standardForm -- convert to standard form

Synopsis

Usage:

standardForm f
Outputs:
- a hash table, the polynomial or monomial in a form involving hash tables.

Description

A polynomial is represented by hash tables in which the keys are hash tables representing the monomials and the values are the coefficients. The monomials themselves are represented by hash tables in which the keys are the variables and the values are the corresponding exponents.

i1 : R = ZZ/101[x,y,z];

i2 : standardForm (x^2 - 7 + x*y*z^11 + y)

o2 = HashTable{HashTable{} => -7      }
               HashTable{0 => 1 } => 1
                         1 => 1
                         2 => 11
               HashTable{0 => 2} => 1
               HashTable{1 => 1} => 1

o2 : HashTable

Code

../../../../../Macaulay2/m2/monoids.m2:144:32-148:82: --source code:
standardForm RingElement   := f -> (
    R := ring f;
    k := coefficientRing R;
    (cc, mm) := rawPairs(raw k, raw f);
    new HashTable from toList apply(cc, mm, (c, m) -> (standardForm m, new k from c)))

Ways to use standardForm :

standardForm(MonoidElement)
standardForm(RingElement)

For the programmer

The object standardForm is a method function.