The library source files are:

The Makefile compiles these into a shared library (liberiksson.so on unix, liberiksson.dll on cygwin).

One client file is verify.cpp. The other is deodhar.cpp.

See the README.txt for more information and sample output.

**Usage of deodhar.cpp**

1. First compile the program using "make deodhar".

2. Running without arguments gives help text. Input is sent to the program using command-line parameters.

brant@fuzzy$ ./deodhar No arguments given. Usage: ./deodhar A3 -w 1021 Given a reduced expression for a Deodhar element, returns the Kazhdan-Lusztig basis element. Optional argument: -x3. Passing a Coxeter type prints the Coxeter matrix. The generators are 0, 1, ..., n-1 and theonly prints the polynomial P_{x,w}(q). Optional argument: -mu prints the mu-coefficients. Optional argument: -masks prints all masks.

brant@fuzzy$ ./deodhar A3 Coxeter type A3 with Coxeter matrix: 0 3 2 3 0 3 2 3 0 No w expression given.4. Passing a reduced expression w prints the Kazhdan--Lusztig basis element {C'}_w.

brant@fuzzy$ ./deodhar A3 -w 1201 Coxeter type A3 with Coxeter matrix: 0 3 2 3 0 3 2 3 0 w is using reduced expression ....: ( 1 2 0 1 ). In lex order on reduced expressions: P(( 1 2 0 1 ),( )) = 1 + q P(( 1 2 0 1 ),( 0 )) = 1 P(( 1 2 0 1 ),( 0 1 )) = 1 P(( 1 2 0 1 ),( 0 1 0 )) = 1 P(( 1 2 0 1 ),( 1 )) = 1 + q P(( 1 2 0 1 ),( 1 0 )) = 1 P(( 1 2 0 1 ),( 1 2 )) = 1 P(( 1 2 0 1 ),( 1 2 0 )) = 1 P(( 1 2 0 1 ),( 1 2 0 1 )) = 1 P(( 1 2 0 1 ),( 1 2 1 )) = 1 P(( 1 2 0 1 ),( 2 )) = 1 P(( 1 2 0 1 ),( 2 0 )) = 1 P(( 1 2 0 1 ),( 2 0 1 )) = 1 P(( 1 2 0 1 ),( 2 1 )) = 15. This can be filtered to just compute the Kazhdan--Lusztig polynomial P_{w,x}(q) for a particular x < w.

brant@fuzzy$ ./deodhar A3 -w 1201 -x 1 Coxeter type A3 with Coxeter matrix: 0 3 2 3 0 3 2 3 0 w is using reduced expression ....: ( 1 2 0 1 ). x is using reduced expression ( 1 ). In lex order on reduced expressions: P(( 1 2 0 1 ),( 1 )) = 1 + q6. If the element w is not Deodhar then the basis won't be printed, although mask statistics can still be viewed.

brant@fuzzy$ ./deodhar A3 -w 121 -masks Coxeter type A3 with Coxeter matrix: 0 3 2 3 0 3 2 3 0 w is using reduced expression ....: ( 1 2 1 ). mask: ( 0 0 0 ): 1 mask: ( 1 0 0d): q (not Deodhar) mask: ( 0 1 0 ): 1 mask: ( 1 1 0 ): 1 (mu mask) mask: ( 0 0 1 ): 1 mask: ( 1 0 1d): q (mu mask) mask: ( 0 1 1 ): 1 (mu mask) mask: ( 1 1 1 ): 1