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last edited 10 years ago by Bill Page |
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Editor: Bill Page
Time: 2011/02/08 21:09:14 GMT-8 |
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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
Computer Algebra Systems
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 means fractions of integers, i.e. rational numbers.