bihddlmZmZmZerddlmZ deddeeeffdZdddddeeeffd Zy ) ) TYPE_CHECKINGListTuple) ExpressionexprsrreturncRtd|D}td|D}||fS)zGive the sign resulting from summing a list of expressions. Args: shapes: A list of sign (is pos, is neg) tuples. Returns: The sign (is pos, is neg) of the sum. c3<K|]}|jywN) is_nonneg.0exprs O/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/utilities/sign.py zsum_signs.. 4d!4c3<K|]}|jywr ) is_nonposr s rrzsum_signs..!rr)all)ris_posis_negs r sum_signsrs/4e4 4F 4e4 4F F lh_exprrh_exprc|j}|j}|j}|j}|xr|}|xr|}|xs|}|xs|xr|xs|xr|} |xs|xr|xs|xr|} | | fS)zGive the sign resulting from multiplying two expressions. Args: lh_expr: An expression. rh_expr: An expression. Returns: The sign (is pos, is neg) of the product. )r r) rr lh_nonneg rh_nonneg lh_nonpos rh_nonposlh_zerorh_zerois_zerorrs rmul_signr%%s!!#I!!#I!!#I!!#I%IG%IG G  N0y Ni6MIF  N0y Ni6MIF F rN) typingrrrcvxpy.expressions.expressionrboolrr%rrr*sZ--7" T,' E$*,= l\eD$J>Or