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Question: How do I programatically simplify the output from using Maple's pade function

Question:How do I programatically simplify the output from using Maple's pade function

richinex 10 Maple 2019
substitution simplification eliminate pade
November 15 2022
2

Hello all,

I am fairly new to Maple and would like to programatically simplify the output form using Maple's pade function on an arbitrary function: Y := 1/(R__s + 1/(s*C__dl + 1/(R__ct + 1/(sqrt(s)/sigma + 1/R__w))))
I found that only Maple's pade function was able to convert my function into a rational expression which is quite interesting.

Now I would like to replicate using maple what was manually done in steps 2 - 4 of the attached solution pdf (which was done by hand).

I was only able to do step 1 (as shown in the attached maple worksheet) after which I got stuck.

kindly assist

> 

restart
> 

with(numapprox)

[chebdeg, chebmult, chebpade, chebsort, chebyshev, confracform, hermite_pade, hornerform, infnorm, laurent, minimax, pade, remez]

 (1)
> 

s = I*omega

s = I*omega

 (2)
> 

Y := 1/(R__s+1/(s*C__dl+1/(R__ct+1/(sqrt(s)/sigma+1/R__w))))

1/(R__s+1/(s*C__dl+1/(R__ct+1/(s^(1/2)/sigma+1/R__w))))

 (3)
> 

padey := pade(Y, x = sqrt(s), [1, 1])

(C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w)

 (4)
> 

collect((C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w), s)

(C__dl*s^(3/2)*R__ct*R__w+(C__dl*R__ct*sigma+C__dl*R__w*sigma)*s+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+(C__dl*R__ct*R__s*sigma+C__dl*R__s*R__w*sigma)*s+(R__ct*R__w+R__s*R__w)*s^(1/2)+R__ct*sigma+R__s*sigma+sigma*R__w)

 (5)
> 

padey2 := collect((C__dl*s^(3/2)*R__ct*R__w+C__dl*R__ct*s*sigma+C__dl*R__w*s*sigma+s^(1/2)*R__w+sigma)/(C__dl*s^(3/2)*R__ct*R__s*R__w+C__dl*R__ct*R__s*s*sigma+C__dl*R__s*R__w*s*sigma+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w+R__ct*sigma+R__s*sigma+sigma*R__w), sigma)

((C__dl*R__ct*s+C__dl*R__w*s+1)*sigma+C__dl*s^(3/2)*R__ct*R__w+s^(1/2)*R__w)/((C__dl*R__ct*R__s*s+C__dl*R__s*R__w*s+R__ct+R__s+R__w)*sigma+C__dl*s^(3/2)*R__ct*R__s*R__w+s^(1/2)*R__ct*R__w+s^(1/2)*R__s*R__w)

 (6)

Download maple_attempt.mw

solution.pdf
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