piecewise

Robert Israel — Thu, 11 Mar 2010 11:09:00 Z

Well, you don't need all those x[i] <= x clauses:
piecewise(x < x[1], hz[1], x < x[2], hz[2], etc)
would do. But if you want to use x as a symbolic variable, it's probably better to use a different letter for the indexed object, maybe X[i] rather than x[i].

And for producing it, you could use something like

> piecewise(op(ListTools[Flatten]([seq]([x < X[i], hz[i]],i=1..10))));

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alsholm — Thu, 11 Mar 2010 11:30:51 Z

Robert Israel beat me to it, but I'll let the following stay.

Assuming that the values x[i] are sorted increasingly, you can do

piecewise(t < x[1], hz[1], t < x[2], hz[2], t< x[3], hz[3], t < x[4], hz[4], t < x[5], hz[5],t < x[6], hz[6], t < x[7], hz[7], t< x[8], hz[8], t < x[9], hz[9], t <= x[10], hz[10]);

since piecewise checks the inequalities from the left and stops if the inequality is satisfied.

Even shorter is

piecewise(op(map(op,[seq([t<x[i],h[i]],i=1..9)])),t<=x[10],hz[10]);

where I have singled out the last one since you want <= (if you really do).

Notice that I have used t instead of x. It is not a good idea to use x as a variable name if x[i] is in use.

Preben Alsholm

MaplePrimes - answers and comments on Question, piecewise or not?

piecewise

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