Creating A Random Quadratic Form

sage.quadratic_forms.random_quadraticform.random_quadraticform(R, n, rand_arg_list=[])

Create a random quadratic form in n variables defined over the ring R.

The last (and optional) argument rand_arg_list is a list of at most 3 elements which is passed (as at most 3 separate variables) into the method R.random_element().

INPUT:

  • R – a ring.
  • n – an integer \ge 0
  • rand_arg_list – a list of at most 3 arguments which can be taken by R.random_element().

OUTPUT:

A quadratic form over the ring R.

EXAMPLES:

sage: random_quadraticform(ZZ, 3, [1,5])    ## RANDOM
Quadratic form in 3 variables over Integer Ring with coefficients:
[ 3 2 3 ]
[ * 1 4 ]
[ * * 3 ]
sage: random_quadraticform(ZZ, 3, [-5,5])    ## RANDOM
Quadratic form in 3 variables over Integer Ring with coefficients:
[ 3 2 -5 ]
[ * 2 -2 ]
[ * * -5 ]
sage: random_quadraticform(ZZ, 3, [-50,50])    ## RANDOM
Quadratic form in 3 variables over Integer Ring with coefficients:
[ 1 8 -23 ]
[ * 0 0 ]
[ * * 6 ]
sage.quadratic_forms.random_quadraticform.random_quadraticform_with_conditions(R, n, condition_list=[], rand_arg_list=[])

Create a random quadratic form in n variables defined over the ring R satisfying a list of boolean (i.e. True/False) conditions.

The conditions c appearing in the list must be boolean functions which can be called either as Q.c() or c(Q), where Q is the random quadratic form.

The last (and optional) argument rand_arg_list is a list of at most 3 elements which is passed (as at most 3 separate variables) into the method R.random_element().

EXAMPLES:

sage: Q = random_quadraticform_with_conditions(ZZ, 3, [QuadraticForm.is_positive_definite], [-5, 5])
sage: Q    ## RANDOM
Quadratic form in 3 variables over Integer Ring with coefficients:
[ 3 -2 -5 ]
[ * 2 2 ]
[ * * 3 ]

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