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I'm learning how to use find_fit and it works great for polynomials, but I'd like to include expressions that require integers. My variables are all integers, and my coefficients are expected to be relatively simple rationals (i.e. small denominators). In particular, I'd like to use a model like:

model(x,y) = (ax+by+c)%(dx+ey+f)

However, I get the expected error:

TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

If I try to convert (dx+ey+f) to an integer within the model using int(), ceiling(), etc. then it won't convert, since of course it's a symbolic expression. Is there a way to round within a symbolic expression? Or any suggestions for other workarounds? Thanks!

I'm learning how to use find_fit and it works great for polynomials, but I'd like to include expressions that require integers. My variables are all integers, and my coefficients are expected to be relatively simple rationals (i.e. small denominators). In particular, I'd like to use a model like:

model(x,y) = (ax+by+c)%(dx+ey+f)
(a*x+b*y+c)%(d*x+e*y+f)

TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'
Ring'

I'm learning how to use find_fit and it works great for polynomials, but I'd like to include expressions that require integers. My variables are all integers, and my coefficients are expected to be relatively simple rationals (i.e. small denominators). In particular, I'd like to use a model like:

model(x,y) = (a*x+b*y+c)%(d*x+e*y+f)

However, I get the expected error:

TypeError: unsupported operand parent(s) for %: 'Symbolic Ring' and 'Symbolic Ring'

If I try to convert (dx+ey+f) to an integer within the model using int(), ceiling(), etc. then it won't convert, since of course it's a symbolic expression. Is there a way to round within a symbolic expression? Or any suggestions for other workarounds? Thanks!

data = [(i,(i%2) ) for i in range(30)]
var('a, b, c, d, x')

def f(x, a, b, c, d): 
    return int(a+b*x)%int(c*x+d)

fit = find_fit(data, f, parameters = [a, b, c, d], variables = [x], solution_dict = True)
print fit

{d: 1.0, c: 1.0, b: 1.0, a: 1.0}

{d: 2.0, c: 0.0, b: 1.0, a: 0.0}