Compute the Jacobi symbol (28/195) and the Legendre symbol (28/13).
Compute the Jacobi symbol (28/195) and the Legendre symbol (28/13).
Homework Answers
8. Compute the following Legendre symbols. Use quadratic reciprocity, in conjunction with the multiplicative property of...
8. Compute the following Legendre symbols. Use quadratic reciprocity, in conjunction with the multiplicative property of the Legendre symbol and the special cases for -1 and 2 29 Note that 541 is prime (a) 541 101 Note that 1987 is prime (b) 1987
43. State the value of the Legendre symbol ) where p is an odd prime, and...
43. State the value of the Legendre symbol ) where p is an odd prime, and prove your result.
(1) The Legendre symbol and Euler's criterion. (1 pt each) Let p be an odd prime and a Z an integ...
(1) The Legendre symbol and Euler's criterion. (1 pt each) Let p be an odd prime and a Z an integer which is not divisible by p. The integer a is called a quadratic residue modulo p if there is b E Z such that a b2 (p), i.e., if a has a square root modulo p. Otherwise a is called a quadratic non-residue. One defines the Legendr symbol as follows: 1 p)=T-i if a is a quadratic residue modulo...
3. [4 marks] Compute the Jacobi matrix of the cornposite mapping z with a - ucosv and y u sin v. ...
3. [4 marks] Compute the Jacobi matrix of the cornposite mapping z with a - ucosv and y u sin v. Simplify the resulting expressions. x2-уг, u:-z?+92
3. [4 marks] Compute the Jacobi matrix of the cornposite mapping z with a - ucosv and y u sin v. Simplify the resulting expressions. x2-уг, u:-z?+92
6. Compute four Legendre polynomials degree 0, 1, 2 and 3, respectively. You can assume that...
6. Compute four Legendre polynomials degree 0, 1, 2 and 3, respectively. You can assume that these polynomials endre polynomial to construct a Gaussian quadrature. Approximate the value of the integral are monic. Use the roots of the cubic Leg- sin(2x) dx using your quadrature rule.
6. Compute four Legendre polynomials degree 0, 1, 2 and 3, respectively. You can assume that these polynomials endre polynomial to construct a Gaussian quadrature. Approximate the value of the integral are monic. Use...
E Law of Quadratic Reciprocity to compute the Legendre sym- bols and answer the questions below: ...
#1 & #2
e Law of Quadratic Reciprocity to compute the Legendre sym- bols and answer the questions below: 85 (a) 101 Is 85 a perfect square modulo 101? 29 (b) 541 Is 29 a perfect square modulo 541? 101 (c) 1987 Is 101 a perfect square modulo 1987? 31706 (d) 43789 Is 31706 a perfect square modulo 43789? b2 (mod 7), then 19a2 (mod 72). 2. Prove that if 19a
e Law of Quadratic Reciprocity to compute the Legendre...
solve the fllowing systems of linear equations by it erative method choose either Jacobi i tre...
solve the fllowing systems of linear equations by it erative method choose either Jacobi i tre method or Causs- Seidet iterative method i 12x + 3x2 - S X3 = 1 Å4 + 5x2 3x3 =28 3x + 7 Az & 13 43 5 766 use an Inital approximation (x, x xx) = , o, jast conduct at at least fine it eration
Question 28 (4 points) The chemical symbol SES means sulfur equals sulfur this is an ionic...
Question 28 (4 points) The chemical symbol SES means sulfur equals sulfur this is an ionic bond with two shared electrons both atoms are bonded and have zero electrons in the outer orbit the atoms are double bonded 13 bong
[-230; -1-2 3; 01-21 *X [160 -40 -160]AT Compute vector X using the following methods a) Jacobi m...
[-230; -1-2 3; 01-21 *X [160 -40 -160]AT Compute vector X using the following methods a) Jacobi method; up to 12 iterations b) Forward Gauss Seidel method; up to 12 iterations c) Symmetric Gauss Seidel method; up to 12 iterations (6 forward and 6 backward iterations) You can use MATLAB to report the final results. However, it is required to calculate at least 3 iterations by hand. You are also expected to compute the spectral radius of the decisive matrix...
answer all steps, please 2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A...
answer all steps, please
2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A-1 and the norms l|All2 and IA12 in MATLAB. c Use MATLAB to compute the condition nmber in norm-2 of A, based on your results from (b). Verify your results in MATLAB using the cond command
2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A-1 and...
8. Compute the following Legendre symbols. Use quadratic reciprocity, in conjunction with the multiplicative property of the Legendre symbol and the special cases for -1 and 2 29 Note that 541 is prime (a) 541 101 Note that 1987 is prime (b) 1987
43. State the value of the Legendre symbol ) where p is an odd prime, and prove your result.
(1) The Legendre symbol and Euler's criterion. (1 pt each) Let p be an odd prime and a Z an integer which is not divisible by p. The integer a is called a quadratic residue modulo p if there is b E Z such that a b2 (p), i.e., if a has a square root modulo p. Otherwise a is called a quadratic non-residue. One defines the Legendr symbol as follows: 1 p)=T-i if a is a quadratic residue modulo...
3. [4 marks] Compute the Jacobi matrix of the cornposite mapping z with a - ucosv and y u sin v. Simplify the resulting expressions. x2-уг, u:-z?+92
3. [4 marks] Compute the Jacobi matrix of the cornposite mapping z with a - ucosv and y u sin v. Simplify the resulting expressions. x2-уг, u:-z?+92
6. Compute four Legendre polynomials degree 0, 1, 2 and 3, respectively. You can assume that these polynomials endre polynomial to construct a Gaussian quadrature. Approximate the value of the integral are monic. Use the roots of the cubic Leg- sin(2x) dx using your quadrature rule.
6. Compute four Legendre polynomials degree 0, 1, 2 and 3, respectively. You can assume that these polynomials endre polynomial to construct a Gaussian quadrature. Approximate the value of the integral are monic. Use...
#1 & #2
e Law of Quadratic Reciprocity to compute the Legendre sym- bols and answer the questions below: 85 (a) 101 Is 85 a perfect square modulo 101? 29 (b) 541 Is 29 a perfect square modulo 541? 101 (c) 1987 Is 101 a perfect square modulo 1987? 31706 (d) 43789 Is 31706 a perfect square modulo 43789? b2 (mod 7), then 19a2 (mod 72). 2. Prove that if 19a
e Law of Quadratic Reciprocity to compute the Legendre...
solve the fllowing systems of linear equations by it erative method choose either Jacobi i tre method or Causs- Seidet iterative method i 12x + 3x2 - S X3 = 1 Å4 + 5x2 3x3 =28 3x + 7 Az & 13 43 5 766 use an Inital approximation (x, x xx) = , o, jast conduct at at least fine it eration
Question 28 (4 points) The chemical symbol SES means sulfur equals sulfur this is an ionic bond with two shared electrons both atoms are bonded and have zero electrons in the outer orbit the atoms are double bonded 13 bong
[-230; -1-2 3; 01-21 *X [160 -40 -160]AT Compute vector X using the following methods a) Jacobi method; up to 12 iterations b) Forward Gauss Seidel method; up to 12 iterations c) Symmetric Gauss Seidel method; up to 12 iterations (6 forward and 6 backward iterations) You can use MATLAB to report the final results. However, it is required to calculate at least 3 iterations by hand. You are also expected to compute the spectral radius of the decisive matrix...
answer all steps, please
2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A-1 and the norms l|All2 and IA12 in MATLAB. c Use MATLAB to compute the condition nmber in norm-2 of A, based on your results from (b). Verify your results in MATLAB using the cond command
2. Let A8 28 -4 -6 13 a) Compute l|All (Frobenius norm), |Alo and ||Alli (by hand b) Compute A-1 and...
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