UserManual

quad

The module `quad' is for computations of imaginary quadratic fields.

Functions

computeClassNumber(disc [,limit_of_disc])

Compute the class number of quadratic forms of discriminant 'disc' and return (a, b). 'a' is the class number and 'b' is the list of representative reduced forms of classes; the forms are instances of the class ReducedQuadraticForm.

computePDF(f_1 ,f_2)

computePDF(f_1 ,f_2) returns the composite of f_1 and f_2.

reducePDF(a)

Return the unique reduced form equivalent to a, 'a' is a positive definite quadratic form.

bsgs(group, lowerbound, upperbound)

bsgs(group, lowerbound, upperbound) returns the order of the group, using Shanks's Baby-Step Giant-Step Method. 'group' is an object that returns an element of the group, when it is called. 'lowerboud' is a lowerbound of the order of the group. 'upperbound' is an upperbound of the order of the group. ' lowerbound' and 'upperbound' have to keep a condition:

upperbound / 2 < lowerbound <= the order <= upperbound

sqrPDF(frm)

sqrPDF returns a positive definite quadratic form that is a squar power of frm.

Classes


Last-modified: 2006-08-08 (Ва) 18:14:43