Leo Butler l.butler at ed.ac.uk
Tue Apr 27 09:50:33 CDT 2010

```
On Tue, 27 Apr 2010, Sheldon Newhouse wrote:

I tried to do the problem
<
< "diff(arccos(x^2+8.363+267)/(sqrt(x^2-4.29x+1042)(x^2+12.8102x+1177))), x);"
<
<
< in Maple with the correct version of parentheses, etc. It computed the
< derivative fine (as maxima does), but it failed to find the zero.

I believe that there is a bug in the present mring.lisp which prevents
this probblem, and similar ones, from being solved by mnewton. The basic
problem is that in trying to create CL complex numbers from a Maxima
expression, float is being called too late. I include the patch below.

(%i2) f:diff(acos(x^2+8.363+267)/(sqrt(x^2-4.29*x+1042)*(x^2+12.8102*x+1177)),x)\$
(%i3) mnewton(f,x,-5.0);

Unable to convert
%i*(2.9524823745650125e-8*sin(1.5*%pi)+1.7009864675953376e-7*sin(0.5*%pi)-4.375144669837393e-7)-2.9524823745650125e-8*cos(1.5*%pi)
%to a complex long fl\
oat
#0:
solve_by_lu(eqs=[(-4.375144669837393e-7*%i-1.7009864675953376e-7/(-1)^0.5-2.9524823745650125e-8/(-1)^1.5)*h[1]+6.978...,vars=[h[1]],field=complexfield)
#1:
mnewton(funclist=-(2*x-4.29)*acos(x^2+275.363)/(2*(x^2-4.29*x+1042)^(3/2)*(x^2+12.8102*x+1177))-(2*x+12.8102)*acos(x^...,varlist=x,guesslist=-5.0)(mnewton.mac
line 1\
13)
-- an error. To debug this try: debugmode(true);
(%i5) mnewton(f,x,-5.0);
(%o5) [[x = 2.013631497110261e-16*%i-5.626466372928149]]

Here is the patch which does the trick

Index: mring.lisp
===================================================================
RCS file: /cvsroot/maxima/maxima/share/linearalgebra/mring.lisp,v
retrieving revision 1.24
diff -u -r1.24 mring.lisp
--- mring.lisp  14 Feb 2008 01:31:37 -0000      1.24
+++ mring.lisp  27 Apr 2010 14:44:58 -0000
@@ -114,10 +114,10 @@
:mring-to-maxima #'(lambda (s) (add (realpart s) (mult '\$%i (imagpart s)))) ;; was complexify
:maxima-to-mring #'(lambda (s)
(progn
-                         (setq s (\$rectform (meval s)))
+                         (setq s (\$float (\$rectform (meval s))))
(if (complex-number-p s 'float-or-rational-p)
-                             (complex (\$float (\$realpart s)) (\$float
(\$imagpart s)))
-                           (merror "Unable to convert ~:M to a complex
long float" s))))))
+                             (complex (\$realpart s) (\$imagpart s))
+                             (merror "Unable to convert ~:M to a complex long float" s))))))

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```