;; -*- Mode:Common-Lisp;Package:mma; Base:10 -*- ;; Mathematica(tm)-like stuff for Maxima. ;; copyright (c) 2011 Richard J. Fateman (in-package :mma) (eval-when (:compile-toplevel :load-toplevel) (if (find-package "MAXIMA") nil (defpackage :maxima))) (defparameter macsubs ;; some of these equivalences are slightly bogus '((|Set| . maxima::msetq) (|Equal| . maxima::mequal) (|Pattern| . maxima::\$Pattern) (|Blank| . maxima::\$Blank) (|Increment| . maxima::\$Increment) (|Part| . maxima::\$Part) (|Greater| . maxima::mgreaterp) (|GreaterEqual| . maxima::mgeqp) (|LessEqual| . maxima::mleqp) (|Plus| . maxima::mplus) (|Times| . maxima::mtimes) (|Power| . maxima::mexpt) (|Sin| . maxima::%sin) (|Cos| . maxima::%cos) (|List| . maxima::mlist) (|N| . maxima::Numeric_eval) (|CompoundExpression| . maxima::mprogn) (|If| . maxima::mcond) (|Module| . maxima::mprog) (/ . maxima::rat) (|Real| . maxima::mplus) )) ;; etc etc (defun mma2max(r) (cond ((atom r) (cond ((numberp r) (cond ((floatp r) r) ((complexp r);; do a+b*%i (list '(maxima::mplus) (mma2max (realpart r)) (list '(maxima::mtimes) 'maxima::\$%i(mma2max (imagpart r))))) #+ignore ((ratiop r) ;; gcl has no ratiop (list '(maxima::rat) (numerator r)(denominator r))) (t r))) ;other number e.g. float ;; an atom but not a number. ;; if it is a user name e.g. foo, do we make it \$foo? ;; how can we tell? ;; for now, we don't. but the dollarsign ((symbolp r) (let ((l (assoc r macsubs))) (cond (l (cdr l)) ;found a translation (t (intern (format nil"\$~a"r) :maxima))))) (t r))) (t (cons (list (mma2max (car r))) (mapcar #'mma2max (cdr r)))))) ;; . while, for, ordinary function calls. ;; while n>0 do (print(n),n:n-1) looks like this... ; ((MDO) NIL NIL NIL NIL NIL ((MNOT) ((MGREATERP) |\$n| 0)) ; ((MPROGN) ((\$PRINT) |\$n|) ((MSETQ) |\$n| ((MPLUS) |\$n| ((MMINUS) 1))))) ;; etc etc (defparameter macsubs-more ;; some of these equivalences are very bogus '()) ;; we could handle Comparison . mockmma doesn't have Inequality, Unequal, Equal. ;; (Comparison x Greater y) <-> ((mgreaterp) \$x \$y) (defun wrapcar(x)(cons (list (car x))(cdr x))) ; change (a b c) to ((a) b c) (defun max2mma(e) (cond ((atom e) (cond ((symbolp e) (st\$ e)) ;;fiddle with stripdollar, ((complexp e)`(|Complex| (realpart e)(imagpart e))) (t e))) (t(cons (max2mmaop (caar e)) (mapcar #'max2mma (cdr e)))))) (defun max2mmaop(k) (let ((r (rassoc k macsubs))) (if r (car r) (intern (symbol-name k) :mma)))) (defun st\$(x) ;; remove \$ if any (let ((r (symbol-name x))) (if (or (char= (aref r 0) #\\$) (char= (aref r 0) #\%)) (intern (subseq r 1) :mma) (intern r :mma) ))) #| problems. Check on "AND" in lisp vs mma. print[mma2max[n]] is no good. n is mapped to "numeric_eval"... what is n//N? in Mathematica, symbol N is protected. symbol n is something else. |# ;;; convert from mma char string to maxima internal form. ;;; Uses mma2max, probably in need of additional diddling around ;;; to convert more "stuff" from mma language to maxima, ;;; and of course some mma stuff, esp. patterns, does not ;;; make much sense in maxima, anyway. Still to do, add a few ;;; hundred special functions etc. if you want them. (defun maxima::\$from_mma (x) (mma::mma2max(mma::pstring x))) ;;; THIS IS THE IMPORTANT INTERFACE PROGRAM, I THINK ;;; Read the char string to mma internal form, then ;;; evaluate it in mma, and then convert the result to maxima. (defun maxima::\$eval_string_mma (x) (mma::mma2max(mma::meval(mma::pstring x)))) ;; One can write simple maxima functions for simple ;; interfaces. Here int_by_mma takes two ;; ordinary maxima arguments f,x and integrates: Int(f,x) in MMA!! ;; It then returns the answer in maxima form. ;; It is a special case of fun_by_mma, for function "Int". ;; Let us say you want to execute the MockMMA function FooBar on arguments ;; x+y, w+z. In Maxima, do this: fun_by_mma("FooBar",x+y,w+z); ;; Thus: int_by_mma(f,x):=fun_by_mma("Int",f,x); (defun maxima::\$fun_by_mma (fun &rest args) (mma::mma2max (mma::meval (cons (mma::pstring fun) (mapcar #'mma::max2mma args))))) ;; eval_string_mma("foo[x_]:=x+42"); ;; eval_string_mma("foo[4]"); ;; or ... ;; fun_by_mma ("foo", sin(q)); ;; eval_string_mma("Clear[a,b,c,x, z,quad]"); ;; eval_string_mma("quad[a_.*z_^2+b_.*z_+c_. ,z_] := ans[a,b,c,z]"); ;; eval_string_mma("quad[z^2+4 z, z]"); ;; returns ans(1,4,0,z)