On 06/01/2012 09:37 AM, Victor Eijkhout wrote:
Can someone tell me if the following can be solved in Axiom, and hence
whether I should bother learning the system?
I have two equations in vectors of arbitrary dimension: z = y + ax (a is
scalar, x,y,z vector) & p^t z = 0
(p another vector). Vectors x,y,p are known, vector z and scalar a are
unknown. Assume no two known vectors are orthogonal.
The solution of this isz = y + a x where a = -(p^t y) / (p^t x).
Is this expressible and solvable in Axiom?
If I understood your problem correctly then you can do it as follows.
Of course you can use that in any dimension.
Ralf
(1) -> V := Vector Fraction Integer
(1) Vector(Fraction(Integer))
Type: Type
(2) -> x: V := [1,2,3]
(2) [1,2,3]
Type: Vector(Fraction(Integer))
(3) -> y: V := [4,5,6]
(3) [4,5,6]
Type: Vector(Fraction(Integer))
(4) -> p: V := [7,8,9]
(4) [7,8,9]
Type: Vector(Fraction(Integer))
(5) -> n := dot(p, y)
(5) 122
Type: Fraction(Integer)
(6) -> d := dot(p, x)
(6) 50
Type: Fraction(Integer)
(7) -> a := -n/d
61
(7) - --
25
Type: Fraction(Integer)
(8) -> z := y+a*x
39 3 33
(8) [--,--,- --]
25 25 25
Type: Vector(Fraction(Integer))
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