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facsum-matrix

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

q3d : 0.5*(q1*wy -q2*...

Calculate

facsum-matrix

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

q3d : 0.5*(q1*wy -q2*...

Calculate

facsum-matrix-true

simplified_output : t...

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

Calculate

facsum-matrix

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

q3d : 0.5*(q1*wy -q2*...

Calculate

facsum-matrix

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

q3d : 0.5*(q1*wy -q2*...

Calculate

facsum-invert-matrix-print

A : matrix( [ s_xSq, ...

b : matrix( [ s_xy ],...

x : invert(A).b;

Calculate

facsum-matrix-true

simplified_output : t...

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

Calculate

facsum-matrix-true

simplified_output : t...

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

Calculate

facsum-matrix-true

simplified_output : t...

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

Calculate

facsum-matrix-true

simplified_output : t...

q1d : 0.5*(q2*wz -q3*...

q2d : 0.5*(-q1*wz +q3...

Calculate

facsum

Run Example
(%i1)display2d:false;

(%o1) false
(%i2) 
e1:-(2*t*yw+(1-t^2)*xw) +(1+t^2)*( -k*cos(q2)*sin(q3)+b*cos(q2)+aaa);

(%o2) -2*t*yw-(1-t^2)*xw+(-k*cos(q2)*sin(q3)+b*cos(q2)+aaa)*(t^2+1)
(%i3) 
e2:-(-(1-t^2)*yw+2*t*xw)+(1+t^2)*(k*cos(q3));

(%o3) -(t^2-1)*yw-2*t*xw+k*cos(q3)*(t^2+1)
(%i4) 
facsum(e1,t^2)-facsum(e2,t^2);

(%o4) t^2*yw-2*t*yw-yw+t^2*xw+2*t*xw-xw-(k*cos(q2)*sin(q3)-b*cos(q2)-aaa)*t^2
            -k*cos(q3)*t^2-k*cos(q2)*sin(q3)-k*cos(q3)+b*cos(q2)+aaa
(%i5) 
Run Example
display2d:false;

(%o1) false
(%i2) 
Nst:(He^2+Cs^2)*(a3*Cs+b3*He)+3*Cs*b2*(Cs^2+He^2-He*b2);

(%o2) 3*b2*Cs*(He^2-b2*He+Cs^2)+(b3*He+a3*Cs)*(He^2+Cs^2)
(%i3) 
Ncs:diff(Nst,Cs);

(%o3) 3*b2*(He^2-b2*He+Cs^2)+a3*(He^2+Cs^2)+2*Cs*(b3*He+a3*Cs)+6*b2*Cs^2
(%i4) 
Nhe:diff(Nst,He);

(%o4) b3*(He^2+Cs^2)+2*He*(b3*He+a3*Cs)+3*b2*Cs*(2*He-b2)
(%i5) 
Cdc: -Ncs*He+Nhe*Cs;

(%o5) He*(-3*b2*(He^2-b2*He+Cs^2)-a3*(He^2+Cs^2)-2*Cs*(b3*He+a3*Cs)-6*b2*Cs^2)
       +Cs*(b3*(He^2+Cs^2)+2*He*(b3*He+a3*Cs)+3*b2*Cs*(2*He-b2))
(%i6) 
ee1:facsum(subst(T*Cs,He,Nst),Cs);

(%o6) Cs^3*(b3*T+3*b2+a3)*(T^2+1)-3*b2^2*Cs^2*T
(%i7) 
ee2:facsum(subst(T*Cs,He,Cdc),Cs);

(%o7) 3*b2^2*Cs^2*(T-1)*(T+1)-Cs^3*(3*b2*T+a3*T-b3)*(T^2+1)
(%i8) 
ee1:facsum(ratsimp(ee1/Cs^2),Cs);

(%o8) Cs*(b3*T+3*b2+a3)*(T^2+1)-3*b2^2*T
(%i9) 
ee2:facsum(ratsimp(ee2/Cs^2),Cs);

(%o9) 3*b2^2*(T-1)*(T+1)-Cs*(3*b2*T+a3*T-b3)*(T^2+1)
(%i10) 
Run Example
x(t) := r(t) * sin(theta(t));
(%o1)                     x(t) := r(t) sin(theta(t))
(%i2) y(t) := r(t) * cos(theta(t));
(%o2)                     y(t) := r(t) cos(theta(t))
(%i3) declare (slope,constant);
(%o3)                                done
(%i4) declare (yintercept,constant);
(%o4)                                done
(%i5) declare (soundvel,constant);
(%o5)                                done
(%i6) assume(soundvel>
0);
(%o6)                           [0 < soundvel]
(%i7) declare (f0, constant);
(%o7)                                done
(%i8) assume(f0>
0);
(%o8)                              [0 < f0]
(%i9) let (diff(r(t),t), (f(t)/f0-1)*soundvel);
                       d                       f(t)
(%o9)                  -- (r(t)) --> soundvel (---- - 1)
                       dt                       f0
(%i10) eq1: y(t)=slope * x(t) + yintercept;
(%o10)    r(t) cos(theta(t)) = slope r(t) sin(theta(t)) + yintercept
(%i11) eq2: diff(y(t),t) = slope * diff(x(t),t);
        d                                              d
(%o11) (-- (r(t))) cos(theta(t)) - r(t) sin(theta(t)) (-- (theta(t))) = 
        dt                                             dt
                                    d                 d
         slope (r(t) cos(theta(t)) (-- (theta(t))) + (-- (r(t))) sin(theta(t)))
                                    dt                dt
(%i12) eq3: letsimp(solve([eq2],r(t)));
(%o12) [r(t) = 
                        soundvel cos(theta(t))
- -------------------------------------------------------------------
                 d                                     d
  sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t)))
                 dt                                    dt
                      slope soundvel sin(theta(t))
 + -------------------------------------------------------------------
                  d                                     d
   sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t)))
                  dt                                    dt
                          soundvel f(t) cos(theta(t))
 + -------------------------------------------------------------------------
                     d                                        d
   f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))
                     dt                                       dt
 + (- (slope soundvel f(t) sin(theta(t)))
                    d                                        d
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))))]
                    dt                                       dt
(%i13) eq4: letsimp(diff(eq3,t));
                     soundvel f(t)
(%o13) [- soundvel + ------------- = 
                          f0
                                         d
           slope soundvel cos(theta(t)) (-- (theta(t)))
                                         dt
-------------------------------------------------------------------
               d                                     d
sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t)))
               dt                                    dt
                                         d
                 soundvel sin(theta(t)) (-- (theta(t)))
                                         dt
 + -------------------------------------------------------------------
                  d                                     d
   sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t)))
                  dt                                    dt
                                d
                      soundvel (-- (f(t))) cos(theta(t))
                                dt
 + -------------------------------------------------------------------------
                     d                                        d
   f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))
                     dt                                       dt
                       d
 + (- (slope soundvel (-- (f(t))) sin(theta(t)))
                       dt
                    d                                        d
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))))
                    dt                                       dt
                                          d
 + (- (slope soundvel f(t) cos(theta(t)) (-- (theta(t))))
                                          dt
                    d                                        d
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))))
                    dt                                       dt
                                    d
 + (- (soundvel f(t) sin(theta(t)) (-- (theta(t))))
                                    dt
                    d                                        d
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))))
                    dt                                       dt
                                            2
                                           d
 + (soundvel cos(theta(t)) (sin(theta(t)) (--- (theta(t)))
                                             2
                                           dt
                         2
                        d                                      d             2
 + slope cos(theta(t)) (--- (theta(t))) - slope sin(theta(t)) (-- (theta(t)))
                          2                                    dt
                        dt
                  d             2
 + cos(theta(t)) (-- (theta(t))) ))
                  dt
                 d                                     d              2
/(sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t))))
                 dt                                    dt
                                                     2
                                                    d
 + (- (slope soundvel sin(theta(t)) (sin(theta(t)) (--- (theta(t)))
                                                      2
                                                    dt
                         2
                        d                                      d             2
 + slope cos(theta(t)) (--- (theta(t))) - slope sin(theta(t)) (-- (theta(t)))
                          2                                    dt
                        dt
                  d             2
 + cos(theta(t)) (-- (theta(t))) ))
                  dt
                 d                                     d              2
/(sin(theta(t)) (-- (theta(t))) + slope cos(theta(t)) (-- (theta(t)))) )
                 dt                                    dt
                                                       2
                                                      d
 + (- (soundvel f(t) cos(theta(t)) (f0 sin(theta(t)) (--- (theta(t)))
                                                        2
                                                      dt
                            2
                           d
 + f0 slope cos(theta(t)) (--- (theta(t)))
                             2
                           dt
                           d             2
 - f0 slope sin(theta(t)) (-- (theta(t)))
                           dt
                     d             2
 + f0 cos(theta(t)) (-- (theta(t))) ))
                     dt
                    d                                        d              2
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))) )
                    dt                                       dt
                                                          2
                                                         d
 + (slope soundvel f(t) sin(theta(t)) (f0 sin(theta(t)) (--- (theta(t)))
                                                           2
                                                         dt
                            2
                           d
 + f0 slope cos(theta(t)) (--- (theta(t)))
                             2
                           dt
                           d             2
 - f0 slope sin(theta(t)) (-- (theta(t)))
                           dt
                     d             2
 + f0 cos(theta(t)) (-- (theta(t))) ))
                     dt
                    d                                        d              2
/(f0 sin(theta(t)) (-- (theta(t))) + f0 slope cos(theta(t)) (-- (theta(t)))) ]
                    dt                                       dt
(%i14) facsum (eq4, slope,yintercept,f0);
        soundvel f(t) - f0 soundvel
(%o14) [--------------------------- = (- soundvel
                    f0
                                     2
                                    d
 (f(t) cos(theta(t)) sin(theta(t)) (--- (theta(t)))
                                      2
                                    dt
           2            d             2           2            d             2
 + f(t) sin (theta(t)) (-- (theta(t)))  + f(t) cos (theta(t)) (-- (theta(t)))
                        dt                                     dt
    d                                       d
 - (-- (f(t))) cos(theta(t)) sin(theta(t)) (-- (theta(t))))
    dt                                      dt
                                                       2
        2                                             d
 + slope  soundvel (f(t) cos(theta(t)) sin(theta(t)) (--- (theta(t)))
                                                        2
                                                      dt
           2            d             2           2            d             2
 - f(t) sin (theta(t)) (-- (theta(t)))  - f(t) cos (theta(t)) (-- (theta(t)))
                        dt                                     dt
    d                                       d
 - (-- (f(t))) cos(theta(t)) sin(theta(t)) (-- (theta(t))))
    dt                                      dt
                                              2
                                             d
 + f0 soundvel (cos(theta(t)) sin(theta(t)) (--- (theta(t)))
                                               2
                                             dt
      2            d             2      2            d             2
 + sin (theta(t)) (-- (theta(t)))  + cos (theta(t)) (-- (theta(t))) )
                   dt                                dt
                                                     2
           2                                        d
 - f0 slope  soundvel (cos(theta(t)) sin(theta(t)) (--- (theta(t)))
                                                      2
                                                    dt
      2            d             2      2            d             2
 - sin (theta(t)) (-- (theta(t)))  - cos (theta(t)) (-- (theta(t))) )
                   dt                                dt
 + slope soundvel (sin(theta(t)) - cos(theta(t)))
                                         2
                                        d
 (sin(theta(t)) + cos(theta(t))) (f(t) (--- (theta(t)))
                                          2
                                        dt
    d           d
 - (-- (f(t))) (-- (theta(t)))) - f0 slope soundvel
    dt          dt
 (sin(theta(t)) - cos(theta(t))) (sin(theta(t)) + cos(theta(t)))
   2
  d                       2            d             2
 (--- (theta(t))))/(f0 sin (theta(t)) (-- (theta(t)))
    2                                  dt
  dt
                                           d             2
 + 2 f0 slope cos(theta(t)) sin(theta(t)) (-- (theta(t)))
                                           dt
           2    2            d             2
 + f0 slope  cos (theta(t)) (-- (theta(t))) )]
                             dt
(%i15) 

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