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2.5.1 qring declaration
- Syntax:
qring name = ideal_expression ;
- Default:
- none
- Purpose:
- declares a quotient ring as the basering modulo ideal_expression. Sets
it as current basering.
- Example:
| ring r=0,(x,y,z,u,v,w),dp;
ncalgebra(-1,0);
// anticommutative algebra
option(redSB);
option(redTail);
ideal i=x^2,y^2,z^2,u^2,v^2,w^2;
qring q=twostd(i);
// now it is an exterior algebra
q;
==> // characteristic : 0
==> // number of vars : 6
==> // block 1 : ordering dp
==> // : names x y z u v w
==> // block 2 : ordering C
==> // noncommutative relations:
==> // yx=-xy
==> // zx=-xz
==> // ux=-xu
==> // vx=-xv
==> // wx=-xw
==> // zy=-yz
==> // uy=-yu
==> // vy=-yv
==> // wy=-yw
==> // uz=-zu
==> // vz=-zv
==> // wz=-zw
==> // vu=-uv
==> // wu=-uw
==> // wv=-vw
==> // quotient ring from ideal
==> _[1]=w2
==> _[2]=v2
==> _[3]=u2
==> _[4]=z2
==> _[5]=y2
==> _[6]=x2
poly k=(x+y)*(y-u)*(zv+u-w);
k;
==> xyzv+y2zv+xzuv+yzuv+xyu+y2u-xu2-yu2-xyw-y2w+xuw+yuw
poly ek=reduce(k,std(0));
ek;
==> xyzv+xzuv+yzuv+xyu-xyw+xuw+yuw
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