On Feb 2, 3:06 pm, Nicolas <[email protected]> wrote: > Here is some to-my-opinion strange behaviour of trig_expand : > > #Declare real variables > var('a b c') > assume([a,'real'],[b,'real'],[c,'real']) > assumptions() > ---> [a is real, b is real, c is real] > > #Case 1 > sin(a+b).trig_expand() > ---> sin(a)*cos(b) + sin(b)*cos(a) > > #Case 2 > sin((a+b)/2).trig_expand() > ---> sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a) > > #Case 3 > sin((a+b)/c).trig_expand() > ---> sin((a + b)/c) > > #Case 4 > sin((a/c+b/c)).trig_expand() > > ________ > In case 3, the expansion is not done. I wonder if it would be possible > to do it. Obviously, if the sine argument was rational expanded before > trig expansion, it would work but none seem to work on the whole > expression. > > Any idea ? > > PS: I am actually using this in an expression where doing this > expansion would simplify a lot and I would have expected simplify_full > to see it... which it does not, I suspect because of this. > ---> sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)
Sage will expand (x+y)/2 into x/2 + y/2, so trig_expand does what you expect. But it leaves (x+y)/a as (x+y)/a, so trig_expand does not change it. sage: sin((x+y)/2) sin(1/2*x + 1/2*y) sage: sin((x+y)/2).trig_expand() sin(1/2*x)*cos(1/2*y) + sin(1/2*y)*cos(1/2*x) sage: sin((x+y)/a) sin((x + y)/a) sage: sin((x+y)/a).trig_expand() sin((x + y)/a) I don't know how to change sin((x+y)/a) to sin(x/a + y/a) in Sage, maybe someone else can help you with that. HTH, Andrej -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
