wxMaxima document 1 / 14
SET A
question 1
func(x):=x^3+x^2−3·x−3.0$
wxplot2d(func(x),[x,1,2]);
bisec(func, a, b, eps,N) :=
block([eps,x0:a,x1:b ,x2, ss, jj:0, jjmax:N ],
/*if length(oa) > 0 then eps : oa[1],*/
x0 : float(a),
x1 : float(b),
do (jj : jj + 1,
if jj > jjmax then print(" exceeded jjmax limit ",return(x2)),
if abs(x0−x1) <= eps then print(jj,"Approximation is :", x2,return (x2)),
if abs(func(x0)−func(x1))<= eps then print(jj,"Approximation is :", x2,return (x2)),
ss : func(x1)· func(x0),
x2: x0+(x1−x0)/2,
if ss > 0 then (print ("zero/root does not lies in the interval, Change the variables"))
else( print(jj, "root is :", x2)),
if func(x0).func(x2)<0 then (x1:x2) else (x0:x2)))$
bisec(func(x), 1.0, 2.0,0.00005,1);
wxMaxima document 2 / 14
1 root is 1.5
: 1.5
wxMaxima document 3 / 14
kill(all);
done
question 2
func(x):=37·x−1$
wxplot2d(func(x),[x,0,0.1]);
bisec(func, a, b, eps,N) :=
block([eps,x0:a,x1:b ,x2, ss, jj:0, jjmax:N ],
/*if length(oa) > 0 then eps : oa[1],*/
x0 : float(a),
x1 : float(b),
do (jj : jj + 1,
if jj > jjmax then print(" exceeded jjmax limit ",return(x2)),
if abs(x0−x1) <= eps then print(jj,"Approximation is :", x2,return (x2)),
if abs(func(x0)−func(x1))<= eps then print(jj,"Approximation is :", x2,return (x2)),
ss : func(x1)· func(x0),
x2: x0+(x1−x0)/2,
if ss > 0 then (print ("zero/root does not lies in the interval, Change the variables"))
else( print(jj, "root is :", x2)),
if func(x0).func(x2)<0 then (x1:x2) else (x0:x2)))$
bisec(func(x), 0, 0.1,0.000005,15);
wxMaxima document 4 / 14
1 root is 0.05
:
wxMaxima document 5 / 14
2 root is 0.025
:
3 root is 0.037500000000000006
:
4 root is 0.03125
:
5 root is 0.028125
:
6 root is 0.026562500000000003
:
7 root is 0.02734375
:
8 root is 0.026953125
:
9 root is 0.0271484375
:
10 root is 0.027050781250000003
:
11 root is 0.027001953125000002
:
12 root is 0.027026367187500004
:
13 root is 0.027038574218750003
:
14 root is 0.027032470703125006
:
15 root is 0.027029418945312505
: 0.027029418945312505
kill(all);
done
question 3
wxMaxima document 6 / 14
A:matrix([2,7,5],[6,20,10],[4,3,0]);
B:matrix([14],[36],[7]);
n:3;
for i:1 thru n do(
for j:1 thru n do(if(i=j) then u[i,j]:1,if (i>j) then u[i,j]:0));
for i:1 thru n do(
for j:1 thru n do(if (j>i) then l[i,j]:0));
for i:1 thru n do(l[i,1]: A[i,1]);
for j:1 thru n do(u[1,j]:A[1,j]/l[1,1]);
for k:2 thru n do(
for i: k thru n do(
l[i,k]: A[i,k]−sum(l[i,j]·u[j,k], j, j:1,j:k−1),
for j: k+1 thru n do(
u[k,j]:(A[k,j]−sum(l[k,m]·u[m,j],m,m:1,m:k−1))/l[k,k])));
l[n,n]: (A[n,n]−sum(l[n,k]·u[k,n],k,k:1, k:n−1));
L:genmatrix(l,n,n);
U:genmatrix(u,n,n);
S:L.U−A;
2 7 5 14
6 20 10 36 3 done done done done done
4 3 0 7
7 5
2 0 0 1 0 0 0
2 2
45 6 −1 0 0 0 0
0 1 5
4 − 11 45 0 0 0
0 0 1
kill(all);
wxMaxima document 7 / 14
done
question 4
'n=n:3;
'a=a:matrix([2,−1,0],[−1,4,2],[0,2,6]);
'x=x:matrix([0],[0],[0]);
'b=b:matrix([−1],[3],[5]);
print("itr","","","","","x1","","","","","x2","","","","","x3")$
for k:1 thru 2 do(for i : 1 thru n do(
y[i]:float((b[i]−sum(a[i,j]·x[j],j,1,i−1)−sum(a[i,j]·x[j],j,i+1,n))/a[i,i])),
for i:1 thru n do(x[i]:y[i]),
print(k," "," "," ",x[1]," "," "," ",x[2]," "," "," ",x[3]))$
for p:1 thru n do print('x[p]=x[p])$
2 −1 0 0 −1
n=3 a= −1 4 2 x= 0 b= 3
0 2 6 0 5
itr x1 x2 x3
1 [ − 0.5 ] [ 0.75 ] [ 0.8333333333333334 ]
2 [ − 0.125 ] [ 0.20833333333333331 ] [ 0.5833333333333333 ]
x = [ − 0.125 ]
1
x = [ 0.20833333333333331 ]
2
x = [ 0.5833333333333333 ]
3
kill(all);
done
wxMaxima document 8 / 14
SET B
question 1
func(x):=float((3·x)/2−6−(1/2)·sin(2·x))$
wxplot2d(func(x),[x,0,6]);
bisec(func, a, b, eps,N) :=
block([eps,x0:a,x1:b ,x2, ss, jj:0, jjmax:N ],
/*if length(oa) > 0 then eps : oa[1],*/
x0 : float(a),
x1 : float(b),
do (jj : jj + 1,
if jj > jjmax then print(" exceeded jjmax limit ",return(x2)),
if abs(x0−x1) <= eps then print(jj,"Approximation is :", x2,return (x2)),
if abs(func(x0)−func(x1))<= eps then print(jj,"Approximation is :", x2,return (x2)),
ss : func(x1)· func(x0),
x2: x0+(x1−x0)/2,
if ss > 0 then (print ("zero/root does not lies in the interval, Change the variables"))
else( print(jj, "root is :", x2)),
if func(x0).func(x2)<0 then (x1:x2) else (x0:x2)))$
bisec(func(x), 0, 6,0.0000001,20);
wxMaxima document 9 / 14
1 root is 3.0
:
wxMaxima document 10 / 14
2 root is 4.5
:
3 root is 3.75
:
4 root is 4.125
:
5 root is 4.3125
:
6 root is 4.21875
:
7 root is 4.265625
:
8 root is 4.2421875
:
9 root is 4.25390625
:
10 root is 4.259765625
:
11 root is 4.2626953125
:
12 root is 4.26123046875
:
13 root is 4.261962890625
:
14 root is 4.2615966796875
:
15 root is 4.26141357421875
:
16 root is 4.261505126953125
:
17 root is 4.2614593505859375
:
18 root is 4.261482238769531
:
19 root is 4.261493682861328
:
20 root is 4.26148796081543
: 4.26148796081543
kill(all);
done
question 2
wxMaxima document 11 / 14
func(x):=float(tan(%pi·x)−x−6)$
wxplot2d(func(x),[x,1,2]);
bisec(func, a, b, eps,N) :=
block([eps,x0:a,x1:b ,x2, ss, jj:0, jjmax:N ],
/*if length(oa) > 0 then eps : oa[1],*/
x0 : float(a),
x1 : float(b),
do (jj : jj + 1,
if jj > jjmax then print(" exceeded jjmax limit ",return(x2)),
if abs(x0−x1) <= eps then print(jj,"Approximation is :", x2,return (x2)),
if abs(func(x0)−func(x1))<= eps then print(jj,"Approximation is :", x2,return (x2)),
ss : func(x1)· func(x0),
x2: x0+(x1−x0)/2,
if ss > 0 then (print ("zero/root does not lies in the interval, Change the variables"))
else( print(jj, "root is :", x2)),
if func(x0).func(x2)<0 then (x1:x2) else (x0:x2)))$
bisec(func(x), 1.4, 1.45,0.00005,10);
wxMaxima document 12 / 14
kill(all);
done
question 3
A:matrix([2,7,5],[6,20,10],[4,3,0]);
B:matrix([−4],[−16],[−7]);
n:3;
/*for i:1 thru n do(
for j:1 thru n do(if(i=j) then u[i,j]:1,if (i>j) then u[i,j]:0));
for i:1 thru n do(
for j:1 thru n do(if (j>i) then l[i,j]:0));*/
for i:1 thru n do(l[i,1]: A[i,1]);
for j:1 thru n do(u[1,j]:A[1,j]/l[1,1]);
for k:2 thru n do(
for i: k thru n do(
l[i,k]: A[i,k]−sum(l[i,j]·u[j,k], j, j:1,j:k−1),
for j: k+1 thru n do(
u[k,j]:(A[k,j]−sum(l[k,m]·u[m,j],m,m:1,m:k−1))/l[k,k])));
l[n,n]: (A[n,n]−sum(l[n,k]·u[k,n],k,k:1, k:n−1));
L:genmatrix(l,n,n);
U:genmatrix(u,n,n);
S:L.U−A;
2 7 5 −4 2 0 0
6 20 10 − 16 3 done done done 45 6 −1 0
4 3 0 −7 4 − 11 45
wxMaxima document 13 / 14
7 5
1 0 0 0
2 2
0 0 0
0 1 5
0 0 0
0 0 1
kill(all);
done
question 4
'n=n:3;
'a=a:matrix([2,−1,0],[−1,4,2],[0,2,6]);
'x=x:matrix([1],[1],[1]);
'b=b:matrix([−1],[3],[5]);
print("itr","","","","","x1","","","","","x2","","","","","x3")$
for k:1 thru 2 do(
for i : 1 thru n do(y[i]:float(
(b[i]−sum(a[i,j]·x[j],j,1,i−1)−sum(a[i,j]·x[j],j,i+1,n))/a[i,i])),
for i:1 thru n do(x[i]:y[i]),
print(k," "," "," ",x[1]," "," "," ",x[2]," "," "," ",x[3]))$
for p:1 thru n do print('x[p]=x[p])$
2 −1 0 1 −1
n=3 a= −1 4 2 x= 1 b= 3
0 2 6 1 5
itr x1 x2 x3
1 [ 0.0 ] [ 0.5 ] [ 0.5 ]
2 [ − 0.25 ] [ 0.5 ] [ 0.6666666666666666 ]
wxMaxima document 14 / 14
x = [ − 0.25 ]
1
x = [ 0.5 ]
2
x = [ 0.6666666666666666 ]
3
kill(all);
done
