The arithmetic |
m_i_i(3L,a); m_i_i(2L,b); m_i_i(5L,c); m_i_i(6L,d); m_ou_b(a,b,koeff1); m_ou_b(c,d,koeff2); squareroot(a,a); mult_apply(a,koeff2); add(koeff1,koeff2,sqrad);You see that m_ou_b() makes fractions, the rest is obvious. Such radicals show up in character tables of alternating groups. These character tables can be evaluated using
an_tafel()Here is the output for A_{5}:
[1:1:1:1:1:]
[-1:-1:1:0:4:]
[0:0:-1:1:5:]
[ 1/2 ( 1 - sqr(5) ): 1/2 ( 1 + sqr(5) ):0:-1:3:]
[ 1/2 ( 1 + sqr(5) ): 1/2 ( 1 - sqr(5) ):0:-1:3:]
At present the input of elements of such extensions of Q is quite cumbersome. For example, if you want to apply symmetry adapted bases to a case with dihedral symmetry, so that you have to enter an irreducible representation of D_{6}, say the representating matrix
then you have to enter
(-1)/(2) (-sqrt(3))/(2) (sqrt(3))/(2) (-1)/(2)
2 2 125
1 4 1 1 1 1 1 2
1 4 1 3 1 -1 1 2
1 4 1 3 1 1 1 2
1 4 1 1 1 1 1 2
We apologize for that! This will be improved in due course.
The arithmetic |