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Date: Fri, 15 May 2009 21:03:00 +0200 Franz Lehner wrote:

Attached is a prototype for tensor products. It is free modules over commutative rings.

TensorProduct? is now included with FriCAS. Thank you Franz!

fricas
M:=FreeModule(Integer,Symbol)
 (1)
Type: Type
fricas
N:=FreeModule(Integer,Symbol)
 (2)
Type: Type
fricas
a1:='a1::M
 (3)
Type: FreeModule(Integer,Symbol)
fricas
a2:='a2::M
 (4)
Type: FreeModule(Integer,Symbol)
fricas
b1:='b1::N
 (5)
Type: FreeModule(Integer,Symbol)
fricas
b2:='b2::N
 (6)
Type: FreeModule(Integer,Symbol)
fricas
MxN:=TensorProduct(Integer,Symbol,Symbol,M,N);
Type: Type
fricas
t := tensor(a1 + a2, b1 + b2)$MxN; Type: TensorProduct?(Integer,Symbol,Symbol,FreeModule(Integer,Symbol),FreeModule(Integer,Symbol)) fricas t  (7) Type: TensorProduct?(Integer,Symbol,Symbol,FreeModule(Integer,Symbol),FreeModule(Integer,Symbol)) fricas leadingMonomial t  (8) Type: Product(Symbol,Symbol) fricas numberOfMonomials t  (9) Type: PositiveInteger? Demonstrating the axioms of the tensor product: fricas x:M Type: Void fricas y:M Type: Void fricas u:M Type: Void fricas p:=2*x+3*u  (10) Type: FreeModule(Integer,Symbol) fricas q:=5*x+7*y+11*u  (11) Type: FreeModule(Integer,Symbol) fricas MxM:=TensorProduct(Integer,Symbol,Symbol,M,M); Type: Type fricas r := tensor(p, q)$MxM
 (12)
Type: TensorProduct?(Integer,Symbol,Symbol,FreeModule(Integer,Symbol),FreeModule(Integer,Symbol))
fricas
w:= 13*y+17*y+19*u
 (13)
Type: FreeModule(Integer,Symbol)
fricas
test( tensor(p + q, w)$MxM = tensor(p, w)$MxM + tensor(q, w)$MxM )  (14) Type: Boolean fricas test( tensor(p, q + w)$MxM = tensor(p, q)$MxM + tensor(p, w)$MxM )
 (15)
Type: Boolean
fricas
test( tensor(p, 23*w)$MxM = 23*tensor(p, w)$MxM )
 (16)
Type: Boolean
fricas
test( tensor(23*p, w)$MxM = 23*tensor(p, w)$MxM )
 (17)
Type: Boolean

first example of a bialgebra --Bill Page, Wed, 13 May 2009 08:06:57 -0700 reply
SandBoxHopfAlgebra

TensorProduct? is now included with FriCAS. Thank you Franz!

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