
SARAG 1.3

Feb 2017 (Merge with fork developed at the Univ. of Rennes 1 + fixes and minor extra features by Fabrizio Caruso)

1. Merge of a separate branch of the SARAG packaged developed at the Univ. of Rennes 1: 
- Univariate certificate is now computed as in Maxima with its usual output format.
- All other files use the updated code developed at the Univ. of Rennes1.

2. Fix multivariate certificate of positivity.
Multivariate certificate is now working and enabled.
No warnings about deprecated gnuplot attributes are any longer displayed by "drawMultiCerticificate".
Moreover a bug on a global variable was fixed in "standard_mid".
Unit-tests have been added into arag_test.mac and 1 computationally heavy test has been added
into hard_test.mac.

3. DRAW_TOPOLOGY (false by default) when set to true, will trigger the display of the topology diagram. 
Remark: When DRAW_TOPOLOGY set to true and you compute a topology, you will need first to close the pop-up windonw to get the result.

4. In order to further simply its use "drawTopology" works with the second output of "topology" as well as the full output of topology

5. New "revRowsCount" function (sign change after i-th row switch) from Maxima version.

6. Verbosity parameters have been removed in almost of functions.

7. Fix of many local variables that were not declared as such.

8. Removed unused files (examples.mac, topology_examples.mac, whichversion.txti, etc.)

9. Fix of multiple misspellings.

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SARAG 1.2

22 may 2016

Merge with external code developed at the Univ. of Rennes 1
by Matthieu Kohli new file quickSignDetermination.mac

slight modification of discriminant 

sylvesterResultant in the case of two polynomials of equal degree fixed
 
coefficients in certificates of positivity changed

newtonFromPoly(pol,var,len) now takes three arguments:
and  computes a sequence of Newton sums of length "len"

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SARAG 1.1

August 3rd 2009


by Fabrizio Caruso (caruso@dm.unipi.it)
with a contribution by Richard Leroy
(multivariate certificate of positivity)

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SARAG 1.1

(1) small fix in the univariate certificate

(2) integration of Richard Leroy's code 
for the multivariate certificate of positivity
("multiCertificateOfPositivity.mac").


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SARAG 1.0.1

(1) certificate of positivity: 
- "certificateOfPositivity.mac"
This files contains routines for the certificate of
positivity, which can be used to produce formal
proof of positivity/negativity or existence of roots
for univariate polynomials. Try for example
"certificateProof((2*x-1)^2+x^4,x,[-1,1]);"
for a proof of positivity in [-1,1]. 

(2) updated "readme.txt" and "arag_test.mac". 

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SARAG 1.0

(Some bug fixes)

(1) gcdFreePart should be now correct

(2) sRem and sSubRes compute sequences that
are now longer by one element


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SARAG beta 0.3

(1) bug fixes
- drawTopology: 
it now computes
the correct topology of points
at infinity

(2) new functions
- echelonMod : 
it computes
the Echelon form of a matrix

(3) test files:
- "arag_test.mac"
It tests the examples contained
in the book "Algorithms in Real
Algebraic Geometry" (which contains
SARAG and uses Maxima in its electronic version)
- "hard_test.mac"
It tests some other commands involve
more computation  (mostly topology computations)

(4) updated "readme.txt"




