Edit detail for SandBoxGroebnerBasis revision 1 of 8

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Adapted from "Ideals, Varieties, and Algorithms Third Edition, 2007":http://www.cs.amherst.edu/~dac/iva.html

Appendix C

  Computer Algebra Systems 

1 AXIOM

For us, the most important AXIOM commands are [normalForm], for doing the division algorithm, and [groebner], for computing a Groebner basis.

A distinctive feature of AXIOM is that every object has a specific type. In particular, this affects the way AXIOM works with monomial orders: an order is encoded in a special kind of type. For example, suppose we want to use lex order on $     \mathbb{Q}[x,y,z]$ with
$$
x > y > z
$$
This is done using the type $$ DMP([x,y,z], FRAC INT) $$ (remember that AXIOM encloses a list inside brackets ![...]). Here $DMP$ stands for "Distributed Multivariate Polynomial", and $FRAC INT" means fractions of integers, i.e. rational numbers.

Adapted from Ideals, Varieties, and Algorithms Third Edition, 2007

Appendix C

Computer Algebra Systems

1. AXIOM

For us, the most important AXIOM commands are [normalForm]?, for doing the division algorithm, and [groebner]?, for computing a Groebner basis.

A distinctive feature of AXIOM is that every object has a specific type. In particular, this affects the way AXIOM works with monomial orders: an order is encoded in a special kind of type. For example, suppose we want to use lex order on with

This is done using the type (remember that AXIOM encloses a list inside brackets [...]). Here stands for "Distributed Multivariate Polynomial", and $FRAC INT" means fractions of integers, i.e. rational numbers.