ApCoCoA-1:Symbolic data Computations: Difference between revisions
New page: Some computation examples |
No edit summary |
||
Line 1: | Line 1: | ||
=== Computation Examples for [[:ApCoCoA:Symbolic data|Non-abelian Groups]] === | |||
==== <div id="Baumslag_groups">Computations of Baumslag groups</div> ==== | |||
The Baumslag (respectively Baumslag-Solitar) groups are examples of two-generator one-relator groups. | |||
The first variante of this group has the presentation <a, b | a^m = b^n = 1 > for m, n natural numbers. | |||
Type Baumslag1(m, n, [DegreeBound, LoopBound]) to calculate the Gröbner base. | |||
The second variante of this group (the Baumslag-Solitar group) has the presentation <a, b | b*a^m = a^n*b> for m, n natural numbers. | |||
Type Baumslag2(m, n, [DegreeBound, LoopBound]) to calculate the Gröbner base. | |||
Baumslag1(m, n, [DegreeBound, LoopBound]) (optional parameters in "[ ]") | |||
Baumslag group with the following presentation < a, b | a^m = b^n = 1 > | |||
Define Baumslag1(...) | |||
If Not Len(ARGV) = 2 And Not Len(ARGV) = 4 Then | |||
Error("Error in Baumslag1(...). There have to be two argument (n and m for exponents) | |||
or four arguments (n, m, degree, loops)"); | |||
EndIf; | |||
For I:= 1 To Len(ARGV) Do | |||
If Not Type(ARGV[I]) = INT Then | |||
Error("Error in Baumslag1(...). The Type of the Arguments must be INT"); | |||
ElIf ARGV[I] < 1 Then | |||
Error("Error in Baumslag1(...). The integer arguments must be positive"); | |||
EndIf; | |||
EndFor; | |||
X:= "ab"; | |||
Ordering:= "LLEX"; | |||
R:= []; | |||
AM:= ""; | |||
BN:= ""; | |||
For I:= 1 To ARGV[1] Do | |||
AM:= AM + "a"; | |||
EndFor; | |||
For I:= 1 To ARGV[2] Do | |||
BN:= BN + "b"; | |||
EndFor; | |||
F:= [[[1, AM], [-1, ""]], [[1, BN], [-1, ""]]]; | |||
If Len(ARGV) = 1 Then | |||
S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F); | |||
Else | |||
S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F, ARGV[2], ARGV[3], 1); | |||
EndIf; | |||
Return S; | |||
EndDefine; | |||
Baumslag2(m, n, [DegreeBound, LoopBound]) (optional parameters in "[ ]") | |||
Baumslag-Solitar group with the following presentation < a, b | b * a^m = a^n * b > | |||
Define Baumslag2(...) | |||
If Not Len(ARGV) = 2 And Not Len(ARGV) = 4 Then | |||
Error("Error in Baumslag1(...). There have to be two argument (n and m for exponents) or four arguments (n, m, degree, loops)"); | |||
EndIf; | |||
For I:= 1 To Len(ARGV) Do | |||
If Not Type(ARGV[I]) = INT Then | |||
Error("Error in Baumslag1(...). The Type of the Arguments must be INT"); | |||
ElIf ARGV[I] < 1 Then | |||
Error("Error in Baumslag1(...). The integer arguments must be positive"); | |||
EndIf; | |||
EndFor; | |||
X:= "abcdABCD"; | |||
Ordering:= "LLEX"; | |||
R:= []; | |||
AM:= ""; | |||
AN:= ""; | |||
For I:= 1 To ARGV[1] Do | |||
AM:= AM + "a"; | |||
EndFor; | |||
For I:= 1 To ARGV[2] Do | |||
AN:= AN + "a"; | |||
EndFor; | |||
F1 := [[1, "aA"], [-1, ""]]; | |||
F2 := [[1, "bB"], [-1, ""]]; | |||
F3 := [[1, "cC"], [-1, ""]]; | |||
F4 := [[1, "dD"], [-1, ""]]; | |||
F5 := [[1, "Aa"], [-1, ""]]; | |||
F6 := [[1, "Bb"], [-1, ""]]; | |||
F7 := [[1, "Cc"], [-1, ""]]; | |||
F8 := [[1, "Dd"], [-1, ""]]; | |||
F:= [F1, F2, F3, F4, F5, F6, F7, F8, [[1, "a"], [-1, "c"]], [[1, "b"], [-1, "d"]], [[1, "b" + AN], [-1, AM + "b"]]]; | |||
If Len(ARGV) = 1 Then | |||
S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F); | |||
Else | |||
S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F, ARGV[2], ARGV[3], 1); | |||
EndIf; | |||
Return S; | |||
EndDefine; |
Revision as of 12:16, 29 May 2013
Computation Examples for Non-abelian Groups
Computations of Baumslag groups
The Baumslag (respectively Baumslag-Solitar) groups are examples of two-generator one-relator groups. The first variante of this group has the presentation <a, b | a^m = b^n = 1 > for m, n natural numbers. Type Baumslag1(m, n, [DegreeBound, LoopBound]) to calculate the Gröbner base. The second variante of this group (the Baumslag-Solitar group) has the presentation <a, b | b*a^m = a^n*b> for m, n natural numbers. Type Baumslag2(m, n, [DegreeBound, LoopBound]) to calculate the Gröbner base.
Baumslag1(m, n, [DegreeBound, LoopBound]) (optional parameters in "[ ]")
Baumslag group with the following presentation < a, b | a^m = b^n = 1 >
Define Baumslag1(...) If Not Len(ARGV) = 2 And Not Len(ARGV) = 4 Then Error("Error in Baumslag1(...). There have to be two argument (n and m for exponents) or four arguments (n, m, degree, loops)"); EndIf; For I:= 1 To Len(ARGV) Do If Not Type(ARGV[I]) = INT Then Error("Error in Baumslag1(...). The Type of the Arguments must be INT"); ElIf ARGV[I] < 1 Then Error("Error in Baumslag1(...). The integer arguments must be positive"); EndIf; EndFor; X:= "ab"; Ordering:= "LLEX"; R:= []; AM:= ""; BN:= ""; For I:= 1 To ARGV[1] Do AM:= AM + "a"; EndFor; For I:= 1 To ARGV[2] Do BN:= BN + "b"; EndFor; F:= [[[1, AM], [-1, ""]], [[1, BN], [-1, ""]]]; If Len(ARGV) = 1 Then S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F); Else S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F, ARGV[2], ARGV[3], 1); EndIf; Return S; EndDefine;
Baumslag2(m, n, [DegreeBound, LoopBound]) (optional parameters in "[ ]")
Baumslag-Solitar group with the following presentation < a, b | b * a^m = a^n * b >
Define Baumslag2(...) If Not Len(ARGV) = 2 And Not Len(ARGV) = 4 Then Error("Error in Baumslag1(...). There have to be two argument (n and m for exponents) or four arguments (n, m, degree, loops)"); EndIf; For I:= 1 To Len(ARGV) Do If Not Type(ARGV[I]) = INT Then Error("Error in Baumslag1(...). The Type of the Arguments must be INT"); ElIf ARGV[I] < 1 Then Error("Error in Baumslag1(...). The integer arguments must be positive"); EndIf; EndFor; X:= "abcdABCD"; Ordering:= "LLEX"; R:= []; AM:= ""; AN:= ""; For I:= 1 To ARGV[1] Do AM:= AM + "a"; EndFor; For I:= 1 To ARGV[2] Do AN:= AN + "a"; EndFor; F1 := [[1, "aA"], [-1, ""]]; F2 := [[1, "bB"], [-1, ""]]; F3 := [[1, "cC"], [-1, ""]]; F4 := [[1, "dD"], [-1, ""]]; F5 := [[1, "Aa"], [-1, ""]]; F6 := [[1, "Bb"], [-1, ""]]; F7 := [[1, "Cc"], [-1, ""]]; F8 := [[1, "Dd"], [-1, ""]]; F:= [F1, F2, F3, F4, F5, F6, F7, F8, [[1, "a"], [-1, "c"]], [[1, "b"], [-1, "d"]], [[1, "b" + AN], [-1, AM + "b"]]]; If Len(ARGV) = 1 Then S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F); Else S:= $apcocoa/gbmr.MRBP(X, Ordering, R, F, ARGV[2], ARGV[3], 1); EndIf; Return S; EndDefine;