#13268: Proposal of a DifferentialAlgebra package, relying on the C BLAD
libraries
-------------------------------------+-------------------------------------
Reporter: boulier | Owner: boulier
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: packages: | Resolution:
optional | Merged in:
Keywords: package, | Reviewers: Charles Bouillaguet,
differential algebra, elimination | Karl-Dieter Crisman
theory | Work issues:
Authors: Nicolas M. | Commit:
Thiéry, François Boulier, Charles | Stopgaps:
Bouillaguet |
Report Upstream: N/A |
Branch: |
Dependencies: |
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Comment (by vbraun):
OK, fair enough. I'm happy with thinking of it as a tool to simplify
differential equations. But then you shouldn't introduce global names like
!DifferentialRing that are likely to be used at one point for the more
abstract ring of differential operators.
In that spirit, it would be nice if the code were organized in the way you
describe it verbally. The starting point should be an object that
encapsulates the differential system, e.g.
{{{
sage: syst = DifferentialAlgebraicSystem(vars=[t], functions=[f,g],
parameters=[phi])
}}}
And then everything is a method of that object. There you need to decide
whether you want !DifferentialAlgebraicSystem to be mutable or immutable;
In the immutable case the user interface would be
{{{
sage: sys_extd = syst.extend_base_field(phi)
sage: sys_reln = sys_extd.add_relation(f(0) == 0)
sage: sys_reln
Differential algebraic system ... over base field RR(phi) with relation
f(0) == 0
sage: ideal = sys_reln.Rosenfeld_Groebner()
}}}
and if it is mutable you'd have
{{{
sage: syst.extend_base_field(phi)
sage: syst.add_relation(f(0) == 0)
sage: syst
Differential algebraic system ... over base field RR(phi) with relation
f(0) == 0
}}}
Mutable is slightly simpler but also means that you can't cache
intermediate results.
In general, your objects should print something more informative than
`regular_differential_chain`. It doesn't necessarily have to print all
equations, but enough to see if its trivial or not would be nice.
--
Ticket URL: <http://trac.sagemath.org/ticket/13268#comment:18>
Sage <http://www.sagemath.org>
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