affine

  1. Bernhard

    Affine Algebraic Curves - Kunz - Theorem 1.3

    I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' proof of Theorem 1.3 ... The relevant text from Kunz is as follows: In the above text we read the following: " ... ... Therefore let p > 0. Since a_p has only...
  2. Bernhard

    Affine Algebraic Curves - Kunz - Definition 1.1

    I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with some aspects of Kunz' Definition 1.1. The relevant text from Kunz' book is as follows: In the above text, Kunz writes the following: " ... ... If K_0 \subset K is a subring and \Gamma = \mathscr{V}...
  3. Bernhard

    Affine Algebraic Curves - Kunz - Exercise 1 - Chapter 1

    I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves" I need help with Exercise 1, Chapter 1 ... Indeed ... I am a bit overwhelmed by this problem .. Exercise 1 reads as follows: Hope someone can help ... ... To give a feel for the context and notation I am providing...
  4. K

    images under composite affine transformations

    Hi I am looking for advice on how to tackle the following problem f and g are both affine transfomrations. the transformation f is rotation about (1-2) through -pi/2 , and the transformation g maps the points (0,0), to (1,0) and (0,1) to the points (2,2) (1,2) (2,1), respectively. find...
  5. F

    Affine Cipher help

    Say we use the ordinary English alphabet A.....Z with letters numbered 0......25. We number digraphs using enumeration to base 26. We encode using the affine transformation: f(x) = 213x + 111 (mod 676) How would i encode the message CREED? Is it possible to do with 5 letters instead of 4 since...
  6. M

    Affine Transformations

    Hi all so ive read all my books and tried searching online and also discussing with my professor but i am still not getting this if anyone could answer and explain for me i would really appreciate it in this question f and g are both affine transformations, the transformation f is...
  7. A

    Affine transformation question...HELP!

    In this question, f and g are both affine transformations. The transformation f is reflection in the line y = x − 1, and the transformation g maps the points (0, 0), (1, 0) and (0, 1) to the points (3,−1), (4,−1) and (3,-2), respectively. (a) Determine g in the form g(x) = Ax + a, where A is...
  8. M

    Affine cipher

    We have Ea,b(x)=(a.x+b)(mod 26). Find a,b if you know 2 values Ea,b(x) Ea,b(3)=5, Ea,b(6)=7 =>(3a+b)%26=5 (6a+b)%26=7 I don't know how to solve these equations, so I can't find a,b Please, help me or give me some ideas to solve it. Thank you very much!
  9. Bernhard

    Affine Varieties - the x-axis in R^2

    In Dummit and Foote, Chapter 15, Section 15.2 Radicals and Affine Varieties, Example 2, page 681 begins as follows: ----------------------------------------------------------------------------------------- "The x-axis in \mathbb{R}^2 is irreducible since it has coordinate ring...
  10. Bernhard

    Affine Variety - Single Points and maximal ideals

    In Dummit and Foote Chapter 15, Section 15.3: Radicals and Affine Varieties on page 679 we find the following definition of affine variety: (see attachment) ------------------------------------------------------------------------------------------------------------------------------------...
  11. Bernhard

    Affine Algebraic Sets - D&F Chapter 15, Section 15.1 - Properties of the map I

    I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, the set \mathcal{I} (A) is defined in the following text on page 660: (see attachment)...
  12. Bernhard

    Affine Algebraic Sets - D&F Chapter 15, Section 15.1 - Example 3 - page 660

    I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, Example 3 on page 660 reads as follows: (see attachment)...
  13. Bernhard

    'Curly' Z and I - Affine algebraic sets

    I am reading Dummit and Foote on affine algebraic sets and wish to create posts refering to such objects. The notation for a subset Z(S) of affine space is a "curly" Z - see attachment - bottom of page 658. Also the notion for the unique largest ideal whose locus determines a particular...
  14. Bernhard

    Affine Algebraic Sets - D&F Chapter 15, Section 15.1

    I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, Example 2 on page 660 reads as follows: (see attachment)...
  15. T

    Pohlig-Hellman Cipher + Affine Hill Cipher, relatively simple (not for me!) questions

    Hi guys, How you all doing? Would be a great help if you could help me solve these equations. I guess more than the answers I need the process by which you get to them. Here are the questions...
  16. A

    Affine Cipher Properties.

    I was working on a problem with an affine cipher. Looking at the properties they say for "f(x)=(ax + b)MOD26 defines a valid affine cipher if a is relatively prime to 26, and b is an integer between 0 and 25." i was working with f(x)=-9x+12(mod26),so K=A, H=B... but f(x)=11x-170(mod26) gives...
  17. J

    Showing that a non-empty subset M is an affine subset of R^4

    Hi, I have to do a project on affine subsets and affine mappings, but I have no clue what they are... We are given only one clue and I can't find many notes on google. I would really appreciate it if someone could help me with this first problem (and if you could also give me a link to some good...
  18. J

    Finite affine plane problem

    Hello, I'm trying to figure out the answer to the following question regarding finite affine planes: My intuition is that there are far too many lines for this to be a finite affine plane. We'd expect there to be n^2+n = 6^2+6 = 42 lines, but when I started computing them there seemed to be...
  19. G

    Are this an affine subset of R^n?

    L=\{x= \[\alpha_1,\ldots,\alpha_n\]^\top\ | \sum_{i=1}^n \alpha_i^2 =615\} And in general how can I show wether a subset of a vector space is affine or not? Thank you!
  20. N

    Affine spaces

    Prove that the solution set of a non-homogeneous system of linear equations is an affine space. What is the dimension of that subspace of which translation is the previously defined affine space?