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abs-depends-hessian

(abs(y-x)+k)/(y+x);

depends (F, [x, y]);

hessian (F, [x, y]);

Calculate

abs-addrow-diff-do-ev-matrix-numer-sin-sqrt

f(x):=sin(x*1/sqrt(2));

d:diff(f(x),x);

a:1;

Calculate

abs-assume-ceiling-declare-floor-max-tex

ceiling (ceiling (x));

ceiling (floor (x));

declare (n, integer);

Calculate

abs-addrow-cos-diff-do-ev-matrix-numer

f(x):=cos(x^2-3*x);

/*funcion*/f(1),numer;

d:diff(f(x),x);

Calculate

abs-diff

x: (h1-h2)/s;

h1: 0.27;

h2: 0.2;

Calculate

abs-carg-expand-float-imagpart-realpart

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

float(u);

expand(u);

Calculate

abs-imagpart-realpart

%i+(%i)^(1/5);

abs(%i+(%i)^(1/5));

realpart(%i+(%i)^(1/5));

Calculate

abs-do-if-is-length-map-ratsimp-realroots-solve

xvals: map(rhs,solve(...

yvals: map(lhs,solve(...

yvals[1] - xvals[1];

Calculate

abs-sqrt

abs(x+1)-sqrt((x+1)^2);

sqrt((x+1)^2);

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]);
plotplot2d([abs(H1(f,16000)),abs(H1(f,20000))],[f,0,500]);float(abs(H1(50,16000)));
(%o4)                          0.88245850910269
(%i5) float(abs(H1(50,20000)));
(%o5)                          0.74462866826056
(%i6) 

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