  This paper addresses the computational challenges of learning strong
substitutes demand when given access to a demand (or valuation) oracle. Strong
substitutes demand generalises the well-studied gross substitutes demand to a
multi-unit setting. Recent work by Baldwin and Klemperer shows that any such
demand can be expressed in a natural way as a finite list of weighted bid
vectors. A simplified version of this bidding language has been used by the
Bank of England.
  Assuming access to a demand oracle, we provide an algorithm that computes the
unique list of weighted bid vectors corresponding to a bidder's demand
preferences. In the special case where their demand can be expressed using
positive bids only, we have an efficient algorithm that learns this list in
linear time. We also show super-polynomial lower bounds on the query complexity
of computing the list of bids in the general case where bids may be positive
and negative. Our algorithms constitute the first systematic approach for
bidders to construct a bid list corresponding to non-trivial demand, allowing
them to participate in `product-mix' auctions.
