Function: Octonion[def_omultable] - define octonionic multiplication table

Calling Sequence:

def_omultable(F);

Parameters:

F - a list of type `Fano_triples`

Description:

Procedure 'def_omultable' allows user to define an octonionic multiplication table which could be different than the deafult one.

The default multiplication table is initialized at the time when the 'OCTONION' package is being loaded. It can also be re-defined by issuing the following command:

> def_omultable(_default_Fano_triples);

where _default_Fano_triples is a global list with default Fano triples. See Octonion[`type/Fano_triples`] for more information.

Use Octonion[omultable] to display currently defined multiplication table.

Use Cliff5[CLIFFORD_ENV] to display current environmental variables used by 'CLIFFORD' and 'Octonion'.

Examples:

> restart:with(Cliff5):with(Octonion);

Warning, new definition for init

> omultable(); #default multiplication table

For example, we get the first row as follows:

> seq(e1 &o e.i,i=1..7);

The second row we get as follows:

> seq(e2 &o e.i,i=1..7);

and so on.

Multiplication table can be erased as follows:

> subsop(4=NULL,eval(omul)):

> omultable();

Finally, we re-initialize the table using the default Fano triples:

> _default_Fano_triples;

> def_omultable(_default_Fano_triples);

> omultable();

However, the following is another valid list of Fano triples:

> new_Fano_triples:=[[6,2,5],[6,3,4],[6,7,1],[2,3,7],[3,1,5],[2,4,1],[4,5,7]];

> type(new_Fano_triples,Fano_triples);

> def_omultable(new_Fano_triples);

> omultable();

>

which is a different multiplication table than before.

See Also: Octonion[`type/Fano_triples`] , Octonion[omultable] , Octonion[omul]