NewGlyph := module ()   



 description "Basic Geometric Algebra Functions";   



 local setup, cleanup;   



 global e; 



 export GAversion,GAinit, GAadd_metric,GAmetric,GAmv;  



 option package, load = setup, unload = cleanup;   



  



 setup := proc ()   



	TypeTools:-AddType(`blade`, proc (a) type(a, indexed) and op(0, a) = 'e' end proc);   



	GAversion();   



	GAinit();   



 end proc;   



 setup(); 



 cleanup:=proc() 



 	TypeTools:-RemoveType(`blade`); 



 end proc; 



    



 GAinit := proc()   



  global   `&@`,  `&.`,  `&^`,   `&x`,    `&s`  , `&/`,   `&l`,   `&v`;   



  protect('`&@`','`&.`', '`&^`', '`&x`', '`&s`', '`&/`', '`&l`', '`&v`');   



  GAadd_metric('default', signum, -infinity, infinity);   



  GAadd_metric('SA', proc () 1 end proc, 1, 3);   



  GAadd_metric('STA', proc (i) `if`(i = 0, 1, -1) end proc, 0, 3);   



  GAadd_metric('MSTA', proc (i) `if`(modp(i, 4) = 0, 1, -1) end proc, 0, infinity);   



  GAadd_metric('Homogeneous', proc () 1 end proc, 0, infinity);   



  GAadd_metric('Conformal', proc (i) `if`(i = -1, -1, 1) end proc, -1, infinity);   



  GAmetric('default');   



 end proc:   



    



 GAversion := proc ()   



	print(`GA Package`);    



	print(`Version 2.0`);   



	print(`Written by: Mark Ashdown, maja1@mrao.cam.ac.uk`);   



	print(`Extended by: Alan Macdonald, macdonal@luther.edu`);   



	print(`Re-Packaged for Maple 2018 by: Ian McCreath`);   



 end proc;   



    



 GAadd_metric := proc (fred::name, signature::procedure, minind::{integer, infinity}, maxind::{integer, infinity})   



	global MetricTable;    



	unprotect('MetricTable');   



	MetricTable['fred'][sig] := eval(signature);    



	if maxind < minind then    



		ERROR(`The minimum index is greater than the maximum index`)   



	end if;   



	MetricTable['fred'][min] := minind;   



	MetricTable['fred'][max] := maxind;   



	protect('MetricTable');   



	print(`The GA package knows about metric ` . fred . `.`)    



 end proc:    



  



 GAmetric := proc (a::name)   



  global  Metric, Sig, MetricTable, MinIndex, MaxIndex;   



	if member([a], [indices(MetricTable)]) then    



		unprotect('Metric', 'Sig', 'MinIndex', 'MaxIndex');   



		Metric := a;   



		Sig := MetricTable[Metric][sig];   



		MinIndex := MetricTable[Metric][min];   



		MaxIndex := MetricTable[Metric][max];   



		protect('Metric', 'Sig', 'MinIndex', 'MaxIndex');   



		print(`Metric is now set to: ` . Metric)   



	else    



		ERROR(`The metric ` . a . ` is unknown to the GA package`)   



	end if   



 end proc:   



 



# Creates multivector with name x of with grade or set of grades g with 



# indices ind 



GAmv := proc(x::name,g::{nonnegint,set(nonnegint)},ind::set(integer)) 



  local i; 



  if g::set then 



    add(procname(x,i,ind), i=g) 



  elif g > nops(ind) then 



    ERROR(`grade too large for number of indices.`) 



  elif g=0 then 



    x[NULL] 



  else 



    add(x[op(i)]*e[op(i)], i=combinat:-choose(sort([op(ind)]),g)) 



  end if 



end: 



     



end module;