2615.sagews

Here we show how to do the following octave/matlab code in Sage:

%initialize 2 vectors in R3 
a=[1 2 3] 
b=[-1 0 5] 
 
%vector sums 
c=a+b 
d=b-a 
 
%vector magnitudes 
lenA = norm(a) 
lenB = norm(b) 
lenC = norm(c) 
lenD = norm(d) 
 
%scalar dot product 
e=a*b' 
f=sum(a.*b) 
g=dot(a,b) 
theta1 = acos(e/lenA/lenB) 
theta2 = theta1*180/pi

a=vector([1,2,3])
b=vector([-1,0,5])
c=a+b
d=b-a
lenA=a.norm()
lenB=norm(b)
lenC=norm(c)
lenD=norm(d)

Multiplying two vectors automatically does the dot product in Sage.

e=a*b
f=sum(ai*bi for ai,bi in zip(a,b))
g=a.dot_product(b)

theta1=arccos(e/lenA/lenB)
theta2=theta1*180/pi

The output is:

SAMPLE OUTPUT Octave file (vector1.txt): 
a = 
 
  1   2   3 
 
b = 
 
 -1   0   5 
 
c = 
 
  0   2   8 
 
d = 
 
 -2  -2   2 
 
lenA =  3.7417 
lenB =  5.0990 
lenC =  8.2462 
lenD =  3.4641 
e =  14 
f =  14 
g =  14 
theta1 =  0.74690 
theta2 =  42.794

a

(1, 2, 3)

b

(-1, 0, 5)

c

(0, 2, 8)

d

(-2, -2, 2)

lenA

sqrt(14)

lenA.n()

3.74165738677394

lenB

sqrt(26)

lenC

2*sqrt(17)

lenD

2*sqrt(3)

e

14

f

14

g

14

theta1

arccos(1/26*sqrt(14)*sqrt(26))

theta1.n()

0.746898593069036

theta2

180*arccos(1/26*sqrt(14)*sqrt(26))/pi

theta2.n()

42.7941371071149

(a.plot(rgbcolor='red')+b.plot(rgbcolor='blue')+c.plot(rgbcolor='green')+d.plot(rgbcolor='orange')).show(aspect_ratio=1)

h=a.transpose();h

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