NEW YORK, NY – JULY 16: Donald Trump announces Indiana Gov. Mike Pence as Vice Presidential running mate at a press conference at the Hilton Hotel on July 16, 2016 in New York City. (Photo by Steve Sands/WireImage)

CLEVELAND ― President Barack Obama never mentioned Donald Trump’s name, but it was clear who he was talking about when he asked ― practically demanded ― that the world of politics cool its rhetoric in the aftermath of yet another police shooting, this one in Baton Rouge.

Separately, but in a related political move, Democrats are stressing the idea that the tumultuous and demanding last week, from Dallas to Istanbul to Baton Rouge, shows experience (of the kind they say Hillary Clinton possesses) is all the more important at a time when the country and the world seem to be flying apart.

Obama noted that the political conventions will be held over the next two weeks, but the one at hand ― and his most immediate concern ― is the Republican convention that begins here Monday.

Trump, the presumptive GOP standard-bearer, has jumped with gusto in the police-versus-community fray by branding himself the “law and order” candidate. It’s a direct reference to the theme Richard Nixon used in 1968 amid the racial and youth turmoil of that time.

“We’re the law and order ticket!” Trump declared time and again since last week.

After Obama’s statement, he immediately took the bait, with two combative tweets aimed at the president.

Trump’s advisors think that the unrest and home and abroad plays into his theme of strength, simplicity and tough talk.

But Obama and the Democrats (some of whom, notably Elizabeth Warren, are deploying some harsh rhetoric themselves) think that Trump’s persona and lack of experience will ultimately make Clinton’s experience a calling card ― and Trump’s bellicosity a liability.

“Trump can’t keep his calm and doesn’t know what he is talking about,” said one top Clinton advisor. “We don’t need a guy who gets angry and hurls accusations every time he opens his mouth. We need Hillary’s experience now more than ever.”

To which a top Trump insider reacted with fury. “Experience?? With the Democrats’s rhetoric these days they are only encouraging criminals and thugs to pretend they are activists.

“She has no experience with this stuff, and her past international decisions only show her bad judgment,” the person said.

With “security” due to be a theme of the first day of the GOP convention here, if not the entire event, Obama tried not only plead for calm and unity but to set a framework for judging Trump.

“Let’s temper our words and open our hearts,” the president pleaded. It was a genuine wish, and there is nothing political in a president wanting to keep the country calm.

But there was a political challenge to Trump: can you cool it? The betting in the White House and the Clinton camp is no.