Singular

Did I screw up my last post ?

I thought that in my last post I also wrote that the computation in polynomial rings over integers
(std(), reduce(), intersect() and others ) in Singular is broken (for years and probably did never work):
[b] for some (not for all ) input the user may and will get incorrect results. [/b]

However, there is ongoing work to fix this issue.


[quote="bughunter"][quote="Bavithra"]NFMora function works only for the fields. We are working on integer rings. Is there any function to reduce in integer rings ?[/quote]
To my knowledge there is no educational implementation over integer rings in Singular.

I'm aware of the following educational alternative:
sagemath.org/doc/reference/polynomial_rings/sage/rings/polynomial/toy_buchberger.html
However, there is no guarantee that this implementation is not buggy, too ( I didn't check )[/quote]

[quote="Bavithra"]NFMora function works only for the fields. We are working on integer rings. Is there any function to reduce in integer rings ?[/quote]
To my knowledge there is no educational implementation over integer rings in Singular.

I'm aware of the following educational alternative:
sagemath.org/doc/reference/polynomial_rings/sage/rings/polynomial/toy_buchberger.html
However, there is no guarantee that this implementation is not buggy, too ( I didn't check )

NFMora function works only for the fields. We are working on integer rings. Is there any function to reduce in integer rings ?

Have a look at NFMora in teachstd.lib and set printlevel to 1 (or higher):
[code]
>LIB "teachstd.lib";
> printlevel=1;
> ring r=0,(x,y,z),dp;
> poly f = x2y2z2+x5+yx3+z6-3y3;
> ideal G = x2y+x2,y3+xyz,xyz2+z6;
> NFMora(f,G);"";

// Input for NFMora is (f,T):
// f:
x2y2z2+z6+x5+x3y-3y3
// T:
T[1]=x2y+x2
T[2]=y3+xyz
T[3]=z6+xyz2
// Reduce f with T, eventually enlarging T for local ordering

// Reduction-step in NFMora: 0
// h = (f after 0 reductions) reduction with g from T:
// g = element of minimal ecart in T s.t. LM(g)|LM(h):
// h:
x2y2z2+z6+x5+x3y-3y3
// g:
x2y+x2
// T-set enlarged for next reduction? (yes/no = 1/0): 0

// Reduction-step in NFMora: 1
// h = (f after 1 reductions) reduction with g from T:
// g = element of minimal ecart in T s.t. LM(g)|LM(h):
// h:
z6+x5-x2yz2+x3y-3y3
// g:
z6+xyz2
// T-set enlarged for next reduction? (yes/no = 1/0): 0

// normal form is:
x5-x2yz2+x3y-xyz2-3y3

[/code]

Is there any option to print each step of "reduce" function.?