symbol is short for Symbolic Name. A value of type symbol
represents a variable name possibly with some integer subscripts
attached. Its primary use is for input and output of polynomials: the
name of each indeterminate in a PolyRing is a symbol, similarly
for a PPMonoid.
A symbol value has two components:
_s
(note no other characters allowed)
Examples of symbols are: (in standard printed forms)
x, X, alpha, z_alpha, x[2], gamma[-2,3,-9] |
It is also possible to create anonymous symbols: they are useful for building (temporary) polynomial extensions of unknown coefficient rings (which may contain any symbol) to guarantee no name conflicts.
Each newly created anonymous symbol has a subscript strictly greater
than that of any previous anonymous symbol. For better readability,
an anonymous symbol prints out as a hash sign followed by the
subscript: e.g. #[12]
Let
head be a std::string,
ind, ind1, ind2, n machine integers,
inds a std::vector<long>.
symbol(head) -- a symbol with no subscripts
symbol(head, ind) -- a symbol with a single subscript
symbol(head, ind1, ind2) -- a symbol with a two subscripts
symbol(head, inds) -- a symbol with the given subscripts
NewSymbol() -- a new anonymous symbol (printed form is like this #[12])
Several polynomial ring pseudo-constructors expect a vector of
symbols to specify the names of the indeterminates. There are
several convenience functions for constructing commonly used
collections of symbols.
symbols(str) -- create a vector<symbol> containing comma-separated symbols in str
SymbolRange(hd, lo, hi) -- create vector of
hd[lo], hd[lo+1], ... hd[hi].
Note that these symbols each have just a single subscript
SymbolRange(sym1, sym2) -- create vector of cartesian product of the
subscripts, e.g. given x[1,3] and x[2,4] produces
x[1,3], x[1,4], x[2,3], x[2,4]
NewSymbols(n) -- create vector of n new anonymous symbols
Let sym, sym1, and sym2 be objects of type symbol
head(sym) -- head of sym as a const ref to std::string
NumSubscripts(sym) -- number of subscripts sym has (0 if sym has no subscripts)
subscript(sym, n) -- gives n-th subscript of sym
cmp(sym1, sym2) -- <0, =0, >0 according as sym1 < = > sym2
(for more info see Maintainer section)
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 (but also see Bugs section)
(expected format is x, y[1], z[2,3], etc.)
AreDistinct(vecsyms) -- true iff all symbols are distinct
AreArityConsistent(vecsyms) -- true iff all symbols with the same head
have the same arity
symbol::IsValidHead(str) -- determine whether the string is a valid head
symbol::IsValidFirstChar(ch) -- determine whether the char is a valid first char of a head
Note: I have used MachineInt as the type for fn args containing
index values because it is safer, and I believe that the run-time
penalty is unimportant. This is a considered exception to the guideline
which says to use long for indexes.
I have decided not to allow big integers as subscripts because I don't see when it could ever be genuinely useful.
The implementation is extremely simple. Efficiency does not seem to be
important (e.g. symbols and SymbolRange copy the vector upon returning).
The implementation of SymbolRange is mildly delicate when we have to make
checks to avoid integer overflow -- see comments in the code.
To make "anonymous" symbols I opted to use a private ctor which
accepts just a single subscript; this ctor is called only by NewSymbol
and NewSymbols.
The printing fn (myOutputSelf) has to check for an empty head, and if
found it prints the string in AnonHead.
We believe a total ordering on symbols could be useful; for instance,
if someone wants to make a std::map using symbols. Currently the
total order is Lex on the heads then lex on the subscript vectors; this
is simple, and is 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.
In redmine 747 there is a suggestion to allow symbol("x[1,2]");
we decided (2016-02-01) to postpone extending symbol in this way.
It might be nice to have a function which returns the vector of subscripts of a name.
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).