### Related

##### abs-exp-plot2d

G(a1,a2,a3,a4,b0,b1,b...

G4(w) := G(-0.9618, 0...

plot2d(abs(G4(w)),[w,...

Calculate

##### abs-plot3d-sin-sqrt

plot3d(2/(1+sqrt(abs(...

Calculate

##### abs-plot2d

f(x):=x^3+x^2+x+1;

roots:[discrete,[[0.1...

P(x):=3.3172811527717...

Calculate

##### abs-define-float

define (f(x), (x^4+3*...

define (g(x),abs(4*x/...

f(3.2);

Calculate

##### abs-define-realroots

define(f(x), (x^4 + 3...

define(g(x), abs(4*x/...

f(3.2);

Calculate

##### abs-ev-eval-plot2d-sin

log10(x):=log(x)/log(...

H(f,d,m):=log10(abs(e...

plot2d(H(f,25,3), [f,...

Calculate

##### abs-define-diff-expand-find_root-float-realroots

define(f(x), (x^4 + 3...

define(g(x), abs(4*x/...

f(3.2);

Calculate

##### abs-define-kill-plot2d-realroots-reset

define(h(x), abs(2*x^...

s: realroots(h(x=40));

kill(all);

Calculate

request_rational_matr...

rowswap(m,i,j) := blo...

Calculate

##### abs-carg-expand-float-imagpart-realpart

u: 230*%e^(%i*%pi/3);

float (u);

expand(u);

Calculate

### abs

Run Example
```(%i1)define(g(x), abs((4*x)/%e));
- 1
(%o1)                       g(x) := 4 %e    abs(x)
(%i2) ```
Run Example
```Puiab:[Pk=abs(ak)^2-abs(bk)^2,Uk=(ak+bk)*sqrt(Z0k), Ik=(ak-bk)/sqrt(Z0k)];
2     2                                  ak - bk
(%o1)     [Pk = ak  - bk , Uk = (bk + ak) sqrt(Z0k), Ik = ---------]
sqrt(Z0k)
(%i2) abUI:[ak=(Uk+Z0k*Ik)/(2*sqrt(Z0k)),bk=(Uk-Z0k*Ik)/(2*sqrt(Z0k))];
Ik Z0k + Uk       Uk - Ik Z0k
(%o2)                [ak = -----------, bk = -----------]
2 sqrt(Z0k)       2 sqrt(Z0k)
(%i3) spoj:[U1=(a1+b1)*sqrt(Z01),  U2=(a2+b2)*sqrt(Z02),I1=(a1-b1)/sqrt(Z01),  I2=(a2-b2)/sqrt(Z02),U1=U2, I1+I2=0];
a1 - b1
(%o3) [U1 = (b1 + a1) sqrt(Z01), U2 = (b2 + a2) sqrt(Z02), I1 = ---------,
sqrt(Z01)
a2 - b2
I2 = ---------, U1 = U2, I2 + I1 = 0]
sqrt(Z02)
(%i4) spoj1:[eliminate(spoj,  [U1, U2, I1, I2])];
(%o4) [[- (- b2 - a2) sqrt(Z02) - (b1 + a1) sqrt(Z01),
b1 sqrt(Z02) - a1 sqrt(Z02) + (b2 - a2) sqrt(Z01)]]
(%i5) ```
Run Example
```H(a1,a2,b0,b1,b2,z):=(b0+b1*z^(-1)+b2*z^(-2))/(1+a1*z^(-1)+a2*z^(-2));
- 1       - 2
b0 + b1 z    + b2 z
(%o1)         H(a1, a2, b0, b1, b2, z) := ----------------------
- 1       - 2
1 + a1 z    + a2 z
(%i2) H1(f,F0):=H(-1.978882,0.979126,0.989502,-1.979004,0.989502,exp(%i*2*%pi*f/F0));
(%o2) H1(f, F0) := H(- 1.978882, 0.979126, 0.989502, - 1.979004, 0.989502,
%i 2 %pi f
exp(----------))
F0
(%i3) plot2d([abs(H1(f,16000)),abs(H1(f,20000))],[f,0,500]);
plotfloat(abs(H1(50,16000)));
(%o4)                          0.88245850910269
(%i5) float(abs(H1(50,20000)));
(%o5)                          0.74462866826056
(%i6) ```

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