symbol

© 2005,2007,2008,2012 John Abbott and Anna M. Bigatti
GNU Free Documentation License, Version 1.2



CoCoALib Documentation Index

Examples

User documentation

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:

Examples of symbols are: (in standard printed forms)

x, X, alpha, z_alpha, x[2], gamma[-2,3,-9]

Anonymous symbols

It is also possible to create anonymous symbols: they are used for building temporary polynomial extensions on unknown coefficient rings (which may contain any symbol).

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 followed by the subscript: e.g. #[12]

Constructors

Let head be a std::string, ind, ind1, ind2, n machine integers, inds a std::vector<long>.

Creating a vector of symbols

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.

Operations on symbols

Let sym, sym1, and sym2 be objects of type symbol

Operations on vectors of symbols

Maintainer documentation for symbol

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.

Bugs, Shortcomings and other ideas

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 subscripts of a name.

Decided not to permit big integers as subscripts; I don't see when it could ever really 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).