In Bayesian inference the following relationship is given between the posterior $P(\theta|X)$, the likelihood function $P(X|\theta)$ and the prior $P(\theta)$:
$$P(\theta|X) \propto P(X|\theta)P(\theta)$$
If the prior $P(\theta)$ is an improper uniform prior on $[-\infty,\infty]$ then does the Bayesian relationship simplify to:
$$P(\theta|X) \propto P(X|\theta)$$
If code is being written for the case of a uniform prior is it correct that the prior probability does not need to be coded?
In the case that $P(\theta)$ is uniform on $[L,U]$ can it be written (excuse my poor notation):
$$P(\theta|X) \propto P(\theta|X) \text{ for }L \leq X \leq U \text{, otherwise 0}$$
Again can the prior probability term need not be considered/coded?