# express an affine space as linear system of equations

Given an affine space, for example {25,27,29,31} in $\mathbb{F}_2^4$, how can I find the equations to express the space as $Ax=b$. I believe there must be some commands in sage can help me. But I can not find them.

edit retag close merge delete

Sort by » oldest newest most voted

Is it homework ? Here are some hints:

• if you remove the first element to all elements of an affine space, you get a vector space (see VectorSpace and its vector_space_span method)
• this vector space has a basis
• turn this basis into a matrix M (by columns)
• the lines of the matrix A you are looking for are a basis of the right kernel of M (write the things down on a paper to get convinced)
• you get the b by plugging any element of your affine space in the equation
more