2022-12-07 19:16:21 +0200 received badge ● Popular Question (source) 2022-08-27 11:59:20 +0200 commented answer How to pick a matrix uniformly from a certain matrix space? Thank you for your response. I understand your answer, but Gaussian distribution is not what I require. I am working in 2022-08-24 12:59:53 +0200 asked a question How to pick a matrix uniformly from a certain matrix space? How to pick a matrix uniformly from a certain matrix space? Hello, I hope everyone is fine. I have a small question. Su 2021-07-14 07:43:44 +0200 asked a question find the first power of $t$ with a non-positive coefficient find the first power of $t$ with a non-positive coefficient.aga Consider the following rational expression in $t$, f( 2021-01-21 11:50:33 +0200 asked a question Which hash function can be used to get $w=H(d)\in F^n$ case? I am trying to implement a cryptographic scheme. For a arbitrary message $d$ , I need a Hash Function $\mathbb{H}$ that can compute the hash value $w=\mathbb{H}(d)\in \mathbb{F}^n$. Here $F$ is a finite field of order four. I can not find any hash function which outputs field values. Can someone please help and show me the right direction? 2021-01-19 10:57:55 +0200 commented answer Multiply polynomials from different rings Don't have words to thank you. I spent a lot of time on this but still was not able to think about it. Have a good day :) 2021-01-19 10:36:55 +0200 asked a question Multiply polynomials from different rings Suppose I take a polynomial from $K[x]$, say $x^2 + 5x$, and another polynomial from $K[y]$, say $y^3$. I want to formally multiply them and get $x^2y^3 + 5xy^3$ as the output. How can I do that? Note: K is the finite field of size 4 in a. My efforts: sage: K. = FiniteField(4) sage: R_1 = PolynomialRing(K, ['z%s' % p for p in range(1, 3)]) sage: R_2 = PolynomialRing(K, ['x%s' % p for p in range(1, 3)]) sage: pp = R_1.random_element() sage: pp (a + 1)*z1^2 + (a)*z1*z2 + (a + 1)*z2 + (a) sage: qq = R_2.random_element() sage: qq x1*x2 + (a + 1)*x2^2 + x1 + 1  When I do pp*qq I get the following output unsupported operand parent(s) for *: 'Multivariate Polynomial Ring in z1, z2 over Finite Field in a of size 2^2' and 'Multivariate Polynomial Ring in x1, x2 over Finite Field in a of size 2^2'  2021-01-19 10:23:59 +0200 received badge ● Scholar (source) 2021-01-19 10:23:47 +0200 received badge ● Supporter (source) 2021-01-19 09:18:54 +0200 received badge ● Student (source) 2021-01-19 07:00:12 +0200 asked a question Random polynomial of degree 1 Having defined the finite field K of size 4 in a a polynomial ring R1 over K one can ask for a random element using the random_element method. The random polynomial I obtained that way was of degree two: sage: K. = FiniteField(4) sage: R1 = PolynomialRing(K, ['z%s' % p for p in range(1, 3)]) sage: R1.random_element() (a)*z1*z2 + (a + 1)*z2^2 + z1 + (a)*z2  If I only want a random linear polynomial from this ring, how can I get one? 2021-01-10 09:38:56 +0200 asked a question Not able to generate a simple list of polynomial. I am getting list of list.  def quad_polynomial(field, n,m): Polynomial_Ring1=PolynomialRing(K,['x%s'%p for p in range(1,n+1)]) x1=Polynomial_Ring1.gens() gen_Polynomial_Ring1 = matrix(x1) list_of_quadratic_part=[0 for i in range(m)] for i in range(m): list_of_quadratic_part[i]=gen_Polynomial_Ring1*(random_matrix(K,n))*gen_Polynomial_Ring1.transpose() #print(list_of_quadratic_part[i]) return list_of_quadratic_part  The output I am getting is like this: quad_polynomial(K,2,3) [[x1*x2 + (a + 1)*x2^2], [x1^2 + (a + 1)*x1*x2], [x1^2 + (a + 1)*x2^2]]  It is giving me list of list. I want a output like  [x1*x2 + (a + 1)*x2^2, x1^2 + (a + 1)*x1*x2, x1^2 + (a + 1)*x2^2]  How can I do it?