### Related

##### num-rat-resultant-sqrt-subst

eq1: (x-x1)^2+(y-y1)^...

eq2: (x-x2)^2+(y-y2)^...

eq3: rat(eq1-eq2,y,x);

Calculate

eqn: 1444/16;

a: num(eqn);

b: den(eqn);

Calculate

##### num-rat-rhs-solve

eqa: (x-xa)^2+(y-ya)^...

eqb: (x-xb)^2+(y-yb)^...

eqc: (x-xc)^2+(y-yc)^...

Calculate

##### num-plot2d-sin

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

Calculate

##### num-plot2d

aInitialValue_num: 0.0;

aFinalValue_num: 1.0;

Calculate

##### num-sum

sum((k*23/3 -77/3), k...

Calculate

##### num-plot2d

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

Calculate

##### num-plot2d-sin

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

Calculate

##### num-plot2d

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

Calculate

##### num-plot2d-sin

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

Calculate

### num

Run Example
```(%i1)eq1:Kp*(1+1/(Ti*s)+Td*s);
1
(%o1)                        Kp (---- + s Td + 1)
s Ti
(%i2) eq2:s = 2/T *((z-1)/(z+1));
2 (z - 1)
(%o2)                            s = ---------
(z + 1) T
(%i3) eq3:factor(subst(eq2,eq1));
2  2        2    2         2                       2
(%o3) (Kp (z  T  + 2 z T  + T  + 2 Ti z  T - 2 Ti T + 4 Td Ti z  - 8 Td Ti z
+ 4 Td Ti))/(2 Ti (z - 1) (z + 1) T)
(%i4) num(eq3);
2  2        2    2         2                       2
(%o4) Kp (z  T  + 2 z T  + T  + 2 Ti z  T - 2 Ti T + 4 Td Ti z  - 8 Td Ti z
+ 4 Td Ti)
(%i5) denom(eq3);
(%o5)                       2 Ti (z - 1) (z + 1) T
(%i6) ```
Run Example
```aInitialValue_num: 1.0;
(%o1)                                 1.0
(%i2) aFinalValue_num: 1.0;
(%o2)                                 1.0
(%o3)                                 4.0
(%i4) lMaxNormalizedDeviation_num: 0.14;
(%o4)                                0.14
(%i5) slow: 1.5;
(%o5)                                 1.5
(%i6) plot2d(aInitialValue_num + aFinalValue_num * (aCurrentTime_num / aDuration_num) + lMaxNormalizedDeviation_num * 0.5 * (1 - cos((aCurrentTime_num / aDuration_num)^slow * 2 * %pi)),[aCurrentTime_num,0,aDuration_num]);
plot```
Run Example
```kill(all);
(%o0)                                done
(%i1) nodev1: 0 = g*(v0 - k*v1 - v2) - (gc*(v1 - 0) - ic1eq), gc=1;
(%o1)                0 = g (- v2 - k v1 + v0) - v1 + ic1eq
(%i2) nodev2: 0 = g*(v1 - 0) - (gc*(v2 - 0) - ic2eq), gc=1;
(%o2)                       0 = - v2 + g v1 + ic2eq
(%i3) sln1: (first(solve([nodev1, nodev2], [v1, v2]))[1]);
g v0 - g ic2eq + ic1eq
(%o3)                     v1 = ----------------------
2
g k + g  + 1
(%i4) sln2: (first(solve([nodev1, nodev2], [v2, v0]))[1]);
(%o4)                          v2 = g v1 + ic2eq
(%i5) sln3: substitute(sln1, sln2);
g (g v0 - g ic2eq + ic1eq)
(%o5)               v2 = -------------------------- + ic2eq
2
g k + g  + 1
(%i6) rat(second(sln3));
2
g  v0 + g ic2eq k + ic2eq + g ic1eq
(%o6)/R/              -----------------------------------
2
g k + g  + 1
(%i7) rat(num(second(ratsimp(sln3))));
2
(%o7)/R/              g  v0 + g ic2eq k + ic2eq + g ic1eq
(%i8) rat(denom(second(ratsimp(sln3))));
2
(%o8)/R/                         g k + g  + 1
(%i9) ```

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