Question: Translate from python to java with comments. def extended_synthetic_division(dividend, divisor): Fast polynomial division by using Extended Synthetic Division. Also works with non-monic polynomials. Dividend and
Translate from python to java with comments.
def extended_synthetic_division(dividend, divisor): """Fast polynomial division by using Extended Synthetic Division. Also works with non-monic polynomials. Dividend and divisor are both polynomials, which are here simply lists of coefficients. E.g.: x**2 + 3*x + 5 will be represented as [1, 3, 5] """ out = list(dividend) # Copy the dividend normalizer = divisor[0] for i in range(len(dividend) - len(divisor) + 1): out[i] /= normalizer # For general polynomial division (when polynomials are non-monic), # we need to normalize by dividing the coefficient with the divisor's first coefficient coef = out[i] if coef != 0: # Useless to multiply if coef is 0 for j in range(1, len(divisor)): # In synthetic division, we always skip the first coefficient of the divisor, # because it is only used to normalize the dividend coefficients out[i + j] += -divisor[j] * coef """ The resulting out contains both the quotient and the remainder, the remainder being the size of the divisor (the remainder has necessarily the same degree as the divisor since it is what we couldn't divide from the dividend), so we compute the index where this separation is, and return the quotient and remainder. """ separator = 1 - len(divisor) return out[:separator], out[separator:] # Return quotient, remainder.
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