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  • Main Page/CoCoA
    <h3>What is CoCoA?</h3> ...sion:''' [http://cocoa.dima.unige.it/cocoa/download/RelNotes.shtml CoCoA-5.4.0] (11.04.2022)
    1 KB (162 words) - 10:27, 15 February 2023
  • Main Page/ApCoCoA-1
    ...ot of additional functionalities like extra packages and access from CoCoA-4 code to external libraries like [https://www.gnu.org/software/glpk/ GLPK], After the end of the developement of CoCoA-4, ApCoCoA-1 soon also stopped being developed.
    888 bytes (128 words) - 10:17, 15 February 2023
  • CoCoA:Main Page
    =What is CoCoA?= ...putations in '''Co'''mmutative '''A'''lgebra. [http://cocoa.dima.unige.it/ CoCoA] is being developed at the University of Genova (Italy).
    2 KB (224 words) - 15:05, 6 March 2023
  • CoCoA:PositiveGrading4
    <short_description>extend a positive grading (for CoCoA-4 CoCoA-4 does not allow zero entries in the first row of the weights matrix.
    1 KB (150 words) - 10:02, 24 October 2007
  • CoCoA:OpenLog
    <short_description>open a log of a CoCoA session</short_description> output from a CoCoA session on D. The <ttref>CloseLog</ttref> closes the
    1 KB (187 words) - 10:02, 24 October 2007
  • CoCoA:HowTo:Contribute a CoCoA 4 function that calls the CoCoAServer
    of creating a new CoCoA 4 function that makes use of the CoCoAServer. There is a CoCoA 4 part and a CoCoAServer part.
    2 KB (318 words) - 09:42, 29 October 2020
  • ApCoCoA-1:CharP.LAAlgorithm
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    3 KB (402 words) - 09:56, 7 October 2020
  • CoCoA:CoCoA4Language Issues
    =Problems with ambiguity in the language in CoCoA 4.X= ...a function F and also a variable F that contains a polynomial. What should CoCoA do when encountering the two constructs from above?
    2 KB (283 words) - 15:20, 16 October 2007
  • CoCoA:CoCoA4.6.90 ReleasePlan
    ...intented as a test for many of the new features that will ship with CoCoA 4.7. ...nature of the new contributors. We hope that this wiki page as well as the CoCoA forum in general will lead to a better release experience.
    2 KB (331 words) - 16:01, 14 October 2007
  • ApCoCoA-1:CharP.BBasisMutantStrategyF2
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    2 KB (309 words) - 09:53, 7 October 2020
  • CoCoASchool2007
    [[:Image:KR_tutorial_4.pdf|Tutorial 4: The BMM-Algorithm: Not a BMW!]] [[:Image:Reduce.coc|CoCoA function for reducing a set of polynomials]] so that they are K-linearly in
    1 KB (186 words) - 13:22, 22 June 2007
  • ApCoCoA-1:CharP.MBBasisF2
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    4 KB (536 words) - 09:56, 7 October 2020
  • ApCoCoA-1:BB.GenMultMat
    ...nomial. The output is a matrix of size <ref>CoCoA:Len|Len</ref>(OO) x <ref>CoCoA:Len|Len</ref>(OO) over the ring <tt>BBS=K[c_{ij}]</tt>. [0, BBS :: c[4,6], BBS :: c[4,5], BBS :: c[4,3]]
    1 KB (194 words) - 09:40, 7 October 2020
  • ApCoCoA-1:CharP.IMBBasisF2
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    4 KB (655 words) - 09:55, 7 October 2020
  • History
    ...mall projects due to A. Giovini and G. Niesi ([https://cocoa.dima.unige.it/cocoa/system/history.html reference]). In late 1987, the prototype of a small sys ==CoCoA (1988-1992)==
    7 KB (987 words) - 10:16, 5 May 2024
  • ApCoCoALib:RingF4
    These files contain an implementation of the field with 4 elements. CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF4();
    3 KB (467 words) - 17:09, 6 March 2008
  • ApCoCoA-1:BB.TransformBBIntoGB
    4*x+5*y+6, 2*x^2*z+4*y^2*z+4*y*z^2+3*x*y+25*y^2+7*x*z+2*y-3*z,
    2 KB (331 words) - 09:43, 7 October 2020
  • ApCoCoA-1:CharP.XLSolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    5 KB (694 words) - 09:57, 7 October 2020
  • CoCoA:In
    In the first form, E is an arbitrary CoCoA expression and B is a [[4, -8], [1, -1], [1, 1], [4, 8]]
    1 KB (228 words) - 10:02, 24 October 2007
  • CoCoA:MDeg
    NB: In CoCoA-5 will me managed differently to allow more flexibility. Use R ::= Q[x,y], Weights(Mat([[1,2],[3,4],[5,6]]));
    925 bytes (110 words) - 10:02, 24 October 2007
  • CoCoA:GBasis5, and more
    function in CoCoA-4, i.e. should give the same output! L := [Randomized(DensePoly(4)) | I In 1..2];
    4 KB (504 words) - 10:02, 24 October 2007
  • ApCoCoA-1:CharP.MXLSolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    6 KB (899 words) - 09:56, 7 October 2020
  • ApCoCoA-1:Examples Tutorial De Equation
    Mit CoCoA ist es ein leichtes, Gleichungssysteme zu lösen, wir müssen sie nur ein w In CoCoA geben wir das Ideal mit dem <tt>Ideal(...);</tt>-Befehl ein, also
    2 KB (241 words) - 19:59, 17 July 2008
  • ApCoCoA-1:CharP.NLASolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    7 KB (905 words) - 09:57, 7 October 2020
  • ApCoCoA-1:CharP.MNLASolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    8 KB (1,077 words) - 09:56, 7 October 2020
  • ApCoCoA-1:CharP.IMXLSolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    8 KB (1,094 words) - 09:56, 7 October 2020
  • CoCoALib:Contribute
    ...py the header file "MyClass.H" into the subdirectory "CoCoALib-xxx/include/CoCoA". # Edit "CoCoALib-xxx/include/CoCoA/library.H":
    3 KB (423 words) - 09:16, 29 October 2020
  • ApCoCoA-1:BB.TransformGBIntoBB
    4*x+5*y+6, 2*x^2*z+4*y^2*z+4*y*z^2+3*x*y+25*y^2+7*x*z+2*y-3*z,
    3 KB (395 words) - 09:43, 7 October 2020
  • Interfaces
    You can download the old ApCoCoA based on CoCoA 4 and Eclipse [[ApCoCoA-1:Downloads|here]]. * On [[ApCoCoA-1:HowTo:Tips for developing (Ap)CoCoA with Eclipse|this page]] you can find information about building (Ap)CoCoAL
    2 KB (277 words) - 09:30, 29 October 2020
  • CoCoA:AffHilbertSeries
    be degree compatible (i.e. for a buggy behaviour of cocoa-4, AffPoincare(R/Ideal(z^4-1, xz^4-y-3));
    2 KB (221 words) - 10:02, 24 October 2007
  • ApCoCoA-1:Weyl.WRGBS
    ...- 3x[1]y[1]^7 - y[1]^8 + 6x[1]^2y[1]^5 - x[1]y[1]^6 + y[1]^7 + 3x[1]^2y[1]^4 - 6x[1]y[1]^5 + 2y[1]^6 + x[1]^2y[1]^3 - 6x[1]y[1]^4 + 4y[1]^5 + x[1]^2y[1]^2 + 2x[1]y[1]^3 + 2x[1]^2y[1] + 2x[1]y[1]^2 - 2y[1]^
    4 KB (571 words) - 10:39, 7 October 2020
  • ApCoCoA-1:CharP.IMNLASolve
    Use Z/(2)[x[1..4]]; x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
    8 KB (1,140 words) - 09:56, 7 October 2020
  • CoCoA:HowTo:Handle Matlab Matrices
    of floats into a presentation CoCoA is able to read. The Code to create a almost CoCoa-like list of lists from a Matrix M in Matlab is the following:
    2 KB (369 words) - 09:42, 29 October 2020
  • ApCoCoALib:RingF16
    The fields representation is ((Z/(2))[x])/(x^4 + x^3 +1). CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF16();
    3 KB (548 words) - 17:14, 6 March 2008
  • CoCoA:CoCoA 4
    CoCoA 4 was first published in July 2000. ===CoCoA 4===
    7 KB (946 words) - 09:20, 16 October 2007
  • CoCoA:KnownIssues
    ...on to this rule. Here are some pointers to the currently known issues with CoCoA. == Open Bugs in CoCoA 4.3==
    5 KB (799 words) - 09:18, 16 October 2007
  • CoCoA:Rand
    NB: every time you restart CoCoA the sequence of random numbers will Rand(-10^4,0);
    1,011 bytes (123 words) - 13:31, 26 April 2008
  • CoCoA:OpenSocket
    CoCoA-4 communicates with the CoCoAServer via socket which, by
    1 KB (150 words) - 10:02, 24 October 2007
  • ApCoCoALib:RingF32
    <-> 0*x^4 + 1*x^3 + 0*x^2 + 1*x^1 + 1*x^0 = x^3 + x + 1 CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF32();
    3 KB (549 words) - 17:17, 6 March 2008
  • ApCoCoALib:RingF64
    <->0*x^5 + 0*x^4 + 1*x^3 + 0*x^2 + 1*x^1 + 1*x^0 = x^3 + x + 1 CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF64();
    3 KB (557 words) - 17:19, 6 March 2008
  • CoCoA:Print
    1 4 9 16 25 36 49 64 81 100 where the E_i are CoCoA expressions.
    1 KB (150 words) - 10:02, 24 October 2007
  • ApCoCoA-1:Examples Tutorial De List
    ...geht sollte man mit Listen arbeiten, da aufgrund der inneren Struktur von CoCoA auf diese und in ihnen ein sehr schneller Zugriff möglich ist. <tt>L:=[0,1,2,3,4,5,6,7,8,9]</tt>. Die Liste trägt nun den Namen <tt>L</tt> und enthält 10
    6 KB (954 words) - 19:08, 17 July 2008
  • CoCoA:NewId
    rings. (CoCoA does not check for the unlikely event that variables of Var(NewId()) := 4;
    2 KB (210 words) - 10:02, 24 October 2007
  • CoCoA:PrintLn
    1 4 9 16 25 36 49 64 81 100 where the E_i are CoCoA expressions.
    984 bytes (124 words) - 10:02, 24 October 2007
  • ApCoCoALib:RingF256
    The fields representation is ((Z/(2))[x])/(x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1). <-> 0*x^7+ 0*x^6 + 0*x^5 + 0*x^4 + 1*x^3 + 0*x^2 + 1*x^1 + 1*x^0
    3 KB (536 words) - 17:26, 6 March 2008
  • CoCoA:GBasis
    I := Ideal(t^3-x,t^4-y); Record[Type = IDEAL, Value = Record[Gens = [t^3 - x, t^4 - y]]]
    2 KB (302 words) - 10:02, 24 October 2007
  • CoCoA:HowTo:Read Matrices
    ...ng how to import [[CoCoA:HowTo:Handle_Matlab_Matrices|matlab matrices into cocoa]]. At the [http://cocoa.mathematik.uni-dortmund.de/forum/ CoCoA Discussion Board] enrico asked how to read
    4 KB (673 words) - 09:43, 29 October 2020
  • ApCoCoA-1:Fundamentals Tutorial De Types
    CoCoA stellt verschiedene Objekttypen zur Verfügung, aber eh wir uns diese genau ...ekte, welche klein geschrieben werden sind Variablen, d.h. aber auch, dass CoCoA zum Beispiel <tt>quit;</tt> als das Produkt <math>q\cdot u\cdot i\cdot t</m
    7 KB (1,129 words) - 19:07, 17 July 2008
  • CoCoA:HilbertSeriesMultiDeg
    CoCoA-4 has an intrinsic limitation on multigradings (<ttref>Weights Modifier</ttre
    1 KB (163 words) - 10:02, 24 October 2007
  • CoCoA:GBasisTimeout
    I := Ideal(t^3-x,t^4-y,t^5-z); <see>Introduction to Groebner Bases in CoCoA</see>
    1 KB (162 words) - 10:02, 24 October 2007
  • Calendar:2009
    | bgcolor="#CCCCFF" | 4 | bgcolor="#FFFFFF" | 4
    11 KB (1,248 words) - 16:18, 28 April 2009
  • CoCoA:CoCoA5Client Overview
    ...ael. It is a collection of thoughts about where we want to go with the new CoCoA 5 client. * We have 2 modes: CoCoA 4 and CoCoA 5
    10 KB (1,564 words) - 17:45, 20 October 2007
  • ApCoCoALib:RingF4096
    The fields representation is ((Z/(2))[x])/(x^12 +x^4 + x^2 +x + 1). CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF4096();
    3 KB (530 words) - 17:35, 6 March 2008
  • ApCoCoALib:RingF128
    <-> 0*x^6 + 0*x^5 + 0*x^4 + 1*x^3 + 0*x^2 + 1*x^1 + 1*x^0 CoCoA::ring R = ApCoCoA::AlgebraicCore::NewRingF128();
    3 KB (525 words) - 17:24, 6 March 2008
  • ApCoCoA-1:CharP.GBasisF16
    This command computes a Groebner basis in the field <tt>F_16 = (Z/(2))[x]/(x^4 + x^3 +1)</tt>. ...:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see>
    3 KB (386 words) - 09:54, 7 October 2020
  • ApCoCoA-1:CharP.GBasisF256
    ...ebner basis in the field <tt>F_256 = (Z/(2))[x]/(x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1)</tt>. ...:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see>
    3 KB (391 words) - 09:54, 7 October 2020
  • CoCoA:HilbertPoly
    the standard CoCoA ring Qt (= Q[t]). H(1) = 4
    1 KB (174 words) - 10:02, 24 October 2007
  • CoCoA:Define
    Sum(1,2,3,4,5); 4. SHORTCUT. The form <tt>F(X_1,...,X_n) := E</tt> is discouraged and may be
    4 KB (605 words) - 10:02, 24 October 2007
  • ApCoCoA-1:LinAlg.Det
    ...erver using LinBox functions. Please note that in contrary to the built in CoCoA <tt>Det</tt> function the entries of <tt>M</tt> are only allowed to be of t LinAlg.Det(Mat([[1,2],[1,4]]));
    2 KB (235 words) - 10:10, 7 October 2020
  • CoCoA:Ext
    VERY IMPORTANT: CoCoA cannot accept the ring R as one of the inputs, Ext(0..4, R/I, R/Ideal(0)); -- another way to define the ring R as a quotient
    4 KB (615 words) - 10:02, 24 October 2007
  • CoCoA:FGLM5
    term ordering. If the parameter M is not specified, CoCoA will assume M = GBOld := [z^4 -3z^3 - 4yz + 2z^2 - y + 2z - 2, yz^2 + 2yz - 2z^2 + 1, y^2 - 2yz + z^2 - z
    1 KB (218 words) - 16:09, 5 November 2008
  • CoCoA:Res
    0 --&gt; R(-4) --&gt; R(-2)(+)R^2(-3) --&gt; R^2(-1)(+)R(-2) --&gt; R <see>Introduction to Groebner Bases in CoCoA</see>
    1 KB (220 words) - 10:02, 24 October 2007
  • ApCoCoALib:Install
    (we use extensively g++ (versions 3.4.n and 4.0.n)) * an installation of GMP (version 4.1.4 or later) -- see http://www.swox.com/gmp/
    3 KB (448 words) - 16:15, 13 December 2007
  • CoCoA:ReducedGBasis
    I := Ideal(t^3-x,t^4-y,t^5-z); <see>Introduction to Groebner Bases in CoCoA</see>
    1 KB (231 words) - 10:02, 24 October 2007
  • HowTo:Term Orderings
    This page is an introduction into term orderings in CoCoA-5 or ApCoCoA-2. In order to understand this topic, we assume that the reade == Term Orderings in CoCoA ==
    8 KB (1,311 words) - 11:26, 14 February 2021
  • CoCoA:Syz
    0 --&gt; R^2(-6) --&gt; R(-4)(+)R^3(-5) --&gt; R^2(-2)(+)R(-3) <see>Introduction to Groebner Bases in CoCoA</see>
    2 KB (258 words) - 10:02, 24 October 2007
  • CoCoA:HowTo:Plot order ideals
    At the [http://cocoa.dima.unige.it/conference/schooliv/ CoCoA Summer School 2005] there was a discussion about the possibility to plot or These tools use [[CoCoA:CoCoA_4|CoCoa 4]] and either [http://povray.com POV-Ray] or Latex.
    15 KB (1,931 words) - 09:42, 29 October 2020
  • ApCoCoA-1:LinBox.Det
    ...erver using LinBox functions. Please note that in contrary to the built in CoCoA <tt>Det</tt> function the entries of <tt>M</tt> are only allowed to be of t LinBox.Det(Mat([[1,2],[1,4]]));
    2 KB (282 words) - 10:11, 7 October 2020
  • ApCoCoA-1:Examples Tutorial De Logic
    4) Projekt <math>C</math> kann nur fertiggestellt werden, wenn Projekt <math> == Lösung mit CoCoA ==
    6 KB (964 words) - 10:11, 18 July 2008
  • CoCoA:Clear
    memory for these rings. For more information on memory in CoCoA, see Z := 4; -- Z is added to the working memory
    2 KB (321 words) - 10:02, 24 October 2007
  • ApCoCoA-1:Representation of finite fields
    So we have a field with 2^2 = 4 elements, namely one representation of F_4. The elements of the field are 0 ...e used to represent F_4[y_1, y_2, y_3]. Therefore, we map Z[y[1..3]] to Z/(4)[y[1..3]] and interpret each integer via the above described map. So the po
    3 KB (438 words) - 10:31, 7 October 2020
  • CoCoA:Toric
    describes three different algorithms; the one implemented in CoCoA is Toric([[1,3,2],[3,4,8]]);
    3 KB (487 words) - 10:02, 24 October 2007
  • CoCoA:Image
    4. The second form of the function does not require the prefix <tt>R::</tt> Module([-ab + c^2 + a, a^3b^2 - 2a^2bc^2 + ac^4], [a, -ab + c^2])
    3 KB (578 words) - 10:02, 24 October 2007
  • CoCoALib:CoCoALib and Cygwin FAQ
    ...tes to C:\cygwin\home\Administrator. Change to /home/Administrator/gmp-4.1.4. Now we have to configure gmp by typing Administrator@sprocket ~/gmp-4.1.4
    8 KB (1,272 words) - 09:21, 16 October 2007
  • Package sagbi
    Analogously to the CoCoA-5 function <code>interreduced</code>, the SAGBI package contains the functi ...*y^2*z^4 +15*x^4*y^4*z^4 -20*x^6*z^6 -10*x^4*y^2*z^6 +20*x^3*y^3*z^6 +20*x^4*z^8 +20*x^2*y^2*z^8 -10*x^2*z^10 +6*x*y*z^10 -y^2*z^10 +3*z^12;
    12 KB (2,168 words) - 20:21, 8 November 2020
  • CoCoA:GroebnerFramework5
    * print special: prints only polynomials which maxDeg<4 or Len<19: The input file has the same format as the communication between CoCoA 4.6 and the CoCoAServer. To create input you need to run the following sequen
    3 KB (445 words) - 17:46, 20 October 2007
  • HowTo:Contribute an ApCoCoA-2 Package
    PrintLn " Version : CoCoA 5.3.2"; -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
    8 KB (1,176 words) - 15:56, 9 February 2021
  • COPYING
    The files in this directory comprise the documentation for the CoCoA Library. All the documentation for the CoCoA Library is made available under the
    20 KB (3,296 words) - 06:31, 20 July 2005
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