Weed?

Can anyone help to ID this weed please. It's low growing with a reddish stem and a long thin root

 

I think. . . .it looks like that veg grown in Africa and has squillions of small red/crimson berry like friuts when mature. (looks like a dock). We took over our allotment from a 'West African' chap and they were still coming up years later. Not very clear I'm afraid, but I hope this helps? Cheers, Tony.

 

"Amaranth" that's the name I was struggling with. Cheers, Tony.

 

Thanks Tony - it sounds rather nice. Obviously needs a bit of care though to make sure it doesn't get too carried away with itself. An 'international' garden hey?!