TASK DEFINITION: Given a sentence in English, provide an equivalent paraphrased translation in French that retains the same meaning both through the translation and the paraphrase.
PROBLEM: A semilinear transformation is a transformation which is linear " up to a twist " , meaning " up to a field automorphism under scalar multiplication " .

SOLUTION: Une transformation semi-linéaire est une transformation qui est "jusqu'à une torsion", ce qui signifie "pour un automorphisme de champ sous une multiplication scalaire".

PROBLEM: Brockton is approximately 25 miles northeast of Providence , Rhode Island , and 30 miles south of Boston .

SOLUTION: Brockton est situé à environ 25 miles au nord-est de Providence, dans le Rhode Island et à 30 miles au sud de Boston.

PROBLEM: The old high school became the Upper School , while the new building became lower school .

SOLUTION:
L'ancien lycée est devenu le lycée, tandis que le nouveau bâtiment est devenu le lycée.