Just what kind of a political beast is Julia Gillard?

She's been Australia's Prime Minister for more than 100 days now, and has in that time faced a series of trials whose difficulty and danger owe more to ancient Greece than 21st century Australia.

Having slaughtered the perennially-alert Lion of Nambour, haggled a deal with the Miners of the West, avoided the certain death that results from looking directly into the eyes of Labor's modern Medusa Mark Latham, and prevailed narrowly over the multi-headed Hydra that is her new House of Representatives, Ms Gillard has still got a pulse.

But what sort of prime minister is she?

Perhaps we should borrow the filing system of former British Labour figurehead Tony Benn, who used to say that politicians could be classed into three categories: fixers, straight men or maddies.

Julia Gillard is a fixer; it's no accident that she was the most attractive option for federal Labor when the Government found itself, nearing the end of its first term, in such a mess.

Perhaps her arrival is part of the cycle; Labor is long overdue for a fixer, because it hasn't had one since Bob Hawke.

A Bennite chart of the Labor leadership pattern since 1983 (Hawke, Keating, Beazley, Crean, Latham, Beazley, Rudd, Gillard) would look something like this: Fixer, Maddie, Straight Man, Straight Man, Maddie, Straight Man, Maddie, Fixer.

(Kevin Rudd, as ever, is stubbornly resistant to classification. As leader, he had the obsessive compulsive tendencies of the Maddie, and the sweeping ambitions, but not the Maddie's proud indifference to popular opinion. He couldn't be called a Fixer, because he was terrible at fixing things, and he was far too complicated to be Straight. So I've left him as a Maddie, though I must say I'm not entirely happy with it.)

Why do I classify Julia Gillard as a fixer?

Because she is a pragmatist and a person who thrives on problems.

The recent election campaign taught us a lot about Julia Gillard, the most important element among which being that she is not very good at articulating a vision.

The Julia Gillard whose political agility, personal charm and intelligence were commonly to be observed as she went about removing WorkChoices and tinkering with the schools system during the Rudd government's interrupted term, was strangely absent for most of the campaign.

"Today I want to speak to you from the heart," she began, when she launched her party's campaign in Brisbane.

But what an oddly dispassionate heart it seemed.

Ms Gillard's speech sounded more like a removalist's inventory of what a Labor heart should contain (belief in the transformative power of education, commitment to a fair go in the workplace, a brief mention of Indigenous affairs and so on) than a communique from the muscle itself.

She sparked up during the campaign on a couple of occasions - usually when provoked by a journalist into a display of disciplined and articulate anger, which was far more compelling than her placid dismantlement of Kevin Rudd's legacy: otherwise her main task for the campaign.

The truth is that Julia Gillard is far more comfortable when she has an adversary to destroy, or a problem to navigate, than she is with unilateral dissertations on principle.

Julia Gillard is a fixer.

Faced with the wild topiary of Kevin Rudd's political bequest to her - a mutinous business sector, an emissions trading scheme bizarrely scuppered by bipolar excesses of compromise and absolutism, and a climbing number of boat arrivals - Ms Gillard produced her garden shears and went to work.

In the end, her hasty refashioning of the Labor proposition was enough to get her government returned, by the most infinitesimal of margins, to nominal control of an opulently unorthodox chamber.

Hand-wringers worry about legislative paralysis, and how the Gillard agenda will possibly survive an Australian bicameral system that now looks more like a commando course than a parliament.

But let's not overstate the extent of the "Gillard agenda".

The Gillard agenda, in essence, is to fix the bits of the Rudd agenda that blew up and to excise from the public mind the bits that are unfixable.

Julia Gillard, Prime Minister, is principally occupied with fixing the mess that is Labor's climate change policy, fixing the future of the National Broadband Network, and fixing the schisms within her own party over its ability to extract crisis from a situation of profound political advantage.

The new circumstances require the Prime Minister to be capable of dealing patiently with a disparate group containing various single-issue nutters whose purposes seem - at first blush - to be entirely inconsistent with each other, and whose personal animosities within the political sphere run back, in some cases, decades.

It sounds daunting, until you remember that Julia Gillard comes from the left wing of the Labor Party in Victoria, which is a sort of terrorist training camp for exactly this tricky assignment.

Little did young Julia know, when she was navigating 'twixt Trots, Zionists, Eurocommunists and the like in the fevered Petri dish of Labor culture that was left-wing student politics in the 1980s, that what she was really doing was training for the prime ministership two decades hence.

The characteristic that has always kept Julia Gillard personally at something of an arms' length from her colleagues in Labor's Left - her pragmatism - becomes a distinct advantage in this terrain.

Australian politics continues to yield fascinating patterns and symmetries.

For many years, the electorate has given with one hand and taken with the other; given government to one party in the House of Representatives with one hand, for example, while with the other inflicting an exasperating balance of power in the Senate.

In 2010, the Australian electorate finally made good on its ability to deliver a hung parliament.

But it was delivered to a prime minister probably better able to cope with it than any recent incumbent; a fixer, who will moreover be spared the sight of her grand vision becoming hopelessly snagged in the parliament by virtue of the inherent - in this environment - advantage of not really having one.

Annabel Crabb is ABC Online's chief political writer.