It might help you to remember that we are talking about sine
and to recall what a sine wave looks like--this is a periodic
function--there are only four points that you need to correct.
In the function sin(y) is given in radians. The value 2π corresponds
to 360 degrees (a circle and the reason Dr Iverson chose o. to
represent these functions. Sine is 0 for 0 degrees or 0 radians,
180 degrees or π radians and again at 360 degrees or 2π radians.
At 90 degrees or 0.5 π the value is +1 and at 270 degrees or 1.5 π
the value
is -1. For angles in between, Taylor series can be use to get
a good approximation of the non integer values but it is
useful to know that you do not have to do this for arguments
from minus infinity to plus infinity but only form 0 to 2π .
The Cos function is similar but out of phase so that Cos is 0 at
90 degrees and 270 degrees and 1 at 0 degrees and -1 at 180.
Currently J produces the following results and if this is not a
problem for the J community, I guess any user that cares
will have to fix these values for themselves when it matters:
1 o. 0 0.5 1 1.5 2 * o.1
0 1 1.22461e_16 _1 _2.44921e_16
2 o. 0 0.5 1 1.5 2 * o.1
1 6.12303e_17 _1 _1.83691e_16 1
dly
[EMAIL PROTECTED]
On 8-Dec-06, at 6:56 AM, Roger Hui wrote:
Actually, symbolic computations can be done as
yet another datatype and the only cost ("sacrifice")
would be implementation effort that could be
expended in other areas. You can look at f&.g and
f b. _1 for indications of what can be done with
symbolics in J.
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