Quadratic Forms Software (C++, SAGE)

This is the C++/Magma code designed to answer the question:

"What numbers are represented by a positive definite integer-valued quadratic form in 4 variables?"

It was originally written in C++/MAGMA, but will be included with the freely available SAGE Project! =)

Earlier versions of this code were used to:

• Prove that x² + 3y² + 5z² + 7w² represents all positive integers except for 2 and 22. (Kneser's Conjecture)
• Prove that every positive definite integer-valued quadratic form which represents the 29 numbers

  1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290

  represents all positive integers. (Conway's 290-Conjecture)