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hw2.py
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hw2.py
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# version code 761
# Please fill out this stencil and submit using the provided submission script.
from vec import Vec
## Problem 1
def vec_select(veclist, k):
'''
>>> D = {'a','b','c'}
>>> v1 = Vec(D, {'a': 1})
>>> v2 = Vec(D, {'a': 0, 'b': 1})
>>> v3 = Vec(D, { 'b': 2})
>>> v4 = Vec(D, {'a': 10, 'b': 10})
>>> vec_select([v1, v2, v3, v4], 'a') == [Vec(D,{'b': 1}), Vec(D,{'b': 2})]
True
'''
return [ x for x in veclist if x[k] == 0 ]
def vec_sum(veclist, D):
'''
>>> D = {'a','b','c'}
>>> v1 = Vec(D, {'a': 1})
>>> v2 = Vec(D, {'a': 0, 'b': 1})
>>> v3 = Vec(D, { 'b': 2})
>>> v4 = Vec(D, {'a': 10, 'b': 10})
>>> vec_sum([v1, v2, v3, v4], D) == Vec(D, {'b': 13, 'a': 11})
True
'''
from vecutil import zero_vec
return sum(veclist,zero_vec(D))
def vec_select_sum(veclist, k, D):
'''
>>> D = {'a','b','c'}
>>> v1 = Vec(D, {'a': 1})
>>> v2 = Vec(D, {'a': 0, 'b': 1})
>>> v3 = Vec(D, { 'b': 2})
>>> v4 = Vec(D, {'a': 10, 'b': 10})
>>> vec_select_sum([v1, v2, v3, v4], 'a', D) == Vec(D, {'b': 3})
True
'''
selected_veclist = vec_select(veclist, k)
return vec_sum(selected_veclist, D)
## Problem 2
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,3}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> scale_vecs({3: v1, 5: v2}) == [Vec({1,2,3},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})]
True
'''
return [ (1/i)*vecdict[i] for i in vecdict.keys() ]
## Problem 3
def GF2_span(D, L):
'''
>>> from GF2 import one
>>> D = {'a', 'b', 'c'}
>>> L = [Vec(D, {'a': one, 'c': one}), Vec(D, {'b': one})]
>>> len(GF2_span(D, L))
4
>>> Vec(D, {}) in GF2_span(D, L)
True
>>> Vec(D, {'b': one}) in GF2_span(D, L)
True
>>> Vec(D, {'a':one, 'c':one}) in GF2_span(D, L)
True
>>> Vec(D, {x:one for x in D}) in GF2_span(D, L)
True
'''
from GF2 import one
from itertools import product
return [ x[0]*L[0] + x[1]*L[1] for x in product([0,1],repeat=len(L)) ]
## Problem 4
# Answer with a boolean, please.
is_it_a_vector_space_1 = True
is_it_a_vector_space_2 = False
## Problem 5
is_it_a_vector_space_3 = True
is_it_a_vector_space_4 = False
## Problem 6
is_it_a_vector_space_5 = True
is_it_a_vector_space_6 = False