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expandwrt-ratsimp-solve-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

expandwrt-ratsimp

r1:(x+y+1/(x+y));

r2:ratsimp(r1,(y+x));

expandwrt(r2);

Calculate

expandwrt-ratsimp-solve-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

expandwrt-ratsimp-solve-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

expandwrt

poly:(x-a)*(x-b)*(x-c...

expandwrt(poly,a,b,c,...

Calculate

expandwrt-ratsimp-solve-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

expandwrt

poly(x):=(x-a)*(x-b)*...

expandwrt(poly,x);

Calculate

expandwrt

expandwrt(eq1);

Calculate

expandwrt-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

expandwrt

E_gu: n_g*E;

E_gw: (1-n_g)*E;

E_su: n_s*E_gw;

Calculate

expandwrt

Run Example
(%i1)expandwrt((1-a) * (1+z), z);
(%o1)                          (1 - a) z - a + 1
(%i2) expandwrt(2 * (1-a*z), z);
(%o2)                              2 - 2 a z
(%i3) expandwrt((1-a) * (1-z), z);
(%o3)                         - (1 - a) z - a + 1
(%i4) expandwrt(2 * (1+a*z), z);
(%o4)                              2 a z + 2
(%i5) H4: G*(z-1)*(z+1) / ((z-%i*r)*(z+%i*r));
                               (z - 1) (z + 1) G
(%o5)                        ---------------------
                             (z - %i r) (z + %i r)
(%i6) 
Run Example
display2d:false;

(%o1) false
(%i2) 
x1: a2*z1^2 + b2*z1 +c2;

(%o2) a2*z1^2+b2*z1+c2
(%i3) 
y1: a1*z1^2 + b1*z1 +c1;

(%o3) a1*z1^2+b1*z1+c1
(%i4) 
e: A * x1^2 - B1 * x1  - x^2 * y1 + x * y1 * x1  + C1 = 0;

(%o4) C1-(a2*z1^2+b2*z1+c2)*B1+(a2*z1^2+b2*z1+c2)^2*A
        +x*(a1*z1^2+b1*z1+c1)*(a2*z1^2+b2*z1+c2)-x^2*(a1*z1^2+b1*z1+c1)
        = 0
(%i5) 
expandwrt(expand(e), z1);

(%o5) C1-a2*z1^2*B1-b2*z1*B1-c2*B1+a2^2*z1^4*A+2*a2*b2*z1^3*A+2*a2*c2*z1^2*A
        +b2^2*z1^2*A+2*b2*c2*z1*A+c2^2*A+a1*a2*x*z1^4+a1*b2*x*z1^3
        +a2*b1*x*z1^3-a1*x^2*z1^2+a1*c2*x*z1^2+a2*c1*x*z1^2+b1*b2*x*z1^2
        -b1*x^2*z1+b1*c2*x*z1+b2*c1*x*z1-c1*x^2+c1*c2*x
        = 0
(%i6) 
Run Example
myDot(f,g):= integrate(f*g,x,-Pi,Pi);
(%o1)             myDot(f, g) := integrate(f g, x, - Pi, Pi)
(%i2) myNorm(v) := sqrt(myDot(v,v));
(%o2)                   myNorm(v) := sqrt(myDot(v, v))
(%i3) proj(w,v) := (myDot(w,v)/myDot(v,v)) * v;
                                        myDot(w, v)
(%o3)                     proj(w, v) := ----------- v
                                        myDot(v, v)
(%i4) u : [1, x, x^2, x^3];
                                        2   3
(%o4)                           [1, x, x , x ]
(%i5) proj(u,1);
                                         2
                                       Pi
(%o5)                           [1, 0, ---, 0]
                                        3
(%i6) u[2] : x - proj(x,1);
(%o6)                                  x
(%i7) u[3] : x^2 - proj(x^2,1) - proj(x^2,x);
                                          2
                                    2   Pi
(%o7)                              x  - ---
                                         3
(%i8) u[4] : x^3 - proj(x^3,1) - proj(x^3,x) - proj(x^3,x^2);
                                          2
                                  3   3 Pi  x
(%o8)                            x  - -------
                                         5
(%i9) q : expandwrt(u/myNorm(u),x);
                                                   2
              1            sqrt(3) x    3 sqrt(5) x       sqrt(5)
(%o9) [----------------, -------------, ------------ - -------------, 
       sqrt(2) sqrt(Pi)            3/2    3/2   5/2     3/2
                         sqrt(2) Pi      2    Pi       2    sqrt(Pi)
                                                               3
                                                    5 sqrt(7) x    3 sqrt(7) x
                                                    ------------ - -----------]
                                                      3/2   7/2     3/2   3/2
                                                     2    Pi       2    Pi
(%i10) 

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