WASHINGTON — On the stump this fall, President Obama boasted that he had ‘‘brought more trade cases against China’’ than his predecessor had. In an ad, he asserted that his challenger ‘‘never stood up to China.’’ During a debate, Obama said he expanded trade with other Asian nations ‘‘so that China starts feeling more pressure’’ to play by the rules.

The contest with Mitt Romney is done, but the contest with China is only gathering steam. After a political campaign spent talking about how tough he was with Beijing, the president left for Asia on Saturday for his first postelection overseas trip, a whirlwind swing through China’s backyard that is laden with geopolitical implications.