====================================================================
StochasticDifferential examples
====================================================================
A basic implementation of StochasticDifferential(R) using the
associated domain BasicStochasticDifferential in the underlying 
representation as sparse multivariate polynomials. The domain is 
a module over Expression(R), and is a ring without identity 
(AXIOM term is "Rng"). Note that separate instances, for example 
using R=Integer and R=Float, have different hidden structure 
(multiplication and drift tables).

dt := introduce!(t,dt)
   dt

dX := introduce!(X,dX)
   dX

dY := introduce!(Y,dY)
   dY

copyBSD()
   [dX,dY,dt]

copyIto()
   table(t= dt,Y= dY,X= dX)

copyQuadVar()             -- display of multiplication table
   table()

statusIto()
   +B S D   :  dX  dY  dt+
   |                     |
   |drift   :  ?   ?   ? |
   |                     |
   |  *                  |
   |                     |
   |  dX    :  ?   ?   ? |
   |                     |
   |  dY    :  ?   ?   ? |
   |                     |
   +  dt    :  ?   ?   ? +

copyDrift()       -- display of drift list
   table()

nbsd := #copyBSD()
   3

ItoMultArray:ARRAY2(SD INT) :=new(nbsd,nbsd,0$SD(INT))
   +0  0  0+
   |       |
   |0  0  0|
   |       |
   +0  0  0+

ItoMultArray
   +0  0  0+
   |       |
   |0  0  0|
   |       |
   +0  0  0+

statusIto()
   +B S D   :  dX  dY  dt+
   |                     |
   |drift   :  ?   ?   ? |
   |                     |
   |  *                  |
   |                     |
   |  dX    :  ?   ?   ? |
   |                     |
   |  dY    :  ?   ?   ? |
   |                     |
   +  dt    :  ?   ?   ? +
 

See Also:
o )help BasicStochasticDifferential
o )show StochasticDifferential

