#16508: Add Commutative graded differential algebras.
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Reporter: mmarco | Owner:
Type: PLEASE | Status: new
CHANGE | Milestone: sage-6.3
Priority: major | Keywords: sd58, algebras,
Component: algebra | nonconmutative, graded
Merged in: | Authors: mmarco
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This patch adds basic CDGA's.
They work as follows, first you create the algebra:
{{{
sage: A = CDGAlgebra(QQ, 'x,y,t', degrees = (1, 1, 2))
sage: A
Commutative Graded Differential Algebra over Rational Field with
generators ('x', 'y', 't')
sage: A.inject_variables()
Defining x, y, t
}}}
Then define the differential:
{{{
sage: D = A.differential({x: x*y , y: x*y })
sage: D
Differential map in Commutative Graded Differential Algebra over Rational
Field with generators ('x', 'y', 't')
sending:
x --> x*y
y --> x*y
t --> 0
}}}
Now you can compute things like a basis of each homogeneous part:
{{{
sage: A.homogeneous_part(5)
[y*t^2, x*t^2]
}}}
Or the cohomology at each degree:
{{{
sage: A.cohomology(4, D)
Vector space quotient V/W of dimension 1 over Rational Field where
V: Vector space of degree 2 and dimension 2 over Rational Field
Basis matrix:
[1 0]
[0 1]
W: Vector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[0 1]
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16508>
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