On Jan 1, 2008 1:31 PM, [EMAIL PROTECTED]
<[EMAIL PROTECTED]> wrote:
>
> After executing the following commands in Sage:
>
> QQi.<I>=QQ.extension([x^2+1]);
> R.<a,b,f0,f1,f2,f3,f4>=MPolynomialRing(QQi,order='lex')
> T1_Pxxx=3*a^2*b+(1-a)^2*(1-b)-f0
> T1_Pxxy=3*(1-a)^2*b+3*a^2*(1-b)+6*a^2*b-f2
> T1_Pxyz=6*(1-a)*a*b+6*a*(1-a)*b+6*a^2*(1-b)+6*a^2*b-f1
> T1_Pyxx=3*(1-a)*a*b+3*a*(1-a)*(1-b)+6*a^2*b-(1-f0-f1-f2)/2
> T1_Pxyx=T1_Pyxx
> T1_I= R.ideal(T1_Pxxx,T1_Pxyz,T1_Pxxy,T1_Pyxx)
> T1_Gb=R.ideal(T1_I.groebner_basis())
>
> I try to evaluate polynomials in R with certain values, for instance:
>
> sage: p
> 300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 +
> (-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 +
> 3264*f2^3 + 108*f2^2
> sage: p.subs({f0:1/5,f1:1/5,f2:1/5,f3:1/5,f4:1/5})
> 300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 +
> (-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 +
> 3264*f2^3 + 108*f2^2
>
> which doesn't seem to do anything. Any suggestions?
This works fine for me. Maybe you did something funny
in between? Try the following:
sage: QQi.<I>=QQ.extension([x^2+1]);
sage: R.<a,b,f0,f1,f2,f3,f4>=MPolynomialRing(QQi,order='lex')
sage: T1_Pxxx=3*a^2*b+(1-a)^2*(1-b)-f0
sage: T1_Pxxy=3*(1-a)^2*b+3*a^2*(1-b)+6*a^2*b-f2
sage: T1_Pxyz=6*(1-a)*a*b+6*a*(1-a)*b+6*a^2*(1-b)+6*a^2*b-f1
sage: T1_Pyxx=3*(1-a)*a*b+3*a*(1-a)*(1-b)+6*a^2*b-(1-f0-f1-f2)/2
sage: T1_Pxyx=T1_Pyxx
sage: T1_I= R.ideal(T1_Pxxx,T1_Pxyz,T1_Pxxy,T1_Pyxx)
sage: T1_Gb=R.ideal(T1_I.groebner_basis())
sage: p = 300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 + \
sage: (-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 + \
sage: 3264*f2^3 + 108*f2^2
sage: p
300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 +
(-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 +
3264*f2^3 + 108*f2^2
sage: p.subs({f0:1/5,f1:1/5,f2:1/5,f3:1/5,f4:1/5})
116159/625
Or as a Worksheet:
Untitled
system:sage
{{{id=0|
QQi.<I>=QQ.extension([x^2+1]);
R.<a,b,f0,f1,f2,f3,f4>=MPolynomialRing(QQi,order='lex')
T1_Pxxx=3*a^2*b+(1-a)^2*(1-b)-f0
T1_Pxxy=3*(1-a)^2*b+3*a^2*(1-b)+6*a^2*b-f2
T1_Pxyz=6*(1-a)*a*b+6*a*(1-a)*b+6*a^2*(1-b)+6*a^2*b-f1
T1_Pyxx=3*(1-a)*a*b+3*a*(1-a)*(1-b)+6*a^2*b-(1-f0-f1-f2)/2
T1_Pxyx=T1_Pyxx
T1_I= R.ideal(T1_Pxxx,T1_Pxyz,T1_Pxxy,T1_Pyxx)
T1_Gb=R.ideal(T1_I.groebner_basis())
}}}
{{{id=1|
p = 300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 + \
(-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 + \
3264*f2^3 + 108*f2^2
}}}
{{{id=2|
p
///
300*f1^3 + (-400)*f1^2*f2^2 + 720*f1^2*f2 + (-4581)*f1^2 +
(-960)*f1*f2^3 + 2640*f1*f2^2 + 6732*f1*f2 + 216*f1 + (-576)*f2^4 +
3264*f2^3 + 108*f2^2
}}}
{{{id=3|
p.subs({f0:1/5,f1:1/5,f2:1/5,f3:1/5,f4:1/5})
///
116159/625
}}}
{{{id=4|
}}}
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