Subject: proposal for object-oriented dispatch on sign
From: Dieter Kaiser
Date: Mon, 20 Jun 2011 23:02:18 +0200
Am Montag, den 20.06.2011, 13:01 -0500 schrieb Barton Willis:
> Proposal: Modify sign (not $sign) to use object-oriented dispatch.
> The function associated with %asin extends the current sign function, I think:
>
> (%i1) assume(-1 < x, x < 0);
> (%o1) [x > - 1, x < 0]
>
> (%i2) sign(asin(x));
> (%o2) neg
>
> The code (the frob macro is based on similar code in trigi): Comments?
>
> (defvar *sign-function* (make-hash-table :size 32)
> "Hash table mapping a maxima function identifier to a CL function that determines the
> sign of an expression.")
>
> (macrolet ((frob (fun sign-fun) `(setf (gethash ',fun *sign-function*) ,sign-fun)))
> (frob mtimes 'sign-mtimes)
> (frob mplus 'sign-mplus)
> (frob mexpt 'sign-mexpt)
> (frob %log 'sign-log)
> (frob mabs 'sign-mabs)
> (frob $min #'(lambda (x) (sign-minmax (caar x) (cdr x))))
> (frob $max #'(lambda (x) (sign-minmax (caar x) (cdr x))))
> (frob %csc #'(lambda (x) (sign (inv* (cons (ncons (zl-get (caar x) 'recip)) (cdr x))))))
> (frob %csch #'(lambda (x) (sign (inv* (cons (ncons (zl-get (caar x) 'recip)) (cdr x))))))
> (frob %asin #'(lambda (x) (if (and (eq t (mgrp (cadr x) -1)) (eq t (mgrp 1 (cadr x)))) (sign (cadr x)) (sign-any x))))
> (frob %signum #'(lambda (x) (sign (cadr x))))
> (frob %erf #'(lambda (x) (sign (cadr x)))))
>
> (defmfun sign (x)
> (cond ((mnump x) (setq sign (rgrp x 0) minus nil odds nil evens nil))
> ((and *complexsign* (atom x) (eq x '$%i))
> ;; In Complex Mode the sign of %i is $imaginary.
> (setq sign '$imaginary))
> ((atom x) (if (eq x '$%i) (imag-err x)) (sign-any x))
> ((gethash (mop x) *sign-function*) (funcall (gethash (mop x) *sign-function*) x))
> ((specrepp x) (sign (specdisrep x)))
> ((kindp (caar x) '$posfun) (sign-posfun x))
> ((and (kindp (caar x) '$oddfun) (kindp (caar x) '$increasing)) (sign-oddinc x))
> (t (sign-any x))))
Hello Barton,
I like this style of programming very much. I would appreciate an
implementation which uses the properties of a symbol. The code is easier
to extend and to maintain.
I have already used this style for implementing the properties
'simplim-%function, 'integral, and 'risplit-function. There are more
places which could use this style of programming.
It might be useful to extend the Maxima function $properties
accordingly. So the user might see, that Maxima knows sign properties of
the function.
Dieter Kaiser