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7.3.19 oppose

Syntax:
oppose ( ring_name, name )
Type:
poly, vector, ideal, module or matrix (the same type as the second argument)
Purpose:
for a given object in the given ring, creates its opposite object in the opposite ( opposite) ring (the last one is assumed to be the current ring).
Remark:
for any object $O, \; (O^{opp})^{opp} = O$.
 
LIB "ncalg.lib";
def R = makeUsl2();
setring R;
matrix m[3][4];
poly   p  = (h^2-1)*f*e;
vector v  = [1,e*h,0,p];
ideal  i  = h*e, f^2*e,h*f*e;
m         = e,f,h,1,0,h^2, p,0,0,1,e^2,e*f*h+1;
module mm = module(m);
def b     = opposite(R);
setring b; b;
==> // coefficients: QQ
==> // number of vars : 3
==> //        block   1 : ordering a
==> //                  : names    H F E
==> //                  : weights  1 1 1
==> //        block   2 : ordering ls
==> //                  : names    H F E
==> //        block   3 : ordering C
==> // noncommutative relations:
==> //    FH=HF-2F
==> //    EH=HE+2E
==> //    EF=FE-H
// we will oppose these objects: p,v,i,m,mm
poly P    = oppose(R,p);
vector V  = oppose(R,v);
ideal  I  = oppose(R,i);
matrix M  = oppose(R,m);
module MM = oppose(R,mm);
def c = opposite(b);
setring c;   // now let's check the correctness:
// print compact presentations of objects
print(oppose(b,P)-imap(R,p));
==> 0
print(oppose(b,V)-imap(R,v));
==> [0]
print(matrix(oppose(b,I))-imap(R,i));
==> 0,0,0
print(matrix(oppose(b,M))-imap(R,m));
==> 0,0,0,0,
==> 0,0,0,0,
==> 0,0,0,0 
print(matrix(oppose(b,MM))-imap(R,mm));
==> 0,0,0,0,
==> 0,0,0,0,
==> 0,0,0,0 
See envelope; opposite.