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Calculate

Calculate

Run Example
```(%i1)depends(z1,t);
(%o1)                               [z1(t)]
(%i2) depends(z2,t);
(%o2)                               [z2(t)]
(%i3) depends(z3,t);
(%o3)                               [z3(t)]
(%i4) depends(z4,t);
(%o4)                               [z4(t)]
(%i5) z1_d(z2,z3):= E/(x_0zyl*A_zyl+A_zyl*(x_s_max-z2))*(u+A_zyl*z3);
E
(%o5) z1_d(z2, z3) := ----------------------------------- (u + A_zyl z3)
x_0zyl A_zyl + A_zyl (x_s_max - z2)
(%i6) z2_d(z3):= z3;
(%o6)                           z2_d(z3) := z3
(%i7) z3_d(z4,z3,z2,z1):= 1/m*(-beta_s1*z4-beta_s2*z4^2-d_s*z3+F_F0s-c_s*z2-z1*A_zyl);
1                             2
(%o7) z3_d(z4, z3, z2, z1) := - ((- beta_s1) z4 - beta_s2 z4  + (- d_s) z3
m
+ F_F0s + (- c_s) z2 + (- z1) A_zyl)
(%i8) z4_d(z2,z4):= E/V_verb*(-(beta_vol1+beta_vol2*z2)*N*w/(2*pi)+alpha*A_verb*sqrt(abs(p_T-z4)*2/rho));
E     (- (beta_vol1 + beta_vol2 z2)) N w
(%o8) z4_d(z2, z4) := ------ (----------------------------------
V_verb                 2 pi
abs(p_T - z4) 2
+ alpha A_verb sqrt(---------------))
rho
(%i9) a=diff(z4_d(z2,z4),t);
1   dz4                          dz2
alpha A_verb sqrt(---) --- (p_T - z4)   beta_vol2 w --- N
rho  dt                           dt
E (- ------------------------------------- - -----------------)
3/2                2 pi
sqrt(2) abs(p_T - z4)
(%o9) a = ---------------------------------------------------------------
V_verb
(%i10) b=ratsubst(c,diff(z4,t),a);
(%o10)                               b = a
(%i11) ratsubst(u,sqrt(x),x);
(%o11)                                 x
(%o12)                               true
(%i13) ```
Run Example
```ev(ratsubst(z,sqrt(x),sqrt((x+sqrt(x)))),radsubstflag:true,logexpand:false);
log(z + 1)   log(x)
---------- + ------
2          4
(%o1)                        %e
(%i2) ```
Run Example
```radexpand:all;
(%o1)                                 all
(%o2)                                true
(%i3) ratsimp (0.5 * 0.5* sqrt((1 + qx - qy - qz)  * (1 - qx + qy - qz)) - 0.5 * 0.5 * sqrt((1 + qx + qy + qz) * (1 - qx - qy + qz)));

rat: replaced 0.25 by 1/4 = 0.25

rat: replaced -0.25 by -1/4 = -0.25
(%o3) - (sqrt(qz - qy - qx + 1) sqrt(qz + qy + qx + 1)
- sqrt(- qz - qy + qx + 1) sqrt(- qz + qy - qx + 1))/4
(%i4) ```