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Problem 17

For Exercises 14 through 17, let power products in \(\mathbb{R}[x, y, z]\) have order lex where \(z

Problem 20

In Exercises 20 through 22 , find a Gröbner basis for the indicated ideal in \(\mathbb{R}[x]\). $$ \left(x^{4}+x^{3}-3 x^{2}-4 x-4, x^{3}+x^{2}-4 x-4\right\rangle $$

Problem 21

In Exercises 20 through 22 , find a Gröbner basis for the indicated ideal in \(\mathbb{R}[x]\). $$ \left(x^{4}-4 x^{3}+5 x^{2}-2 x, x^{3}-x^{2}-4 x+4, x^{3}-3 x+2\right\rangle $$

Problem 22

In Exercises 20 through 22 , find a Gröbner basis for the indicated ideal in \(\mathbb{R}[x]\). $$ \left(x^{5}+x^{2}+2 x-5, x^{3}-x^{2}+x-1\right) $$

Problem 23

In Exercises 23 through 26 , find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

Problem 24

In Exercises 23 through 26 , find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

Problem 24

Find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

Problem 25

Find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

Problem 25

In Exercises 23 through 26 , find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

Problem 26

Find a Gröbner basis for the given ideal in \(\mathbb{R}[x, y]\). Consider the order of power products to be lex with \(y

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