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poly_intspoly_int also provides routines for calculating lower and upper bounds:
Assert that a is nonnegative and return the smallest value it can have.
Return a value that is always less than or equal to both a and b. It will be the greatest such value for some indeterminate values but necessarily for all.
Return a value that is always greater than or equal to both a and b. It will be the least such value for some indeterminate values but necessarily for all.