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Edit detail for SandBoxGroebnerBasis revision 2 of 8

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Editor: Bill Page
Time: 2011/02/08 21:09:14 GMT-8
Note: inline alignment

changed:
-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.
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 \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.