row-end "</mrow>")
  (row-begin "<mrow>")
  (mPr_engine (caddr mexpress) 'mparen 'mparen)
  (row-end "</mrow></mfrac>"))

(defun mPr-rat (mexpress) (mPr-quotient mexpress))

;;      this function handles binomial coefficients
;;
(defun mPr-binomial(mexpress)
    (row-begin "<mrow><mfenced open='(' close=')'><mfrac linethickness='0'><mrow>")
       (mPr_engine (cadr mexpress) 'mparen 'mparen)
       (tprinc "</mrow><mrow>")
       (mPr_engine (caddr mexpress) 'mparen 'mparen)
    (row-end  "</mrow></mfrac></mfenced></mrow>")
)

;;      this function handles sqrt
;;
(defun mPr-sqrt (mexpress)
  (tprinc "<msqrt>")
  (mPr_engine (cadr mexpress) 'mparen 'mparen)
  (tprinc "</msqrt>"))
    
;;      This function taks care both sum(exp,ind,lo,hi) and 
;; product(exp,ind,lo,hi)
;;ind
;;low
;; hi
;;exp
(defun mPr-sumprod (mexpress)
  (row-begin "<mrow>")(tprinc "<munderover>")
  (p-op (getsymbol (caar mexpress)))
  (row-begin "<mrow>")
  (mPr_engine (caddr mexpress) 'mparen 'mequal)
  (tprinc "<mo>=</mo>")
  (mPr_engine (meval 
    (list '($substitute) '((mminus) $inf) '$minf (cadddr mexpress)))
    'mequal 'mparen)
  (row-end "</mrow>")
  (mPr_engine  (meval
    (list '($substitute) '((mminus) $inf) '$minf (car (cddddr mexpress))))
    'mparen 'mparen)
  (tprinc "</munderover>")
  (mPr_engine (cadr mexpress) 'mparen rop)
  (row-end "</mrow>"))
;;      mPr-times a function handle multiplication
(defun mPr-times (mexpress)
  (let ((lop 'mtimes) (rop 'mtimes)) (mPr-infix mexpress)))

(defun mathml-presentation-lambda (mexpress)
  (let
    ((op (caar mexpress))
     (args (cdr (cadr mexpress)))
     (body (cddr mexpress)))
    (mPr_engine op 'mparen 'mparen)
    (if (= (length args) 1)
      (mPr_engine (car args) 'mparen 'mparen)
      (mPr-listparen args))
    (mPr_engine "." 'mparen 'mparen)
    (if (= (length body) 1)
      (mPr_engine (car body) 'mparen 'mparen)
      (mPr-listparen body))))

;; An improvement on the default, but not much.
;; Could benefit from just a little more attention.
(defun mathml-presentation-buildinfo (mexpress)
  (mPr_engine `(($matrix) ,@(mapcar #'(lambda (e) `((mlist) ,e)) (cdr mexpress))) 'mparen 'mparen))

;;;;;;; Operators

(setup '(mlist (mPrprocess mPr-list)))

(setup '(mplus (mPrprocess mPr-plus) (mPr-lbp 100) (mPr-rbp 100)
               (chchr "+")))

(setup '(mminus (mPrprocess mPr-prefix) (mPr-lbp 100) (mPr-rbp 100)
                (chchr "-")))

(setup '(mquote (mPrprocess mPr-prefix) (mPr-rbp 201) (chchr "'")))

(setup '(mand (mPrprocess mPr-infix) (mPr-lbp 60) (mPr-rbp 60)
              (chchr "and")))

(setup '(mor (mPrprocess mPr-infix) (mPr-lbp 50) (mPr-rbp 50)
             (chchr "or")))

(setup '(mnot (mPrprocess mPr-prefix) (mPr-rbp 70) (chchr "&not;")))

(setup '(mgreaterp (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
            (chchr "&gt;")))

(setup '(mgeqp (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
               (chchr "&ge;")))


(setup '(mnotequal (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
            (chchr "&NotEqual;")))

(setup '(mleqp (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
               (chchr "&le;")))

(setup '(mlessp (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
                (chchr "&lt;")))

(setup '(msetq (mPrprocess mPr-infix) (mPr-lbp 180) (mPr-rbp 20)
               (chchr "&Assign;")))

(setup '(mset (mPrprocess mPr-infix) (mPr-lbp 180) (mPr-rbp 20)
               (chchr "&Assign;")))  ;;; This is not math

(setup '(mdefine (mPrprocess mPr-infix) (mPr-lbp 180) (mPr-rbp 20)
                 (chchr ":=")))

(setup '(mfactorial (mPrprocess mPr-postfix) (mPr-lbp 160) (chchr "!")))

(setup '(mabs (mPrprocess mPr-abs)))

(setup '(%abs (mPrprocess mPr-abs)))

(setup '($conjugate (mPrprocess mPr-conjugate)))

(setup '(mnctimes (mPrprocess mPr-infix) (mPr-lbp 110) (mPr-rbp 109)
            (chchr "&CenterDot;")))

(setup '(marrow (mPrprocess mPr-infix) (mPr-lbp 180) (mPr-rbp 20)
                (chchr "&RightArrow;")))

(setup '(mrarrow (mPrprocess mPr-prefix) (mPr-lbp 180) (mPr-rbp 20)
                (chchr "&RightArrow;")))

(setup '(mdif (mPrprocess mPr-infix) (mPr-lbp 100) (mPr-rbp 100)
              (chchr "-")))

(setup '(mtimes (mPrprocess mPr-times) (mPr-lbp 120) (mPr-rbp 120)
                (chchr "&InvisibleTimes;")))

(setup '(mdottimes (mPrprocess mPr-infix) (mPr-lbp 120) (mPr-rbp 120)
            (chchr "&CenterDot;")))

(setup '(mexpt (mPrprocess mPr-expt) (mPr-lbp 140) (mPr-rbp 139)))

(setup '(mncexpt (mPrprocess mPr-expt) (mPr-lbp 135) (mPr-rbp 134)))

(setup '(%at (mPrprocess mPr-at)))

(setup '($at (mPrprocess mPr-at)))

(setup '($det (mPrprocess mPr-det)))

(setup '(%determinant (mPrprocess mPr-det)))

(setup '($binomial (mPrprocess mPr-binomial)))

(setup '(%binomial (mPrprocess mPr-binomial)))

(setup '(%sum (mPrprocess mPr-sumprod) (chchr "&Sum;")))

(setup '($sum (mPrprocess mPr-sumprod) (chchr "&Sum;")))

(setup '($product (mPrprocess mPr-sumprod) (chchr "&Prod;")))

(setup '(%product (mPrprocess mPr-sumprod) (chchr "&Prod;")))

(setup '($integrate (mPrprocess mPr-integrate) (chchr "&Integral;")))

(setup '(%integrate (mPrprocess mPr-integrate) (chchr "&Integral;")))

(setup '($diff (mPrprocess mPr-diff) (chchr "<mo>&dd;</mo>")))

(setup '(%derivative (mPrprocess mPr-diff) (chchr "<mo>&dd;</mo>")))

(setup '($limit (mPrprocess mPr-limit)))

(setup '(%limit (mPrprocess mPr-limit)))

(setup '($sqrt (mPrprocess mPr-sqrt) (chchr "&Sqrt;")))

(setup '(%sqrt (mPrprocess mPr-sqrt) (chchr "&Sqrt;")))

(setup '(%binomial (mPrprocess mPr-binomial)))

(setup '(mquotient (mPrprocess mPr-quotient) (mPr-lbp 122)
            (mPr-rbp 123) (chchr "<mo>/</mo>"))) 

(setup '(rat (mPrprocess mPr-rat) (mPr-lbp 120) (mPr-rbp 121)))

(setup '(mconc (mPrprocess mPr-infix) (chchr " ")))

(setup '(mparen (chchr " "))) 

(setup '(mbrak (chchr " "))) 

(setup '(mequal (mPrprocess mPr-infix) (mPr-lbp 80) (mPr-rbp 80)
                (chchr "=")))

;;(setup '(mmsubs (mPrprocess mPr-mmsubs) (chchr "&")))

(setup '(mqapply (mPrprocess mPr-mqapply))) 

(setup '(mmfunct (mPrprocess mPr-funct))) 

(setup '($matrix (mPrprocess mPr-matrix)))

(setup '(lambda (mPrprocess mathml-presentation-lambda)))

(setup '(%build_info (mPrprocess mathml-presentation-buildinfo)))

(setup '($%pi (chchr "&pi;")))

(setup '($%e (chchr "&ee;")))

(setup '($%gamma (chchr "&gamma;")))

(setup '($%phi (chchr "&phi;")))

(setup '(& (chchr "&amp;")))

(setup '(% (chchr "%")))

(setup '($ (chchr "$")))

(setup '(_ (chchr "_")))

(setup '($minus (chchr "-")))

(setup '($plus (chchr "+")))
;;

(setup '(mprog (chchr "block")))

(setup '($$block (chchr "block")))

(setup '($$boldif (chchr "if")))

(setup '($$boldthen (chchr "then")))

(setup '($$boldelse (chchr "else")))


;;;; routines to access these fields

;;      The following are databases for special characters

(setf (get '$inf 'chchr) '"&infin;")
;;;(setf (get '$minf 'chchr) '"<mo>-</mo>&infin;")

;;      lower case greek database

(setf (get '$alpha 'chchr) '"&alpha;")
(setf (get '%alpha 'chchr) '"&alpha;")
(setf (get '$beta 'chchr) '"&beta;")
(setf (get '$gamma 'chchr) '"&gamma;")
(setf (get '%gamma 'chchr) '"&gamma;")
(setf (get '%gamma_incomplete 'chchr) '"&Gamma;")
(setf (get '%gamma_incomplete_generalized 'chchr) '"&Gamma;")
(setf (get '%gamma_incomplete_regularized 'chchr) '"Q")
(setf (get '$gamma_greek 'chchr) '"&gamma;")
(setf (get '$delta 'chchr) '"&delta;")
(setf (get '$epsilon 'chchr) '"&epsilon;")
(setf (get '$varepsilon 'chchr) '"&varepsilon;")
(setf (get '$zeta 'chchr) '"&zeta;")
(setf (get '$eta 'chchr) '"&eta;")
(setf (get '$theta 'chchr) '"&theta;")
(setf (get '$vartheta 'chchr) '"&vartheta;")
(setf (get '$iota 'chchr) '"&iota;")
(setf (get '$kappa 'chchr) '"&kappa;")
(setf (get '$lambda 'chchr) '"&lambda;")
(setf (get 'lambda 'chchr) '"&lambda;")
(setf (get '$mu 'chchr) '"&mu;")
(setf (get '$nu 'chchr) '"&nu;")
(setf (get '$xi 'chchr) '"&xi;")
(setf (get '$pi 'chchr) '"&pi;")
(setf (get '$varpi 'chchr) '"&varpi;")
(setf (get '$rho 'chchr) '"&rho;")
(setf (get '$varrho 'chchr) '"&varrho;")
(setf (get '$sigma 'chchr) '"&sigma;")
(setf (get '$varsigma 'chchr) '"&varsigma;")
(setf (get '$tau 'chchr) '"&tau;")
(setf (get '$upsilon 'chchr) '"&upsilon;")
(setf (get '$phi 'chchr) '"&phi;")
(setf (get '$varphi 'chchr) '"&varphi;")
(setf (get '$chi 'chchr) '"&chi;")
(setf (get '$psi 'chchr) '"&psi;")
(setf (get '$omega 'chchr) '"&omega;")

;;      Greek Upper Case Database

(setf (get '|$Alpha| 'chchr) '"&Alpha;")
(setf (get '|$Gamma| 'chchr) '"&Gamma;")
(setf (get '|$Delta| 'chchr) '"&Delta;")
(setf (get '|$Theta| 'chchr) '"&Theta;")
(setf (get '|$Lambda| 'chchr) '"&Lambda;")
(setf (get '|$Xi| 'chchr) '"&Xi;")
(setf (get '|$Pi| 'chchr) '"&Pi;")
(setf (get '|$Sigma| 'chchr) '"&Sigma;")
(setf (get '|$Upsilon| 'chchr) '"&Upsilon;")
(setf (get '|$Phi| 'chchr) '"&Phi;")
(setf (get '|$Psi| 'chchr) '"&Psi;")
(setf (get '|$Omega| 'chchr) '"&Omega;")
(setf (get '|$Re| 'chchr) '"&Re;")
(setf (get '|$Im| 'chchr) '"&Im;")

;;      Miscellaneous symbols

(setf (get '$aleph 'chchr) '"&aleph;")
(setf (get '$hbar 'chchr) '"&hbar;")
(setf (get '$%i 'chchr) '"&ii;")
(setf (get '$%j 'chchr) '"&ij")
(setf (get '$ell 'chchr) '"&ell;")
(setf (get '$wp 'chchr) '"&wp;")
(setf (get '$mho 'chchr) '"&mho;")
(setf (get '$infty 'chchr) '"&infty;")
(setf (get '$nabla 'chchr) '"&nabla;")
(setf (get '$partial 'chchr) '"&PartialD;")
(setf (get '$triangle 'chchr) '"&triangle;")


(setup '(%sin (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sin")))
(setup '(%cos (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cos")))
(setup '(%tan (mPrprocess mPr-function) (mPr-rbp 110) (chchr"tan")))
(setup '(%cot (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cot")))
(setup '(%sec (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sec")))
(setup '(%csc (mPrprocess mPr-function) (mPr-rbp 110) (chchr"csc")))

(setup '(%asin (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arcsin")))
(setup '(%acos (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arccos")))
(setup '(%atan (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arctan")))
(setup '(%acot (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acot")))
(setup '(%asec (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asec")))
(setup '(%acsc (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acsc")))
(setup '(%sinh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sinh")))
(setup '(%cosh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cosh")))
(setup '(%tanh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"tanh")))
(setup '(%coth (mPrprocess mPr-function) (mPr-rbp 110) (chchr"coth")))
(setup '(%sech (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sec")))
(setup '(%csch (mPrprocess mPr-function) (mPr-rbp 110) (chchr"csch")))


(setup '(%asinh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asinh")))
(setup '(%acosh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acosh")))
(setup '(%atanh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"atanh")))
(setup '(%acoth (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acoth")))
(setup '(%asech (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asec")))
(setup '(%acsch (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acsch")))

(setup '(%ln (mPrprocess mPr-function) (mPr-rbp 110) (chchr"ln")))
(setup '(%log (mPrprocess mPr-function) (mPr-rbp 110) (chchr"log")))

(setup '($sin (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sin")))
(setup '($cos (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cos")))
(setup '($tan (mPrprocess mPr-function) (mPr-rbp 110) (chchr"tan")))
(setup '($cot (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cot")))
(setup '($sec (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sec")))
(setup '($csc (mPrprocess mPr-function) (mPr-rbp 110) (chchr"csc")))

(setup '($asin (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arcsin")))
(setup '($acos (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arccos")))
(setup '($atan (mPrprocess mPr-function) (mPr-rbp 110) (chchr"arctan")))
(setup '($acot (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acot")))
(setup '($asec (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asec")))
(setup '($acsc (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acsc")))

(setup '($sinh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sinh")))
(setup '($cosh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"cosh")))
(setup '($tanh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"tanh")))
(setup '($coth (mPrprocess mPr-function) (mPr-rbp 110) (chchr"coth")))
(setup '($sech (mPrprocess mPr-function) (mPr-rbp 110) (chchr"sec")))
(setup '($csch (mPrprocess mPr-function) (mPr-rbp 110) (chchr"csch")))

(setup '($asinh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asinh")))
(setup '($acosh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acosh")))
(setup '($atanh (mPrprocess mPr-function) (mPr-rbp 110) (chchr"atanh")))
(setup '($acoth (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acoth")))
(setup '($asech (mPrprocess mPr-function) (mPr-rbp 110) (chchr"asec")))
(setup '($acsch (mPrprocess mPr-function) (mPr-rbp 110) (chchr"acsch")))
(setup '($ln (mPrprocess mPr-function) (mPr-rbp 110) (chchr"ln")))
(setup '($log (mPrprocess mPr-function) (mPr-rbp 110) (chchr"log")))
(setup '(%gamma (mPrprocess mPr-gamma)))

;;
;;
;;      set the preference feature
;;
($lessparen)
(setq casep nil)                ;set to distinguish a capital or lower case
(setq $mPrworksheet nil)        ;set TeX worksheet mode false
(setq $lamPrworksheet nil)        ;set LaTeX worksheet mode false
(setq $mPrlabelleft nil)        ;set Tex or LaTeX left Labeling mode false
(setq $mPrdisplaytype t)        ;set default for TeX or LaTeX in display type
(setq $mPrevaluate t)   ;set default for evaluating macsyma expression
(setq $mPrautolabel nil) ;set autolabel mode off, can be set to be integer
(setq $lamPrautolabel nil)      ;set LaTeX autolabel mode false

;; The MathML presentation code has been loaded. Run each post-load hook. This
;; let other libraries hook in to the MathML library easily (doing so needs
;; SETUP and MPR_ENGINE to be defined).
;;
;; Each hook should be an idempotent thunk.

(when (boundp '*mathml-presentation-hook*)
  (dolist (hook (symbol-value '*mathml-presentation-hook*))
    (funcall hook)))
