### Related

##### ceiling-float-makelist-sqrt

makelist(ceiling(ii/2...

makelist(float((8*ii-...

makelist(float((8*ii-...

Calculate

##### ceiling-plot2d-subst

plot2d(subst([k=1],(2...

Calculate

##### ceiling-floor-plot2d-sin

plot2d([ceiling(x),fl...

plot2d(sin(x)+1,[x,-%...

Calculate

##### ceiling-float-makelist-subst

f: (2*n+2)*(2*n+1)/(4...

t: 1;

l: makelist(subst([k=...

Calculate

##### ceiling-floor-plot2d-sin

plot2d(sin(x)-1,[x,-%...

plot2d([ceiling(x),fl...

Calculate

##### ceiling-if-mod

/* Input number n and...

m:2;

if (mod((n^m-1)!,n^((...

Calculate

r:15;

n1:5;

n2:3;

Calculate

##### ceiling-expand-sum

k:0;

f: expand(sum((-1)^nn...

g: expand(sum(A[nn],n...

Calculate

##### ceiling-floor-log-sum

n:5;

1+sum((1-floor((1/n)*...

Calculate

##### ceiling-expand-sum

k:1;

f: expand(sum((-1)^nn...

g: expand(sum(A[nn],n...

Calculate

### ceiling

Run Example
```(%i1)load(basic);
define: warning: redefining the built-in function prog1
define: warning: redefining the built-in function symbolcheck
define: warning: redefining the built-in function push
define: warning: redefining the built-in function pop
define: warning: redefining the built-in function tr_ev
(%o1)           /usr/share/maxima/5.21.1/share/macro/basic.mac
(%o2)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i3)  ratprint:false;
(%o3)                                false
(%i4) setify(makelist(1/k, k, 1, ceiling(rat(0.1))));
(%o4)                                 {1}
(%i5) ```
Run Example
```seq(start,stop,[stepping]) := block([ start:floor(start), control:stop, stop:ceiling(stop),n, y:[],stepping: (if (not(emptyp(stepping))) then                     float(first(stepping)) else 1.0),shift: (if (length(stepping)>
1) then                float(second(stepping)) else (0.0)) ],            (n:(float(control-start)/float(stepping))),            (if (start <
stop)            then            (k:if(float(start+shift+(stepping*(i-start)))<
=control)                     then float(start+shift+(stepping*(i-start))) else [],             y:flatten(append([y],                                         makelist(ev(k),                                         i, ceiling(start), ceiling(n+start)))))            else            (m:if(-(float(stop-shift-(stepping*(i-stop))))<
=control)                      then -(float(stop-shift-(stepping*(i-stop)))) else [],              y:flatten(append([y],                                         makelist(ev(m),                                         i, -(n+stop), stop)))))            (if (n>
1.0)                then return(y)                else return([])));
(%o1) seq(start, stop, [stepping]) := block([start : floor(start),
control : stop, stop : ceiling(stop), n, y : [],
stepping : if not emptyp(stepping) then float(first(stepping)) else 1.0,
shift : if length(stepping) > 1 then float(second(stepping)) else 0.0],
float(control - start)
n : ----------------------, if start < stop
float(stepping)
then (k : if float(start + shift + stepping (i - start)) <= control
then float(start + shift + stepping (i - start)) else [],
y : flatten(append([y], makelist(ev(k), i, ceiling(start),
ceiling(n + start))))) else (m : if - float(stop - shift
- stepping (i - stop)) <= control then - float(stop - shift
- stepping (i - stop)) else [], y : flatten(append([y],
makelist(ev(m), i, - (n + stop), stop))))(if n > 1.0 then return(y)
else return([])))
(%i2) seq(1, 10);
(%o2)         [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]
(%i3) seq(1, 10, 0.9);
(%o3) [1.0, 1.9, 2.8, 3.7, 4.6, 5.5, 6.4, 7.3, 8.199999999999999, 9.1, 10.0]
(%i4) seq(0.1, 2*%pi, 0.1);
(%o4) [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3,
1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8,
2.9, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.100000000000001,
4.2, 4.3, 4.4, 4.5, 4.600000000000001, 4.7, 4.800000000000001, 4.9, 5.0,
5.100000000000001, 5.2, 5.300000000000001, 5.4, 5.5, 5.600000000000001, 5.7,
5.800000000000001, 5.9, 6.0, 6.100000000000001, 6.2]
(%i5) ```
Run Example
```makelist(ceiling(ii/2),ii,0,10);
(%o1)                  [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5]
(%i2) makelist(float((8*ii-9+sqrt(16*ii^2+9))/12),ii,0,10);
(%o2) [- 0.5, 0.33333333333333, 1.295333645443128, 2.280776406404415,
3.273235049674975, 4.26864570134639, 5.265564437074637, 6.263354640054787,
7.261693113331366, 8.260398644698073, 9.259361853355262]
(%i3) ```

Help for Ceiling