symbol
is short for "Symbolic Name". A value of type symbol
represents a "variable name" possibly with some integer indices
attached. Its primary use is for input and output of polynomials: the
name of each indeterminate in a polynomial ring is a symbol
, similarly
for a PPMonoid
.
A symbol
value has two components: its head which is a string
comprising letters and underscores (but the first character must be a
letter), and its indices which are a vector of integers (indices may be
negative). Examples of symbol
s are: (in standard printed forms)
x, X, alpha, z_alpha, x[2], gamma[-2,3,-9]
Constructors
symbol(head)
where head is a std::string
symbol
with no indices
symbol(head, ind)
where head is a std::string
and ind a long
symbol
with a single index
symbol(head, ind1, ind2)
where head is a std::string
and ind1, ind2 long
ssymbol
with a two indexes
symbol(head, inds)
where head is a std::string
andstd::vector<long>
this produces a symbol
with indices
Operations on a symbol
Let sym, sym1, and sym2 be objects of type symbol
head(sym) head of sym as a const ref to ``std::string`` NumIndices(sym) number of indices sym has (gives 0 if sym has no indices) index(sym, n) gives n-th index of sym cmp(sym1, sym2) <0, =0, >0 according as sym1 < = > sym2 (using some total ordering: currently lex on heads, then lex on index vectors) sym1 < sym2 comparisons defined in terms of ``cmp`` sym1 <= sym2 sym1 > sym2 sym1 >= sym2 sym1 == sym2 sym1 != sym2 out << sym print sym on out in >> sym read a symbol into sym (NB see "bugs" section) (expected format is x, y[1], z[2,3], etc.)
Several polynomial ring pseudo-constructors expect a vector
of symbol
s
to specify the names of the indeterminates. There are several "convenience"
functions for constructing commonly used collections of symbol
s.
symbols(hd1) create vector of length 1 containing symbol(hd1) symbols(hd1,hd2) ... length 2... symbols(hd1,hd2,hd3) ... length 3... symbols(hd1,hd2,hd3,hd4) ... length 4... SymbolRange(hd, lo, hi) create vector of hd[lo], hd[lo+1], ... hd[hi] SymbolRange(sym1, sym2) create vector of "cartesian product" of the indices, e.g. given x[1,3] and x[2,4] produces x[1,3], x[1,4], x[2,3], x[2,4] AreDistinct(vecsyms) true iff all symbols are distinct AreArityConsistent(vecsyms) true iff all symbols with the same head have the same arity
The implementation is extremely simple. Efficiency does not seem to be
important (e.g. symbols
and SymbolRange
copy the vector upon returning).
Implementation of SymbolRange
is mildly delicate when we have to make
checks to avoid integer overflow -- see comments in the code.
The total ordering could be useful, for instance, if someone wants to
make a std::map
using symbol
s. "Lex on the heads then lex on the
index vectors" seemed simple, and probably fast enough.
The function symbol::myInput
is a stop-gap implementation.
The member function myInput
handles white space wrongly. For CoCoALib
whitespace is space, TAB, or backslash-newline; newline without
backslash is not considered white space.
It might be nice to have a function which returns the vector of indices of a name.
Decided not to permit big integers as indices; I don't see when it could ever be useful.
I wonder what sending a symbol
on an OpenMath channel would mean
(given that OpenMath is supposed to preserve semantics, and a symbolic
name is by definition devoid of semantics).