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分享试题求解
1.Build the Sylvester matrix corresponding to the polynomials in the sub-resultant lecture, i.e:
A(x)= x8+x6-3x4-3x³+8x²+2x-5;
B(x)= 3x6+5x4-4x²-9x+21
Run Bareiss’s algorithm on this to compute the determinant. Note that you have to deal with the case of zero elements on the diagonal.
2.Emulate the Buchberger algorithm on cyclic-3, i.e.:
a+b+c
ab+bc+ca
abc-1
By this I mean that each s-polynomial should be computed and reduced under human control, i.e. the most sophisticated MAPLE commands you can use are of the form s:= 28x*f1-3*y*f2 or S:= s-7*z*f3. how many S-polynomials do you compute? How many of them reduce to zero?
3.Compute, via the Faugère-Gianni-Lazard-Mora(FGLM) algorithm, a purely lexicographical Gröbner base for the cyclic-5 problem: i.e:
a+b+c+d+e
ab+bc+cd+de+ea
abc+bcd+cde+dea+eab
abcd+bcde+cdea+deab+eabc
abcd-1
Hence deduce the number of solutions and a description of them.
A(x)= x8+x6-3x4-3x³+8x²+2x-5;
B(x)= 3x6+5x4-4x²-9x+21
Run Bareiss’s algorithm on this to compute the determinant. Note that you have to deal with the case of zero elements on the diagonal.
2.Emulate the Buchberger algorithm on cyclic-3, i.e.:
a+b+c
ab+bc+ca
abc-1
By this I mean that each s-polynomial should be computed and reduced under human control, i.e. the most sophisticated MAPLE commands you can use are of the form s:= 28x*f1-3*y*f2 or S:= s-7*z*f3. how many S-polynomials do you compute? How many of them reduce to zero?
3.Compute, via the Faugère-Gianni-Lazard-Mora(FGLM) algorithm, a purely lexicographical Gröbner base for the cyclic-5 problem: i.e:
a+b+c+d+e
ab+bc+cd+de+ea
abc+bcd+cde+dea+eab
abcd+bcde+cdea+deab+eabc
abcd-1
Hence deduce the number of solutions and a description of them.
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samchoy 2004-12-23
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怪怪，一个三角怎么能发200分的贴？
Lonelywolf1899 2004-12-23
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忘了给大家介绍，凤凰是Windows区的专家.
其实，凤凰兄是满天星级别的人物哦.
0_0
其实，凤凰兄是满天星级别的人物哦.
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Lonelywolf1899 2004-12-23
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哈哈，凤凰到了这里，只有一条裤衩了......
cczlp 2004-12-23
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怪怪，一个三角怎么能发200分的贴？
同意
同意
sunkevin 2004-12-22
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up
myhgyp 2004-12-22
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看了一点，晕了，帮不了你了
oyljerry 2004-12-21
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好几个算法，楼主先了解一下这几个相关的算法啊
I_Love_CPP 2004-12-21
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读倒是读懂了，但请解释几个名词，先：
Sylvester matrix
Bareiss’s algorithm
Buchberger algorithm
S-polynomials
Faugère-Gianni-Lazard-Mora(FGLM) algorithm
a purely lexicographical Gröbner base for the cyclic-5 problem
我对这个比较感兴趣，关注中。。。。
Sylvester matrix
Bareiss’s algorithm
Buchberger algorithm
S-polynomials
Faugère-Gianni-Lazard-Mora(FGLM) algorithm
a purely lexicographical Gröbner base for the cyclic-5 problem
我对这个比较感兴趣，关注中。。。。
老夏Max 2004-12-21
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我的英语不行啊
danyueer 2004-12-21
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……
