4.9 Lists of expressions
The GiNaC class lst serves for holding a list of arbitrary
expressions. They are not as ubiquitous as in many other computer algebra
packages, but are sometimes used to supply a variable number of arguments of
the same type to GiNaC methods such as subs() and some matrix
constructors, so you should have a basic understanding of them.
Lists can be constructed by assigning a comma-separated sequence of
expressions:
| | {
symbol x("x"), y("y");
lst l;
l = x, 2, y, x+y;
// now, l is a list holding the expressions 'x', '2', 'y', and 'x+y',
// in that order
...
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There are also constructors that allow direct creation of lists of up to
16 expressions, which is often more convenient but slightly less efficient:
| | ...
// This produces the same list 'l' as above:
// lst l(x, 2, y, x+y);
// lst l = lst(x, 2, y, x+y);
...
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Use the nops() method to determine the size (number of expressions) of
a list and the op() method or the [] operator to access
individual elements:
| | ...
cout << l.nops() << endl; // prints '4'
cout << l.op(2) << " " << l[0] << endl; // prints 'y x'
...
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As with the standard list<T> container, accessing random elements of a
lst is generally an operation of order O(N). Faster read-only
sequential access to the elements of a list is possible with the
iterator types provided by the lst class:
| | typedef ... lst::const_iterator;
typedef ... lst::const_reverse_iterator;
lst::const_iterator lst::begin() const;
lst::const_iterator lst::end() const;
lst::const_reverse_iterator lst::rbegin() const;
lst::const_reverse_iterator lst::rend() const;
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For example, to print the elements of a list individually you can use:
| | ...
// O(N)
for (lst::const_iterator i = l.begin(); i != l.end(); ++i)
cout << *i << endl;
...
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which is one order faster than
| | ...
// O(N^2)
for (size_t i = 0; i < l.nops(); ++i)
cout << l.op(i) << endl;
...
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These iterators also allow you to use some of the algorithms provided by
the C++ standard library:
| | ...
// print the elements of the list (requires #include <iterator>)
std::copy(l.begin(), l.end(), ostream_iterator<ex>(cout, "\n"));
// sum up the elements of the list (requires #include <numeric>)
ex sum = std::accumulate(l.begin(), l.end(), ex(0));
cout << sum << endl; // prints '2+2*x+2*y'
...
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lst is one of the few GiNaC classes that allow in-place modifications
(the only other one is matrix). You can modify single elements:
| | ...
l[1] = 42; // l is now {x, 42, y, x+y}
l.let_op(1) = 7; // l is now {x, 7, y, x+y}
...
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You can append or prepend an expression to a list with the append()
and prepend() methods:
| | ...
l.append(4*x); // l is now {x, 7, y, x+y, 4*x}
l.prepend(0); // l is now {0, x, 7, y, x+y, 4*x}
...
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You can remove the first or last element of a list with remove_first()
and remove_last():
| | ...
l.remove_first(); // l is now {x, 7, y, x+y, 4*x}
l.remove_last(); // l is now {x, 7, y, x+y}
...
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You can remove all the elements of a list with remove_all():
| | ...
l.remove_all(); // l is now empty
...
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You can bring the elements of a list into a canonical order with sort():
| | ...
lst l1, l2;
l1 = x, 2, y, x+y;
l2 = 2, x+y, x, y;
l1.sort();
l2.sort();
// l1 and l2 are now equal
...
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Finally, you can remove all but the first element of consecutive groups of
elements with unique():
| | ...
lst l3;
l3 = x, 2, 2, 2, y, x+y, y+x;
l3.unique(); // l3 is now {x, 2, y, x+y}
}
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