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5.1.52 interred
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Syntax: interred (ideal_expression)interred (module_expression)-
Type: the same as the input type
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Purpose: interreduces a set of polynomials/vectors.
input:
output:
with 
and the properties
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for all 
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in the case of a global ordering (polynomial ring):
does not divide m for all monomials m of
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in the case of a local or mixed ordering (localization of polynomial ring):
if
for any ,
then
Here,
denotes the leading term of 
and
.
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Example: ring r=0,(x,y,z),dp; ideal i=x2+z,z,2z; interred(i); → _[1]=z → _[2]=x2 ring R=0,(x,y,z),ds; ideal i=zx+y3,z+y3,z+xy; interred(i); → _[1]=z+xy → _[2]=xy-y3 → _[3]=x2y-y3