How to multiply vector by number

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This behaviour is part of Python (the following code is evaluated in the standard python shell, although it should also work in sage or a sage notebook):

>>> W = [1, 8, 4, 7, 10, 1, 6, 3]
>>> 2*W
[1, 8, 4, 7, 10, 1, 6, 3, 1, 8, 4, 7, 10, 1, 6, 3]

The standard thing to do is to either use list comprehension

>>> [3*i for i in W]
[3, 24, 12, 21, 30, 3, 18, 9]

or map (for a comparison, see http://stackoverflow.com/q/1247486/42...)

>>> map(lambda i: 3*i, W)
[3, 24, 12, 21, 30, 3, 18, 9]

Although, if you're using just numerical lists and are used to matlab, then maybe you should use numpy:

>>> import numpy
>>> npW = numpy.array(W)
>>> npW*3
array([ 3, 24, 12, 21, 30,  3, 18,  9])

For large arrays, NumPy will be faster at this type of operation than the pythonic methods above. For a discussion of NumPy in sage see http://www.sagemath.org/doc/numerical...

Of course, the standard sage approach is to use a vector object (see Laurent's answer)