### Related

##### 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-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-solve

kcl1 : (Vr-Vi)/R1+Vr/...

vos : solve (kcl1, Vo);

facsum(vos, (Vr-Vi));

Calculate

##### facsum-invert-matrix-print

A : matrix( [ s_xSq, ...

b : matrix( [ s_xy ],...

x : invert(A).b;

Calculate

##### facsum

facsum(a * (p1 * omeg...

Calculate

##### facsum-solve

kcl1 : (Vr-Vi)/R1+Vr/...

vos : solve (kcl1, Vo);

facsum(vos, Vr, Vi);

Calculate

##### facsum-first-kill-solve

kill(all);

nodev1: 0 = g*(v0 - k...

nodev2: 0 = g*(v1 - 0...

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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