quhomology: Calculation of Homology of Quandles, Racks, Biquandles and Biracks

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This calculates the Quandle, Rack and Degenerate Homology groups of Racks and Biracks (as well as Quandles and Biquandles). In addition, a test is provided to ascertain if a given set with one or two given functions is indeed a biquandle or not.

Author
Ansgar Wenzel [aut, cre]
Date of publication
2016-05-02 17:59:48
Maintainer
Ansgar Wenzel <ansgar.wenzel@gmail.com>
License
GPL (>= 3)
Version
1.1.0

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Man pages

all_combinations
Calculating all possible permutations
boundary_matrix
This function calculates a boundary matrix.
boundary_matrix_degenerate
Calculation of boundary matrix for degenerate Homology.
boundary_names
Calculation of boundary elements for quandle and rack...
boundary_names_degenerate
Calculation of degenerate boundary elements for boundary...
check_f
Check if the function is bijective
check_more_push
Helper function for Smith Normal Form calculation.
check_permutations
Check if Switch is bijective.
check_YB
Check Young Baxter Equation
degenerate_homology
Calculates the degenerate Homology for a rack/birack.
down_action
The down action for a birack or biquandle.
find_S_result
Calculate the Switch
findX
Calculate the left row action matrix to turn a matrix into...
GaussianElimination
Calculation of Gaussian Form of a matrix.
homology
Calculation of quandle and rack homology groups of a rack /...
matrix_rank
Calculates the rank of a matrix.
output_results
Function that prints the calculated homology group to the...
push_down
Helper Function for Smith Normal Form calculation.
quhomology-package
Calculation of Homology groups of a rack/birack
row_space
Row Space of a Matrix.
rref
Reduced Row Echelon Form of a matrix
smith
Smith Normal Form of a matrix.
S_test
Testing of possible quandle/biquandle actions
up_action
The up action for a birack or biquandle.

Files in this package

quhomology
quhomology/tests
quhomology/tests/testthat.R
quhomology/NAMESPACE
quhomology/R
quhomology/R/Stest.R
quhomology/R/homology_calculation.R
quhomology/R/found_functions.R
quhomology/R/boundary_calculations.R
quhomology/README.md
quhomology/MD5
quhomology/DESCRIPTION
quhomology/man
quhomology/man/all_combinations.Rd
quhomology/man/boundary_names.Rd
quhomology/man/down_action.Rd
quhomology/man/matrix_rank.Rd
quhomology/man/output_results.Rd
quhomology/man/find_S_result.Rd
quhomology/man/quhomology-package.Rd
quhomology/man/boundary_matrix.Rd
quhomology/man/check_f.Rd
quhomology/man/degenerate_homology.Rd
quhomology/man/homology.Rd
quhomology/man/rref.Rd
quhomology/man/up_action.Rd
quhomology/man/check_more_push.Rd
quhomology/man/check_permutations.Rd
quhomology/man/S_test.Rd
quhomology/man/boundary_matrix_degenerate.Rd
quhomology/man/boundary_names_degenerate.Rd
quhomology/man/findX.Rd
quhomology/man/row_space.Rd
quhomology/man/GaussianElimination.Rd
quhomology/man/push_down.Rd
quhomology/man/check_YB.Rd
quhomology/man/smith.Rd