
7.7.2.0. linReduce
Procedure from library bfun.lib (see bfun_lib).
 Usage:
 linReduce(f, I [,s,t,u]); f a poly, I an ideal, s,t,u optional ints
 Return:
 poly or list, linear reductum (over field) of f by elements from I
 Purpose:
 reduce a polynomial only by linear reductions (no monomial multiplications)
 Note:
 If s<>0, a list consisting of the reduced polynomial and the coefficient
vector of the used reductions is returned, otherwise (and by default)
only reduced polynomial is returned.
If t<>0 (and by default) all monomials are reduced (if possible),
otherwise, only leading monomials are reduced.
If u<>0 (and by default), the ideal is linearly prereduced, i.e.
instead of the given ideal, the output of linReduceIdeal is used.
If u is set to 0 and the given ideal does not equal the output of
linReduceIdeal , the result might not be as expected.
 Display:
 If
printlevel =1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
 LIB "bfun.lib";
ring r = 0,(x,y),dp;
ideal I = 1,y,xy;
poly f = 5xy+7y+3;
poly g = 7x+5y+3;
linReduce(g,I); // reduces tails
==> 7x
linReduce(g,I,0,0); // no reductions of tails
==> 7x+5y+3
linReduce(f,I,1); // reduces tails and shows reductions used
==> [1]:
==> 0
==> [2]:
==> 5*gen(3)7*gen(2)3*gen(1)
f = x3+y2+x2+y+x;
I = x3y3, y3x2,x3y2,x2y,y2x;
list l = linReduce(f,I,1);
l;
==> [1]:
==> 5y
==> [2]:
==> gen(5)4*gen(4)+2*gen(3)3*gen(2)3*gen(1)
module M = I;
f  (l[1](M*l[2])[1,1]);
==> 0

