caveat

# Differences

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 — caveat [2014/05/30 11:49] (current) Line 1: Line 1: + + You may have noticed that in the original, mathematical equation at the top of the page, there were **bounds** on the summation, <​latex>​$\sum_{k=1}^{i-1}$​. ​ In the Alphabets program we wrote, we did not include these bounds. ​ In this equation, this is safe, for a rather subtle reason (which will be clearer when you know more about Alpha). ​ In general, it is always safe to include these bounds explicitly in your program by making the reduction body a RestrictExpression to explicitly specify the range of indices where the expression inside the reduction is defined, as shown below. + + ​ + U[i,j] = case + ​{|1==i} : A[i,j]; + ​{|1<​i} : A[i,j] - reduce(+, [k], {|1<​=k<​i} : L[i,​k]*U[k,​j]);​ + esac; +