An important precision : what I said is true about maxima 5.30.0 (i. e.
the latest released maxima, used standalone), *not* 5.29.1 (currently in
sage). See below :
On 14/08/2013 15:04, Emmanuel Charpentier wrote:
[ Snip ... ]
[ 1st part of sage computation ]
sage: Lt
x14^4 + 2*((x14^4)^(1/4)*sqrt(y12^2) - 8)*l + 2*y12^2
sage: Lt.simplify_full()
x14^4 + 2*l*x14*y12 + 2*y12^2 - 16*l
One notes that simplify_full() replaces ((x14^4)^(1/4)*sqrt(y12^2) with
x14*y12.
This might be related to sage's maxima version 5.29.1
Let's compare with maxima :
(%i1) f:x+2*y;
(%o1) 2*y+x
(%i2) g:2*x^(1/4)*y^(1/2);
(%o2) 2*x^(1/4)*sqrt(y)
(%i3) L:f-l*(16-g);
(%o3) 2*y-l*(16-2*x^(1/4)*sqrt(y))+x
(%i4) Lt:ratsimp(factor(radcan(expand(subst([x=x14^4,y=y12^2],L)))));
(%o4) 2*l*abs(x14)*abs(y12)+2*y12^2+x14^4-16*l
One notes that radcan() replaces the same subexpression with
abs(y12)*abs(x14), which is quite different, analysis-wise...
With sage's 5.29.1 maxima, one gets :
maxima: f:x+2*y;
2*y+x
maxima: g:2*x^(1/4)*y^(1/2);
2*x^(1/4)*sqrt(y)
maxima: L:f-l*(16-g);
2*y-l*(16-2*x^(1/4)*sqrt(y))+x
maxima: Lt:ratsimp(factor(radcan(expand(subst([x=x14^4,y=y12^2],L)))));
2*y12^2+2*l*x14*y12+x14^4-16*l
which has the same problem as sage's simplify_full answer...
HTH,
Emmanuel Charpentier
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