Basic question about annihilator

linear-algebra

asked 2016-10-22 18:09:47 +0100

Jsevillamol
169 ●6 ●7 ●18

updated 2016-10-22 19:02:11 +0100

kcrisman
12242 ●42 ●136 ●255

I want to compute the intersection of a plane r spanned by two vectors and another plane s defined by its implicit equation. I thought the following would work:

var('x0,x1,x2')
r0 = vector(QQ,[3,1,-2])
r1 = vector(QQ,[1,-5,3])
r = span([r0,r1])
s = 2*x0 - 3*x1 - 4*x2 == 0
r.annihilator([vector([2,-3,-4])])

But instead I am greeted with an error message saying that AttributeError: 'sage.rings.rational.Rational' object has no attribute '_vector_'.

What am I doing wrong?

edit retag flag offensive close merge delete

add a comment

2 Answers

Sort by » oldest newest most voted

answered 2016-10-23 21:21:29 +0100

tmonteil
27413 ●31 ●204 ●517 http://wiki.sagemath.o...

updated 2016-10-23 21:25:26 +0100

r is correctly defined. For s, i would just do:

sage: s = matrix(QQ,[2,-3,-4]).right_kernel()
sage: s
Vector space of degree 3 and dimension 2 over Rational Field
Basis matrix:
[   1    0  1/2]
[   0    1 -3/4]

Then you can do:

sage: s.intersection(r)
Vector space of degree 3 and dimension 1 over Rational Field
Basis matrix:
[    1    15 -43/4]

And check

sage: r.intersection(s)
Vector space of degree 3 and dimension 1 over Rational Field
Basis matrix:
[    1    15 -43/4]

sage: b = r.intersection(s).basis()[0] ; b
(1, 15, -43/4)
sage: b in r
True
sage: b in s
True

As a general rule, unlike say complex analysis, Sage already offers precise objects to work with linear spaces, polynomials, combinatorics, so that you should avoid the use of fuzzy symbolic things.

edit flag offensive delete link

add a comment

answered 2016-10-22 19:13:00 +0100

kcrisman
12242 ●42 ●136 ●255

If you use the syntax in r.annihilator? then it makes it one step further:

sage: r.annihilator([2,-3,-4])
...
AttributeError: 'FreeModule_submodule_field_with_category' object has no attribute 'from_vector'

But I think you meant one vector, not three rationals, so that isn't helpful. I have opened Trac 21742 for this; I suspect this simply isn't a case where this was intended to be used.

edit flag offensive delete link

Comments

My intention was to filter the elements of r such that they satisfied s's equation. That is, the elements of r which map to 0 when you do the dot vector with [2,-3,-4]. What would be the canonical way of doing this?

Jsevillamol ( 2016-10-22 20:47:44 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Basic question about annihilator

2 Answers

Comments

Your Answer

Question Tools

Stats

Related questions

Basic question about annihilator edit

2 Answers

Comments

Your Answer

Question Tools

Stats

Related questions

Basic question about annihilator