Assuming many variables at once

Question

I'm trying to set up the following constraints:

assume(E1A::integer,E2A::integer,...,E2B::integer,...,E3C::integer)

additionally(E1A>=0,E2A>=0,...,E3C>=0)

additionally(E1A<=3,E2A<=3,...,E3C<=3)

is there any way to do this without typing out all the terms E1A, E2A,...,E3C? I tried doing

for i from 0 to 3 do (assume(EiA::integer)) end do

as a shortcut, but Maple didn't like that, presumably because it didn't view the i as an indexing variable.

Answer 1

You can form names by concatenation.

restart:

assume( seq( cat(`E`,i,`A`)::integer, i=1..3 ) );

And now, to test,

[ seq( cat(`E`,i,`A`), i=1..3 ) ]:
map( about, % ):

  Originally E1A, renamed E1A~:
    is assumed to be: integer

  Originally E2A, renamed E2A~:
    is assumed to be: integer

  Originally E3A, renamed E3A~:
    is assumed to be: integer

You can also nest seq, eg,

restart:
assume( seq( seq( cat(`E`,i,abc)::integer, i=1..3), abc=[A,B,C] ) );

[ seq( seq( cat(`E`,i,abc), i=1..3), abc=[A,B,C] ) ]:
map( about, % ):

Answer 2

With the elementwise operator and the concatenation operator you can get all your assuming down to one line:

assume(E||(1..3)||A ::~ AndProp(integer, RealRange(0,3)));