[Scilab-users] Strange behaviour of prod on rationals

[Federico Miyara]

Dear all,

Look at this code (the coefficients are actually the result of pevious 
calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
        8.336136 + 7.0282601*%s + %s^2]
q = NUM./DEN

Running it yields

    5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s²
    ---------------------------------- ----------------------------------
        0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²

This is, correctly, a two-component rational vector with the expected 
numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, 
complex, booleans, polynomials or rational fractions". It should provide 
the rational obtained by multiplying the twonumrators and the two 
denominators. However, we get

    3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
    ------------------------------------------------------------
                                 1

The numeratoris right, but the expected denominator has been just 
replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

    3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴
    ------------------------------------------------------------
        1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

    1 -s  2 -s
    ----  ----
    1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!

    2 -3s +s²
    ---------
    2 +3s +s²

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20200317/20ee0c30/attachment.htm>