trick is to define (interpreter) variables a, b and c which point to
objects in the desired distributed domain, which are a, b, c. This
forces the interpreter not to choose Polynomal Integer , but direktly
allows to do the desired operation in dmp.
True.
Actually, I am not so sure to suggest this. Recently, I worked quite
some bit in the interpreter and I must say that with a not well planned
session, it is sometimes inconvenient having types declared on some
identifiers.
The reason is that if I can say
(210) -> foo := 1
(210) 1
Type: PositiveInteger
(211) -> foo := "hello"
(211) "hello"
Type: String
(212) -> foo
(212) "hello"
Type: String
But I get
b(213) -> bar: Integer := 1
(213) 1
Type: Integer
(214) -> bar := "hola"
Cannot convert right-hand side of assignment
"hola"
to an object of the type Integer of the left-hand side.
(214) -> bar: String := "hola"
You cannot declare bar to be of type String because either the
declared type of bar or the type of the value of bar is different
from String .
No, I am not saying that this behaviour of FriCAS is bad. Actually, I
rather like it. The point is that I did not know until I figured out
that there is a different behaviour for undeclared and declared identifiers.
However, good that you mentioned it. I will also put this into the
notebook. It's good if beginners learn that right away.
Some addition here.
(7) -> dmp := DMP([a,b,c], Integer)
(7) DistributedMultivariatePolynomial([a,b,c],Integer)
Type: Type
(8) -> a : dmp := a
Line (8) seems to look pretty stupid, but, in fact, almost all computer
algebra systems have this. The a on the left of := is actually an
identifier of the SPAD language (like in any other programming
language). On the right of := the a is a value.
(214) -> dmp := DMP([a,b,c], Integer)
(214) DistributedMultivariatePolynomial([a,b,c],Integer)
Type: Type
(215) -> a
(215) a
Type: Variable(a)
Hmmmm, the a on the lefthand side is of type Variable(a). It shouldn't
be possible to assign this to some identifier that has type dmp.
Again, the interpreter jumps in and tries to convert the a of type
Variable(a) into the value a of type
DistributedMultivariatePolynomial([a,b,c],Integer) and then assign it to
the identifier a. So when we now enter a, the interpreter interprets
this as the identifier a and this identifier has a value, namely a
(being of type DistributedMultivariatePolynomial([a,b,c],Integer).
(216) -> a : dmp := a
(216) a
Type: DistributedMultivariatePolynomial([a,b,c],Integer)
(217) -> a
(217) a
Type: DistributedMultivariatePolynomial([a,b,c],Integer)
Ralf
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