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How do I create and plot a vector from the difference between two points?

asked 2015-03-07 15:43:41 -0500

nardaen gravatar image

updated 2015-03-07 15:57:24 -0500

Having points $a$ and $b$, how do I create a vector that goes from $a$ to $b$? I'm trying the following but I get an error:

a=[(1,0,0)]
b=[(0,-1,0)]
u=vector(b-a)

Then, how do I plot $a$, $b$ and $u$ at the position of $a$? The error is

File "/tmp/tmpoTA_jw/___code___.py", line 6, in <module> exec compile(u'u=vector(b-a) File "", line 1, in <module> TypeError: unsupported operand type(s) for -: 'list' and 'list'

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answered 2015-03-07 15:57:46 -0500

tmonteil gravatar image

When you write a=[(1,0,0)], a becomes the name of a list that contains a single element, which is the tuple (1,0,0), list and tuples are Python objects.

Note that tuples can be added, but since most Python programmers are not mathematicians, the most useful way to define addition is by concatenation:

sage: (1,0,0) + (3,4)
(1, 0, 0, 3, 4)
sage: (1,0,0) + ('a','b')
(1, 0, 0, 'a', 'b')

For tuples and lists, subtraction is not defined:

sage: (1,0,0) - (3,4,4)
TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'

So, it s better to define points in a vector space as vectors themselves, and the vector joining the two points is just their difference:

sage: a = vector((1,0,0))
sage: b = vector((0,-1,0))
sage: u = b-a
sage: u
(-1, -1, 0)
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Asked: 2015-03-07 15:43:41 -0500

Seen: 673 times

Last updated: Mar 07 '15