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From ApCoCoAWiki
- 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
- 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
- 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, also2 KB (241 words) - 19:59, 17 July 2008
- 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
- 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
- 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
- ...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
- 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
- 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)CoCoAL2 KB (277 words) - 09:30, 29 October 2020
- 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
- ...- 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
- 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
- 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
- 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 4 was first published in July 2000. ===CoCoA 4===7 KB (946 words) - 09:20, 16 October 2007
- ...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
- 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-4 communicates with the CoCoAServer via socket which, by1 KB (150 words) - 10:02, 24 October 2007
- <-> 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
- <->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
- 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
- ...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 106 KB (954 words) - 19:08, 17 July 2008
- rings. (CoCoA does not check for the unlikely event that variables of Var(NewId()) := 4;2 KB (210 words) - 10:02, 24 October 2007
- 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
- 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^03 KB (536 words) - 17:26, 6 March 2008
- 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
- ...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 read4 KB (673 words) - 09:43, 29 October 2020
- 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</m7 KB (1,129 words) - 19:07, 17 July 2008
- CoCoA-4 has an intrinsic limitation on multigradings (<ttref>Weights Modifier</ttre1 KB (163 words) - 10:02, 24 October 2007
- 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
- | bgcolor="#CCCCFF" | 4 | bgcolor="#FFFFFF" | 411 KB (1,248 words) - 16:18, 28 April 2009
- ...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 510 KB (1,564 words) - 17:45, 20 October 2007
- 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
- <-> 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
- 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
- ...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
- the standard CoCoA ring Qt (= Q[t]). H(1) = 41 KB (174 words) - 10:02, 24 October 2007
- Sum(1,2,3,4,5); 4. SHORTCUT. The form <tt>F(X_1,...,X_n) := E</tt> is discouraged and may be4 KB (605 words) - 10:02, 24 October 2007
- ...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
- 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 quotient4 KB (615 words) - 10:02, 24 October 2007
- 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 - z1 KB (218 words) - 16:09, 5 November 2008
- 0 --> R(-4) --> R(-2)(+)R^2(-3) --> R^2(-1)(+)R(-2) --> R <see>Introduction to Groebner Bases in CoCoA</see>1 KB (220 words) - 10:02, 24 October 2007
- (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
- 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
- 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
- 0 --> R^2(-6) --> R(-4)(+)R^3(-5) --> R^2(-2)(+)R(-3) <see>Introduction to Groebner Bases in CoCoA</see>2 KB (258 words) - 10:02, 24 October 2007
- 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
- ...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
- 4) Projekt <math>C</math> kann nur fertiggestellt werden, wenn Projekt <math> == Lösung mit CoCoA ==6 KB (964 words) - 10:11, 18 July 2008
- memory for these rings. For more information on memory in CoCoA, see Z := 4; -- Z is added to the working memory2 KB (321 words) - 10:02, 24 October 2007
- 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 po3 KB (438 words) - 10:31, 7 October 2020
- 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
- 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
- ...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-4.1.48 KB (1,272 words) - 09:21, 16 October 2007
- 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
- * 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 sequen3 KB (445 words) - 17:46, 20 October 2007
- PrintLn " Version : CoCoA 5.3.2"; -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^48 KB (1,176 words) - 15:56, 9 February 2021
- The files in this directory comprise the documentation for the CoCoA Library. All the documentation for the CoCoA Library is made available under the20 KB (3,296 words) - 06:31, 20 July 2005
