jrive

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These are questions asked by jrive

I can't figure how to simplify

 V:= V1*R2/(s*C*R1*R2+R1_R2)

into

V = V1 *R2/(R1+R2)/(C*R1*R2*s/(R1+R2)+1)

with Maple

Basically, divide numerator and denominator by the s^0 coefficient.

This is the sort of thing that drives me nuts with Maple.

in the example below, how do I factor (L-Lm) so that the answer is in the form L1 :=L(1-k) instead of -L(k-1)?

Lm := (simplify(k*sqrt(L*L)) assuming (0 < L));
                           Lm := k L

L1 := (factor(L - Lm) assuming (0 < L and 0 < Lm and 0 <= k));
                        L1 := -L (k - 1)

in this simple case, it is easy to understand the result.  However, these kind of  representations in more complex solutions may obfuscate the result making it difficult to interpret its meaning, where as the meaning may be more obvious if the simplification or factorization led to a result formatted more similarly to the way a human would do it.  How do I get Maple to simplify things the more "traditional" way?

How do I simplify :

Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);
 

so that there are no imaginary terms in the denominator?  

I've tried, 

assum := Rin::real, omega::real, L::real, RL::real, 0 < Rin, 0 < omega, 0 < RL, 0 < L
Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);
 
(simplify(Zin) assuming assum);

but this doesn't work.

I'm trying to solve a coupled inductor problem.  All I'm trying to do is solve for the currents (which I could do), then solve for resonance by setting the imaginary part of I1 to 0 and solving for omega.  I then want to plug this resonant frequency back into I1 and evaluate it for some component values and coupling coefficient.

The problem is that even though I define the various variables as real,  Maple doesn't seem to recognize them as such.  I suspect I've failed to define one of them, and that is why it is responding like it is, but I can't find it.  

I'm also getting some weird behavior.....for example if I type :  wres0, I get the value I assigned to it --that's fine.  But then, when I type : wres0/(2*pi), I get an error, "Error, unable to parse 'mverbatim"   --- what does this mean?

This should be a pretty straight forward calculation on Maple, but at this point, I think I may be better off doing it by hand!  I appreciate any help you can provide.  Thank you.

reflected_load.mw

 I can't seem to figure out how to use arctan on a complex number in Maple.  I expect arctan(a+jb) assuming a and b are real to return atan(b/a).  Instead, returns arctan(a+Ib).  How do I do this?

restart

````

assum := R1::real, C1::real, omega::real, vab::real

R1::real, C1::real, omega::real, vab::real

(1)

Pab := expand(rationalize(vab/(R1-I/(omega*C1))))``

vab*omega^2*C1^2*R1/(C1^2*R1^2*omega^2+1)+I*vab*omega*C1/(C1^2*R1^2*omega^2+1)

(2)

Pabmag := `assuming`([abs(Pab)], [assum])

(vab^2*omega^4*C1^4*R1^2/(C1^2*R1^2*omega^2+1)^2+vab^2*omega^2*C1^2/(C1^2*R1^2*omega^2+1)^2)^(1/2)

(3)

Pabang := `assuming`([arctan(Pab)], [assum])

arctan(vab*omega^2*C1^2*R1/(C1^2*R1^2*omega^2+1)+I*vab*omega*C1/(C1^2*R1^2*omega^2+1))

(4)

``

test out how to use arctan....

`assuming`([arctan(a+I*b)], [a::real, b::real])

arctan(a+I*b)

(5)

``

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