zev Options [-G] Matrix [Poly [Group]]
The program was specifically designed to assist in the calculation of the Brauer characters of diagonalizable matrices, with the text giving the complex number which is the Brauer character of the companion matrix for that polynomial. Usually the polynomials have been prepared in a separate data file and are fed into zev by giving the file name or by redirecting its input. The preparation of the input polynomials is generally a time-consuming task if it is done by hand, but there are data files available for the most commonly used fields. These files should be located in the library directory. They are distributed with this release of the C MeatAxe. If the user is familiar with the computer program system GAP, he will find it easy to create his own data files.
If the nullity is not a multiple of the degree, zev prints a warning message.
The file is read and interpreted line by line. There are three types of lines:
[space]Name Coefficientswhere Name is any text (up to 1023 characters), and Coefficients are the coefficients of the polynomial (in free format). Note that the first character must be an ordinary space charcter, a TAB is not allowed! The coefficients must use the names as specified by the arithmetic --- usually 0,1,...q-1. The one exception is -1, which the program treats specially as "0-1" so that the cyclotomic polynomials can be used over all fields. The coefficients are in decreasing degree, starting with the coefficient of the highest power of x and continuing, ending up with the constant term.
Here is an example:
# Sample input file for zev # Some polynomials over GF(5) # p11b11 1 1 4 b11 1 4 4 1 3 4 -1-b11 1 2 4 1 1 4 p13c13 1 1 4 c13 1 3 0 3 1 c13*3 1 1 4 1 1 c13*9 1 2 1 2 1This file contains 7 polynomials in two groups. The polynomial "b11" in group "p11b11" is x5+4x4+4x3+x2+3x+4.
$ zev mat poly3 p8i2 p8i2 1 1 1 p8i2 -1 1 4 p8i2 0 2 2 p8i2 i2 2 0 p8i2 -i2 2 1 $ zev -G mat poly3 p8i2 MeatAxe.BrauerChar := 1*(1) + 4*(-1) + 2*(0) + 1*(-i2);Note that "i2" does not appear in the expression because its coefficient is zero.
It is not checked that the input file is a matrix. TAB characters at the beginning of a line are not interpreted as space.