{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

College Algebra Exam Review 69

# College Algebra Exam Review 69 - 1.12 AN APPLICATION TO...

This preview shows page 1. Sign up to view the full content.

1.12. AN APPLICATION TO CRYPTOGRAPHY 79 1.11.3. A Laurent polynomial is a ”polynomial” in which negative as well as positive powers of the variable x are allowed, for example, p.x/ D 7x 3 C 4x 2 C 4 C 2x . Show that the set of Laurent polynomials with coefficients in a field K forms a ring with identity. This ring is denoted by KOEx; x 1 Ł . (If you prefer, you may take K D R .) What are the units? 1.11.4. A trigonometric polynomial is a finite linear combination of the functions t 7! e int , where n is an integer; for example, f .t/ D 3e i2t C 4e it C i p 3e i7t . Show that the set of trigonometric polynomials is a sub- ring of the ring of continuous complex–valued functions on R . Show that the ring of trigonometric polynomials is isomorphic to the ring of Laurent polynomials with complex coefficients. 1.11.5. Show that the set of polynomials with real coefficients in three variables, R OEx; y; zŁ is a ring with identity. What are the units?
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern