LLL_for_knapsack_problems.sagews

prices = [2.15, 2.75, 3.35, 3.55, 4.20, 5.80]
target = 15.05

I = identity_matrix(3)

print "Hello"

Hello

%md

# This is HTML

This is HTML

I.determinant()

1

C = 10^5 #big constant
d = len(prices)+1
I = identity_matrix(d)
X = Matrix(ZZ,d,1)
X[0,0] = -floor(target*C)
for i in range(1,d):
    X[i,0] = floor(C*prices[i-1])
M = I.augment(X)
print M

[ 1 0 0 0 0 0 0 -1505000] [ 0 1 0 0 0 0 0 215000] [ 0 0 1 0 0 0 0 275000] [ 0 0 0 1 0 0 0 335000] [ 0 0 0 0 1 0 0 355000] [ 0 0 0 0 0 1 0 420000] [ 0 0 0 0 0 0 1 580000]

M.commutator?

File: /projects/sage/sage-6.9/src/sage/matrix/matrix0.pyx
Signature : M.commutator()
Docstring :
Return the commutator self*other - other*self.

EXAMPLES:

   sage: A = Matrix(ZZ, 2, 2, range(4))
   sage: B = Matrix(ZZ, 2, 2, [0, 1, 0, 0])
   sage: A.commutator(B)
   [-2 -3]
   [ 0  2]
   sage: A.commutator(B) == -B.commutator(A)
   True

M.LLL()

[ 0 1 -2 1 0 0 0 0] [ 1 1 0 0 2 0 1 0] [ 0 1 0 1 -2 -1 1 0] [ 1 -1 1 2 1 1 0 0] [ 1 -2 0 0 1 1 2 0] [ 0 2 0 -1 -1 2 -1 0] [ 0 0 -1 1 1 -1 0 -5000]

In this case an acceptable answer will have 1 in the first column and positive integers in the all but the last column. So I would put an order in for Mixed Fruit, 2 orders of Hot Wings, and a Sampler Plate.