Hi Sid, two points:
1.VectorSpaceBasis is not exposed, so interpreter cannot find its functions.
2. coordinatesIfCan requires as second argument a basis, i.e. an element
of VectorSpaceBasis(F), not just a list of vectors.
Here is the corrected code:
(1) -> )r isBasis
)expose VectorSpaceBasis
VectorSpaceBasis is already explicitly exposed in frame frame1
F ==> PF 11
Type: Void
VF ==> Vector F
Type: Void
(v1,v2,v3) : VF
Type: Void
v1 := [1,1,2]
(4) [1, 1, 2]
Type: Vector(PrimeField(11))
v2 := [2,1,2]
(5) [2, 1, 2]
Type: Vector(PrimeField(11))
v3 := [1,2,1]
(6) [1, 2, 1]
Type: Vector(PrimeField(11))
M : Matrix F := [v1,v2,v3]
+1 1 2+
| |
(7) |2 1 2|
| |
+1 2 1+
Type: Matrix(PrimeField(11))
rank M
(8) 3
Type: PositiveInteger
isBasis?([v1,v2,v3])
(9) true
Type: Boolean
w : VF := [2,3,10]
(10) [2, 3, 10]
Type: Vector(PrimeField(11))
b := basis [v1,v2,v3]
(11) VectorSpace [[1, 1, 2], [2, 1, 2], [1, 2, 1]]
Type: VectorSpaceBasis(PrimeField(11))
coordinatesIfCan(w,b)
(12) [8, 5, 6]
Type: Union(Vector(PrimeField(11)),...)
Am 12.12.23 um 16:18 schrieb Sid Andal:
The function isBasis?() returns with non-trivial linear combination when
applied to linearly independent vectors:
(1) -> F ==> PF 11
(2) -> VF ==> Vector F
(9) -> (v1,v2,v3) : VF
(11) -> v1 := [1,1,2]
(11) [1, 1, 2]
(12) -> v2 := [2,1,2]
(12) [2, 1, 2]
(13) -> v3 := [1,2,1]
(13) [1, 2, 1]
(14) -> M : Matrix F := [v1,v2,v3]
┌1 1 2┐
│ │
│2 1 2│
│ │
└1 2 1┘
(15) -> rank M
(15) 3
Applying isBasis:
(17) -> isBasis?([v1,v2,v3])
(17) isBasis?
1, 2, 1
It should've returned 0,0,0.
Now, trying to express a vector, w, in terms of the new basis {v1,v2,v3}
also runs into problem:
(16) -> w : VF := [2,3,10]
(16) [2, 3, 10]
(17) -> coordinatesIfCan(w,[v1,v2,v3])
There are no exposed library operations named coordinatesIfCan but
there is one unexposed operation with that name. Use HyperDoc
Browse or issue
)display op coordinatesIfCan
to learn more about the available operation.
Cannot find a definition or applicable library operation named
coordinatesIfCan with argument type(s)
Vector(PrimeField(11))
List(Vector(PrimeField(11)))
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
Are the two functions applied the wrong way in the above cases?
Thanks,
SWA
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