Top
Back: crystallographicGroupCM
Forward: crystallographicGroupP4
FastBack:
FastForward:
Up: fpalgebras_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
7.7.8.0. crystallographicGroupC2MM
Procedure from library fpalgebras.lib (see fpalgebras_lib).

Usage:
crystallographicGroupC2MM(d); d an integer

Return:
ring

Note:
- the ring contains the ideal I, which contains the required relations - c2mm group with the following presentation
< x, y, m, r | [x, y] = m^2 = r^2 = 1, m^-1*y*m = y^-1, m^-1*x*m = x*y, r^-1*y*r = y^-1, r^-1*x*r = x^-1, m^-1*r*m = r^-1 > - d gives the degreebound for the Letterplace ring

Example:
 
LIB "fpalgebras.lib";
def R = crystallographicGroupC2MM(5); setring R;
I;
==> I[1]=x(1)*y(2)+y(1)*x(2)+1
==> I[2]=x(1)*y(2)+y(1)*x(2)+m(1)*m(2)
==> I[3]=x(1)*y(2)+y(1)*x(2)+r(1)*r(2)
==> I[4]=m(1)*m(2)+1
==> I[5]=r(1)*r(2)+1
==> I[6]=m(1)*m(2)+r(1)*r(2)
==> I[7]=m(1)*y(2)*m(3)+Y(1)
==> I[8]=m(1)*x(2)*m(3)+x(1)*y(2)
==> I[9]=y(2)*r(3)+Y(1)
==> I[10]=r(1)*x(2)*r(3)+X(1)
==> I[11]=m(1)*r(2)*m(3)+r(1)
==> I[12]=X(1)*x(2)+1
==> I[13]=x(1)*X(2)+1
==> I[14]=Y(1)*y(2)+1
==> I[15]=y(1)*Y(2)+1


Top Back: crystallographicGroupCM Forward: crystallographicGroupP4 FastBack: FastForward: Up: fpalgebras_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4-1-1p3, 2018, generated by texi2html.