symbol

© 2005,2007,2008,2012,2014,2015 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]

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]

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

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.

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.

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).