I am interested in expressions like
w=2*cos(3/7*pi) - 2*cos(2/7*pi) + 2*cos(1/7*pi) - 1
w is exactly 0, as is easily verified by expressing each cosine as sum of powers of a 7'th root of -1; Sage can verify this approximately by evaluating w as real.
I have tried to apply all simplify methods to w, to no avail. All return the same expression. Have I reached a Sage limitation, or is there some way of making it handle such expression?
I am using version 8.2.
One way to know if the expression is zero is to ask.
Typing w == 0 will return a symbolic equation, but using bool
can evaluate it to a boolean.
sage: w = 2*cos(3/7*pi) - 2*cos(2/7*pi) + 2*cos(1/7*pi) - 1
sage: w == 0
2*cos(3/7*pi) - 2*cos(2/7*pi) + 2*cos(1/7*pi) - 1 == 0
sage: bool(w == 0)
True
Another way is to convert w to the field of algebraic numbers, QQbar.
sage: ww = QQbar(w)
sage: ww
0
Note: a similar question was asked and answered as