Represents an expression involving generators from a group presentation or a free group. More...
#include <algebra/grouppresentation.h>
Inheritance diagram for regina::GroupExpression:
Public Member Functions | |
| GroupExpression () | |
| The terms that make up this expression. More... | |
| GroupExpression (const GroupExpression &cloneMe)=default | |
| Creates a new expression that is a clone of the given expression. More... | |
| GroupExpression (const std::string &input, bool *valid=nullptr) | |
| Attempts to interpret the given input string as a word in a group. More... | |
| GroupExpression & | operator= (const GroupExpression &cloneMe)=default |
| Makes this expression a clone of the given expression. More... | |
| bool | operator== (const GroupExpression &comp) const |
| Equality operator. More... | |
| bool | operator!= (const GroupExpression &comp) const |
| Inequality operator. More... | |
| std::list< GroupExpressionTerm > & | terms () |
| Returns the list of terms in this expression. More... | |
| const std::list< GroupExpressionTerm > & | terms () const |
| Returns a constant reference to the list of terms in this expression. More... | |
| size_t | countTerms () const |
| Returns the number of terms in this expression. More... | |
| size_t | wordLength () const |
| Returns the length of the word, i.e. More... | |
| bool | isTrivial () const |
| Tests whether this is the trivial (unit) word. More... | |
| void | erase () |
| Erases all terms from this this word. More... | |
| GroupExpressionTerm & | term (size_t index) |
| Returns the term at the given index in this expression. More... | |
| const GroupExpressionTerm & | term (size_t index) const |
| Returns a constant reference to the term at the given index in this expression. More... | |
| unsigned long | generator (size_t index) const |
| Returns the generator corresonding to the term at the given index in this expression. More... | |
| long | exponent (size_t index) const |
| Returns the exponent corresonding to the term at the given index in this expression. More... | |
| void | addTermFirst (const GroupExpressionTerm &term) |
| Adds the given term to the beginning of this expression. More... | |
| void | addTermFirst (unsigned long generator, long exponent) |
| Adds the given term to the beginning of this expression. More... | |
| void | addTermLast (const GroupExpressionTerm &term) |
| Adds the given term to the end of this expression. More... | |
| void | addTermLast (unsigned long generator, long exponent) |
| Adds the given term to the end of this expression. More... | |
| void | addTermsFirst (const GroupExpression &word) |
| Multiplies this expression on the left by the given word. More... | |
| void | addTermsLast (const GroupExpression &word) |
| Multiplies this expression on the right by the given word. More... | |
| bool | addStringFirst (const std::string &input) |
| Multiplies this expression on the left by the word respresented by the given string. More... | |
| bool | addStringLast (const std::string &input) |
| Multiplies this expression on the right by the word respresented by the given string. More... | |
| void | cycleRight () |
| Cycles this word by moving the leftmost term around to the rightmost. More... | |
| void | cycleLeft () |
| Cycles this word by moving the rightmost term around to the leftmost. More... | |
| GroupExpression * | inverse () const |
| Returns a newly created expression that is the inverse of this expression. More... | |
| void | invert () |
| Inverts this expression. More... | |
| GroupExpression * | power (long exponent) const |
| Returns a newly created expression that is this expression raised to the given power. More... | |
| bool | simplify (bool cyclic=false) |
| Simplifies this expression. More... | |
| bool | substitute (unsigned long generator, const GroupExpression &expansion, bool cyclic=false) |
| Replaces every occurrence of the given generator with the given substite expression. More... | |
| std::list< std::map< unsigned long, GroupExpressionTerm > > | relabellingsThisToOther (const GroupExpression &other, bool cyclic=false) const |
| Determines whether or not one can relabel the generators in this word to obtain the given other word. More... | |
| void | writeXMLData (std::ostream &out) const |
| Writes a chunk of XML containing this expression. More... | |
| std::string | toTeX () const |
| Returns a TeX representation of this expression. More... | |
| void | writeTeX (std::ostream &out) const |
| Writes a TeX represesentation of this expression to the given output stream. More... | |
| void | writeText (std::ostream &out, bool shortword=false, bool utf8=false) const |
| Writes a text representation of this expression to the given output stream, using either numbered generators or alphabetic generators. More... | |
| void | writeTextShort (std::ostream &out) const |
| Writes a short text representation of this object to the given output stream. More... | |
| void | writeTextLong (std::ostream &out) const |
| A default implementation for detailed output. More... | |
| std::string | str () const |
| Returns a short text representation of this object. More... | |
| std::string | utf8 () const |
| Returns a short text representation of this object using unicode characters. More... | |
| std::string | detail () const |
| Returns a detailed text representation of this object. More... | |
Detailed Description
Represents an expression involving generators from a group presentation or a free group.
An expression is represented as word, i.e, a sequence of powers of generators all of which are multiplied in order. Each power of a generator corresponds to an individual GroupExpressionTerm.
For instance, the expression g1^2 g3^-1 g6 contains the three terms g1^2, g3^-1 and g6^1 in that order.
Member Function Documentation
◆ writeTextLong()
|
inlineinherited |
A default implementation for detailed output.
This routine simply calls T::writeTextShort() and appends a final newline.
- Python
- Not present.
- Parameters
-
out the output stream to which to write.
The documentation for this class was generated from the following file:
- algebra/grouppresentation.h