ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 29 May 2013 04:02:26 -0500Compare elements of a recursive defined sequencehttp://ask.sagemath.org/question/10163/compare-elements-of-a-recursive-defined-sequence/I define the recursive sequence as:
A, b, c = var('A, b, c')
def Sequence_rec(k):
x = 0
for i in range(1,k+1):
x = x + (A - x)/((c-i+2)^b)
return x
For the parameters the assumptions are:
assume(A>0,c>0,b>0)
assume(c, 'integer')
I'm interested in the elements of Sequence_rec(k) with k<=c. The following relation has to be true for the defined sequence considering the given assumptions:
assume(c>2)
bool(Sequence_rec(4) > Sequence_rec(3))
But Sage computes it is false! The following plot shows the difference is positive:
plot((Sequence_rec(4) - Sequence_rec(3))(A=1,c=3),b,(0,100))
How can I force Sage to compare the elements of the sequence `bool(Sequence_rec(n+1) > Sequence_rec(n)) = true` for any positive integer n correctly? Thank you for your advice!
Kurt
KurtMWed, 29 May 2013 04:02:26 -0500http://ask.sagemath.org/question/10163/bool returns false with arcsin(x) and 2*arctan(x/(1+sqrt(1-x^2)))http://ask.sagemath.org/question/7762/bool-returns-false-with-arcsinx-and-2arctanx1sqrt1-x2/The two expression should be equal
but when I write
bool(arcsin(x) == 2*arctan(x/(1+sqrt(1-x^2))))
it returns false.
Any clue - Why it does that? Any get around?ShuFri, 12 Nov 2010 07:40:25 -0600http://ask.sagemath.org/question/7762/