By Laurie Boswell, Timothy D. Kanold, Lee Stiff, Holt Mcdougal

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Publication via Garnett, J.

**An introduction to Gröbner bases**

Because the fundamental software for doing specific computations in polynomial earrings in lots of variables, Gröbner bases are a tremendous element of all machine algebra platforms. also they are very important in computational commutative algebra and algebraic geometry. This e-book presents a leisurely and reasonably accomplished creation to Gröbner bases and their purposes.

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A. 2x º 1 < 8 2(4) º 1 < 8 ? b. x + 4 > 9 4+4>9 ? c. x º 3 ≥ 1 EXAMPLE 5 FOCUS ON CAREERS 4º3≥1 RESULT CONCLUSION 7<8 4 is a solution. 8>9 4 is not a solution. 1≥1 4 is a solution. Checking Solutions in Real Life VETERINARIAN Your vet told you to restrict your cat’s caloric intake to no more than 500 calories each day. Three times a day, you give your cat a serving of food containing x calories. Do the following values of x meet the vet’s restriction? a. 170 calories b. 165 calories SOLUTION 3x ≤ 500 a.

On the other hand, “the sum of six and a number” can be written as 6 + x or x + 6. EXAMPLE 1 Translating Verbal Phrases into Algebra Translate the phrase into an algebraic expression. SOLUTION a. Three more than the quantity five times a number n 5n + 3 Think: 3 more than what? b. Two less than the sum of six and a number m (6 + m) º 2 Think: 2 less than what? c. A number x decreased by the sum of 10 and the square of a number y x º (10 + y 2) 32 Chapter 1 Connections to Algebra Think: x decreased by what?

50. Assign labels and write an algebraic model based on your verbal model. 51. Use mental math to solve the equation. 52. How many subscriptions does the science club need to sell to raise $315? 53. Check to see if your answer is reasonable. LAW ENFORCEMENT In Exercises 54–57, use the following information. com for help with problem solving in Exs. 54–57. Jeff lives in a state in which speeders are fined $20 for each mile per hour (mi/h) over the speed limit. Jeff was given a ticket for $260 for speeding on a road where the speed limit is 45 miles per hour.