Open rtoy opened 2 months ago
Imported from SourceForge on 2024-07-03 01:03:06 Created by aleksasd on 2012-02-07 06:38:07 Original: https://sourceforge.net/p/maxima/bugs/2353/#418a
(%i1) r:(sqrt(2)+1)^(2/3)$
(%i2) r=expand(r^3)^(1/3); (%o2) (sqrt(2)+1)^(2/3)=(2^(3/2)+3)^(1/3)
(%i3) 2*r=expand((2*r)^3)^(1/3); (%o3) 2*(sqrt(2)+1)^(2/3)=(2^(9/2)+24)^(1/3)
Aleksas
Imported from SourceForge on 2024-07-03 01:03:10 Created by aleksasd on 2012-02-07 07:38:52 Original: https://sourceforge.net/p/maxima/bugs/2353/#c00a
How simplify (%i1) ex:(sqrt(2)+1)^(2/3); (%o1) (sqrt(2)+1)^(2/3)
(%i2) ex^3=expand(ex^3); (%o2) (sqrt(2)+1)^2=2^(3/2)+3 (%i3) %^(1/3); (%o3) (sqrt(2)+1)^(2/3)=(2^(3/2)+3)^(1/3)
Other example. How simplify (%i4) ex:4*atan(1/5)-atan(1/239); (%o4) 4*atan(1/5)-atan(1/239)
(%i5) tan(ex)=trigexpand(trigexpand(tan(ex))); (%o5) tan(4*atan(1/5)-atan(1/239))=1 (%i6) atan(%); (%o6) 4*atan(1/5)-atan(1/239)=%pi/4
Aleksas D
Imported from SourceForge on 2024-07-03 01:03:13 Created by aleksasd on 2012-02-07 11:04:25 Original: https://sourceforge.net/p/maxima/bugs/2353/#bce2
Next example. see http://www.math.utexas.edu/pipermail/maxima/2012/027666.html How simplify (%i7) ex:sqrt(1-x^2)/(2-2*x^2)$
(%i8) assume(abs(x)<1)$ We define transformation funkcion f(t) and its inverse g(t): (%i9) f(t):=(2*t)^2$ g(t):=sqrt(t)/2$ (%i11) assume(t>0)$ (%i12) f(g(t)); g(f(t)); (%o12) t (%o13) t
(%i14) f(ex)=ratsimp(f(ex)); (%o14) (4*(1-x^2))/(2-2*x^2)^2=-1/(x^2-1) (%i15) g(%); (%o15) sqrt(1-x^2)/(2-2*x^2)=1/(2*sqrt(1-x^2))
Aleksas D
Imported from SourceForge on 2024-07-03 01:03:05 Created by macrakis on 2012-02-06 17:28:23 Original: https://sourceforge.net/p/maxima/bugs/2353
ex: (sqrt(2)+1)^(2/3)$
rootscontract(ex)=> (sqrt(2)+1)^(2/3) <<< does nothing rootscontract(2*ex) => 2*(2^(3/2)+3)^(1/3) <<< squares the inner expression
Though the documentation is not explicit about what it should do in this case (it only talks about products of roots, not about powers of roots), the second behavior is more useful -- if it isn't provided by rootscontract, it should be provided by *some* function.
Practical result of this anomaly:
rootscontract( (2^(3/2)+3)^(1/3)-(sqrt(2)+1)^(2/3) ) => 0 (I don't know any other way to do this simplification in Maxima) but rootscontract( -( (2^(3/2)+3)^(1/3)-(sqrt(2)+1)^(2/3) )) => remains unsimplified