This repository contains the author's C-code for efficient manipulation of Steenrod algebra related structures; this includes enumeration of Steenrod algebra elements and optimized multiplication routines. All computations take place in the Milnor basis. The library is meant to be used through its Tcl interface; its primary purpose is to function as the main "engine" underlying the author's Sage/Yacop project.
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Make sure you have Tcl headers and development libraries installed. On Ubuntu you need, for example, to install the tcl-dev package - other distributions will offer similar packages. For the graphical demo resolver you also need the "tk" package with its "wish" executable.
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To build, create a subdirectory "build" and cd into it. Then run "../configure", "make", and "sudo make install"
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After running "make install" you can run "make bigtest" to run some consistency tests.
Change to directory demo. Then try some of the following command lines
wish ./resolver.tcl -prime 3 -algebra '0 -1 {9 9 9 9 9 9 9 9} 0' -maxdim 80 -maxs 25
wish ./resolver.tcl -prime 2 -algebra '0 0 {9 9 9 9 9 9 9 9} 0' -maxdim 130 -maxs 25 -viewtype even
wish ./resolver.tcl -prime 2 -algebra '0 0 {3 2 1} 0' -maxdim 80 -maxs 25 -viewtype even
The algebra format deserves some explanation: the algebra is specified as a list of 4 entries, 2 of which are actually ignored. The meaning of the 4 constituents is this:
"0" coefficient (ignored)
"-1" bitmask, specifying the Bocksteins (all in this case)
"9 9 9 9 9" profile of the reduced part of the subalgebra
"0" generator id (ignored)
The resolutions are recomputed from scratch on every run, nothing is saved.
The status line of the resolver shows
- the prime
- the subalgebra A that is being resolved
- an auxiliary subalgebra B that is used to divide the computation into smaller pieces
- the dimension of the matrices for the initial homology calculation
- the dimension of the matrix involved in the current lifting problem
There is also a non-graphical version that runs when you specify "-usegui 0".