# How to define a matrix conditional to a list of strings

Need a little help. suppose I have the following list :

signs=['=','=','>=','>=','>=','<=','<=','<=','<=','<=']


with this list I need to create in Sagemath a matrix with 10 lines and 18 columns each equality/inequality sign correspond to a line with

'=' gives 1 on the corresponding line the other 17 enters being 0
'>=' gives - 1, 1 on the corresponding line the other 16 enters being 0
'<=' gives 1, 1 on the corresponding line the other 16 enters being 0


and of course, there is only one 1 (-1) in each column.

What I want is a function. Someone will tell me that I must learn Python (smile) but each of my tentatives fails.

Thank in advance for the help

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signs = ['=','=','>=','>=','>=','<=','<=','<=','<=','<=']
# lines: will be the rows of the matrix
lines = []
# column: where to put the next nonzero entry
column = 0
# total number of columns in matrix
size = sum(len(s) for s in signs)
for s in signs:
if s == '=':
new = column * [0] + [1] + (size - column - 1) * [0]
column += 1
elif s == '>=':
new = column * [0] + [-1, 1] + (size - column - 2) * [0]
column += 2
elif s == '<=':
new = column * [0] + [1, 1] + (size - column - 2) * [0]
column += 2
lines.append(new)
mat = matrix(lines)

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In a compact form:

signs = ['=','=','>=','>=','>=','<=','<=','<=','<=','<=']
shift = [sum(len(signs[i]) for i in range(j)) for j in range(len(signs))]
Matrix(ZZ, 10, 18, lambda i,j: 0 if j<shift[i] or j>shift[i]+1 else -1 if j==shift[i] and signs[i]=='>=' else 0 if j==shift[i]+1 and signs[i]=='=' else 1)

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