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...W^n</tt>, we define word orderings LLEX, ELIM, LRLEX, and DEGREVLEX on <tt>W^n</tt> as follows. ...tt>len(W)=len(W')</tt> and <tt>W</tt> is lexicographically larger than <tt>W'</tt>.</item>

Use R ::= Q[x,y,z,w]; TensorMat(Mat([[1,-1],[2,-2],[3,-3]]),Mat([[x,y],[z,w]]));

<tt>w</tt> or <tt>W</tt> then it immediately erases the file S. D := OpenOFile(<quotes>my-test</quotes>,<quotes>w</quotes>); -- clear <quotes>my-test</quotes>

...ynomial in Weyl algebra <tt>A_n</tt> with respect to the weight vector <tt>W=(u_i,v_i)</tt>.</short_description> Weyl.Inw(P:POLY,W:LIST):POLY

Use R ::= Q[x,y,z,w]; Homogenized(w, x^3-y);

Use Q[x,y,z,w[3..5]], Weights([7, 4, 3, 1, 1, 1]); x - 7413431 w[4]^7 - 9162341 w[3]*w[4]*w[5]^5,

<short_description>Retrieves polynomials from <tt>W'</tt>.</short_description> This command retrieves all polynomials from <tt>W'</tt>.

BBSGen.NonStand(OO,BO,N,W); BBSGen.NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST

<short_description>Retrieves leading terms of polynomials of <tt>W'</tt>.</short_description> ...eves the leading terms of degree <tt>Degree</tt> of the polynomials of <tt>W'</tt>.

BBSGen.Poldeg(F,OO,BO,N,W); BBSGen.Poldeg(F:POLY,OO:LIST,BO:LIST,N:INT,W:MAT):VECTOR;

...t>, or if we have <tt>W1=W*x_{i}*W3, W2=W*x_{j}*W4</tt> for some words <tt>W,W3,W4</tt> in <tt>&lt;X&gt;</tt> and some letters <tt>x_{i},x_{j}</tt> in < ...len(W')</tt>, or <tt>len(W)=len(W')</tt> and <tt>W</tt> is larger than <tt>W'</tt> by the non-commutative right-to-left lexicographic ordering.</item>

...we define deg_{W}(c_ij)=log(b_j)-log(t_i)=(u_1,...,u_m)=u in Z^m, where W is the grading matrix. W:=BBSGen.Wmat(OO,BO,N);

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

Use R ::= Q[w,x,y,z]; I := Ideal(z^2-xy,xz^2+w^3);

BBSGen.NonStandPoly(OO,BO,W,N); BBSGen.NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST

BBSGen.NonTriv(OO,BO,W,N); BBSGen.NonTriv(OO:LIST,BO:LIST,W:MATRIX,N:INT):LIST;

...>I</tt> in Weyl algebra <tt>A_n</tt> with respect to the weight vector <tt>W=(u_i,v_i)</tt>.</short_description> Weyl.InIw(I:IDEAL,W:LIST):IDEAL

...where <tt>s</tt> commutes with all <tt>x_i</tt> and <tt>y_i</tt>'s and <tt>w</tt> is redundant indeterminate used just to create internal structure of t <item>@return An ideal in <tt>A_s=QQ[x1, ..., xn,y1, ...,yn, s,w]</tt>.</item>

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,"xy

Use R ::= Q[t,s,x,y,z,w]; Elim(t..x,Ideal(t-x^2zw,x^2-t,y^2t-w)); -- Note the use of t..x.

Use R ::= Q[w,x,y,z]; I := Ideal(z^2-xy,xz^2+w^3);

G := Product([W[1]^W[2] | W In It]); -- check solution

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

BBSGen.BBFinder(LF:LIST,OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST W:=BBSGen.Wmat(OO,BO,N);

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. Each word in <tt>&lt;X&gt;</tt> is represented as a STRING. For example, t Gb := NCo.GB(G); -- compute Groebner basis of &lt;G&gt; w.r.t. ELIM

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

Use Q[u]; -- note that <quotes>Use</quotes> can be used w/out a ring identifier

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

hello w

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

Eric W. Weisstein: Math World, Icosahedral Group

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy NCo.MRHF(X, Ordering, Relations, G, 5); --G is a Groeber basis (w.r.t. LLEX) of the two-sided ideal generated by G

W:=BBSGen.Wmat(OO,BO,N);

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

Coxeter, H. S. M. and Moser, W. O. J. (1980), Generators and Relations for Discrete Groups. New York: Spri

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

<item><em>W'</em> Set of polynomials with pairwise different leading terms; represents

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

...[C, W] where W is a word in <tt>&lt;X&gt;</tt> and C is the coefficient of W. For example, the polynomial <tt>f=xy-y+1</tt> is represented as F:=[[1,"xy

WA::=QQ[u,w,t,x,v[1..2],d,y],Elim(u);Use WA; GbI_elim:=Weyl.WGB(I,[1,2]); --eliminate u and w

...x}} w</math> if either '''''v = w''''' or the first non-zero entry of '''''w-v''''' is positive. Then '''''Ord(M)''''' is defined by

Tastenkombination: <tt>Strg + W</tt> (Windows/Linux) / <tt>Apfel + W</tt> (Mac)

* '''CTRL-W''': Close the current document

..."The Numerical Solution of Systems of Polynomials" by A. J. Sommese and C. W. Wampler. ...tt>, for an affine algebraic set <tt>Z</tt>. Find the decomposition of <tt>W</tt> into a numerical irreducible decomposition for <tt>Z</tt>.

...TATIONS OF FINITE SIMPLE GROUPS: A COMPUTATIONAL APPROACH R. M. GURALNICK, W. M. KANTOR, M. KASSABOV, AND A. LUBOTZKY

Gross, Jonathan L.; Tucker, Thomas W. (2001), "6.2.8 Triangle Groups", Topological graph theory, Courier Dover P

W. Magnus, Braid groups: A survey, Proceedings of the Second International C

W:=BBSGen.Wmat(OO,BO,N);

Use R ::= Q[x,y,z,w]; must be homogeneous (w.r.t. the first row of the weights matrix).

Use S ::= QQ[x,y,z,w]; Use S ::= QQ[x,y,z,w];

..."The Numerical Solution of Systems of Polynomials" by A. J. Sommese and C. W. Wampler.

F := OpenOFile("/Users/bigatti/Desktop/POV-Anna/monomials.inc", "w");