2021-04-05 10:55:19 +0200 received badge ● Notable Question (source) 2020-11-11 21:27:27 +0200 received badge ● Notable Question (source) 2020-06-24 12:21:49 +0200 received badge ● Popular Question (source) 2019-08-19 23:16:49 +0200 received badge ● Popular Question (source) 2018-10-08 17:15:43 +0200 received badge ● Popular Question (source) 2017-02-12 03:38:38 +0200 received badge ● Editor (source) 2017-02-12 03:31:11 +0200 asked a question solution to homogeneous system of linear equations with coefficients over field $\mathbb{F}_2$ Solve the following homogeneous systems of linear equations with coefficients over field $\mathbb{F}_2$:  x1+x2+x3+x4+x5+x6+x7 = 0 x1=0 x2+x3+x4 =0 x5=0  I want to output on the sage following: x1=x5=0 x6=x7 x2+x3+x4=0  I want to solve a general homogeneous systems with coefficients over field $\mathbb{F}_2$ and output same as above. I hope that someone can help. Thanks! 2017-02-12 03:08:47 +0200 asked a question Code error in sagemath My code in sagemath  def bruteforce count = 0 s = [0, 1, 2, 4, 8] s.each do |a| s.each do |b| s.each do |c| s.each do |d| s.each do |e| if a+b+c+d+e == 8 count += 1 puts "#{count}.: #{a}+#{b}+#{c}+#{d}+#{e}" end end end end end end count end  but it was an error as below  File "", line 1 def brutefor SyntaxError: invalid syntax  2017-02-11 14:06:26 +0200 received badge ● Student (source) 2017-02-11 13:40:43 +0200 asked a question Find all non-negative integer solutions of $a+b+c+d+e = 8$ in Sagemath Find all non-negative integer a, b, c,d, e such that $$a+b+c+d+e = 8$$ Is there any method for this? I have no idea. I can just fix the limit. 2017-02-11 04:01:50 +0200 commented answer Construction of formula in Sagemath program I use the code above but it error. File "", line 3 Multivariate Polynomial Ring in x1, x2, x3, x4 over Finite Field of size Integer(2) SyntaxError: invalid syntax 2017-02-10 16:24:29 +0200 asked a question Construction of formula in Sagemath program Let $P_k:= \mathbb{F}_2[x_1,x_2,\ldots ,x_k]$ be the polynomial algebra in $k$ variables with the degree of each $x_i$ being $1,$ regarded as a module over the mod-$2$ Steenrod algebra $\mathcal{A}.$ Here $\mathcal{A} = \langle Sq^{2^m}\,\,|\,\,m\geq 0\rangle.$ Being the cohomology of a space, $P_k$ is a module over the mod-2 Steenrod algebra $\mathscr{A}.$ The action of $\mathscr{A}$ on $P_k$ is explicitly given by the formula $$Sq^m(x_j^d) = \binom{d}{m}x_j^{m+d},$$ where $\binom{d}{m}$ is reduced mod-2 and $\binom{d}{m} = 0$ if $m > d.$ Now, I want to use the Steenrod algebra package and Multi Polynomial ring package and using formular above to construction of formula following in Sagemath program $$Sq^m(f) = \sum\limits_{2^{m_1} + 2^{m_2} + \cdots + 2^{m_k}= m}\binom{d_1}{2^{m_1}}x_1^{2^{m_1}+d_1}\binom{d_1}{2^{m_2}}x_2^{2^{m_2}+d_2}\ldots \binom{d_k}{2^{m_k}}x_k^{2^{m_k}+d_k}.$$ forall $f = x_1^{d_1}x_2^{d_2}\ldots x_k^{d_k}\in P_k$ Example: Let $k = 5, m = 2$ and $f = x_1^2x_2^3x_3^2x_4x_5\in P_5.$ We have $$Sq^2(x_1^2x_2^3x_3^2x_4x_5) = x_1^4x_2^3x_3^2x_4x_5 + x_1^2x_2^5x_3^2x_4x_5 + x_1^2x_2^3x_3^4x_4x_5 +x_1^2x_2^3x_3^2x_4^2x_5^2 + x_1^2x_2^4x_3^2x_4x_5^2 + x_1^2x_2^4x_3^2x_4^2x_5^1.$$ I hope that someone can help. Thanks!