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PURRS
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PURRS: The Parma University's Recurrence Relation Solver
Welcome
to the home page of the Parma University's Recurrence Relation Solver,
Parma Recurrence Relation Solver for short, PURRS for a very short.
PURRS is a C++ library for the (possibly approximate)
solution of
recurrence
relations.
To be more precise, the PURRS already solves or approximates:
In the future, it will also solve
systems of linear recurrence relations with constant coefficients.
More details are available on the capabilities
of the system.
News
| Oct 28, 2004 |
Andrea made it, at last!
Andrea Pescetti got a Laurea degree in Mathematics with full marks
and honors with a dissertation on his implementation of the
Zeilberger algorithm
(advisers
Roberto Bagnara and
Alessandro Zaccagnini).
The thesis defense was really good (which is kind of strange,
since the rehearsal one hour before the real show was deadly boring ;-)
Congratulations, Dottor Pescetti!
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| Aug 18, 2003 |
New paper available
The Automatic
Solution of Recurrence Relations. I. Linear Recurrences of Finite Order
with Constant Coefficients: this is the first in a series
devoted to the presentation of all the mathematics behind
the PURRS project.
This paper describes algorithmic techniques for the efficient
solution of a wide class of linear recurrences of finite order
with constant coefficients.
The presentation is thorough and reasonably
self-contained, covering topics such as the automatic solution of
polynomial equations and efficient, exact symbolic summation of
some special functions.
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For older news items, see the complete news archive.
Try PURRS online!
Here you can try a prototype of the solver. It showcases just the
basic functionalities of PURRS (namely, you cannot solve
multivariate recurrences
through this web interface), but it may be instructive to play with it.
Recurrence relation
The expressions you can enter as the right hand side of the recurrence
may contain the special symbol n (the index of the
recurrence), and the special functional symbol x().
The argument of the functional symbol may be a non negative integer,
an expression of the form n-k where k is a (possibly negative)
integer, or of the form n/k, where k > 1
is an integer.
The expression may also include operators +, -,
*, /, ^ (exponentiation), parentheses,
the functions log, exp and
factorial(n);
the latter may also be written n!.
Any single lower-case letter different from e, n and x
(e.g., a, b, c, z) will be considered as a
parameter. Parameters are allowed to occur in the
non homogeneous part of the recurrence.
All numeric constants must be integers.
A more detailed and precise description of
what you can type and expect
is available.
Beware:
log(n) denotes the natural logarithm of n;
if a base 2 logarithm is what you want, then you can write
log(n)/log(2).
Examples of valid expressions are:
2*x(n-1)+a,
2*x(n-1)-x(n-2),
n*x(n-1)+n,
3*x(n/2)+n*log(n),
3*x(n-1)^2,
and
2*sum(k,0,n-1,x(k))+2*n.
Initial conditions
If you want you can specify initial conditions for the recurrence.
The single initial condition must be of the form
x(i)=k, for i a positive integer and k a
number (not a floating point) or a symbolic expression containing the
parameters a, b,..., z different from n,
x and e. If the initial conditions are more than one,
they must be separated by a semicolon.
Please note: this a very experimental feature and
may give unexpected results.
Examples of valid expressions are:
x(0)=3
x(0)=a; x(1)=b
You can test some individual components of PURRS
in the demos page.
[Page last updated on December 03, 2012, 08:27:55.]
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