2023-01-18 08:31:27 +0200 received badge ● Famous Question (source) 2023-01-18 08:31:27 +0200 received badge ● Notable Question (source) 2022-11-19 03:02:45 +0200 received badge ● Popular Question (source) 2022-09-08 22:26:02 +0200 received badge ● Popular Question (source) 2022-03-01 09:59:43 +0200 marked best answer Writing a polynomial as a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer coefficients, and I know that these factor as product of $t-$ numbers of the form $[k]_t = 1+t+...+t^{k-1}$ . Is there a way to factor the polynomials in sage which readily give the factorization in terms of the $t-$numbers? For example, I have a polynomial $(t^2-t+1)(t^2+t+1)(t+1)^2=(t^5+t^4+t^3+t^2+t+1)(t+1)$. I want the program to return $[6]_t[2]_t$. 2022-03-01 09:59:14 +0200 commented answer Writing a polynomial as a product of t-numbers Thank you, this is very nice. 2022-02-28 22:10:25 +0200 edited question Writing a polynomial as a product of t-numbers Writing polynomial at a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer 2022-02-28 21:38:21 +0200 asked a question Writing a polynomial as a product of t-numbers Writing polynomial at a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer 2021-12-15 17:25:13 +0200 received badge ● Nice Question (source) 2021-12-13 23:38:12 +0200 marked best answer Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say $p(t)$ is unimodal if $a_0 \leq a_1 \leq ... \leq a_k \geq a_{k+1} \geq ... \geq a_n$ i.e, the sequence of coefficients increase at first and then decrease, they don't 'jump around' ; there is no phenomenon like increase then decrease then increase again. Given such a polynomial, how can we check unimodality in sage? 2021-12-13 23:38:07 +0200 commented answer Checking whether a polynomial in unimodal Thank you very much! 2021-12-13 23:07:17 +0200 edited answer Checking whether a polynomial in unimodal From @rburing's answer... slightly modified since taking coefficients in the polynomial ring somehow only gives the non- 2021-12-13 23:06:40 +0200 answered a question Checking whether a polynomial in unimodal From @rburing's answer... slightly modified since taking coefficients in the polynomial ring somehow only gives the non- 2021-12-13 22:40:00 +0200 commented answer Checking whether a polynomial in unimodal No... I meant your earlier program didn't work if there was some internal zeroes 2021-12-13 22:18:16 +0200 received badge ● Commentator 2021-12-13 21:48:53 +0200 commented answer Checking whether a polynomial in unimodal Actually coeffs don't take into account if some coefficient $a_k=0$ in the middle. So this works fine if there is no int 2021-12-13 20:39:20 +0200 received badge ● Organizer (source) 2021-12-13 20:38:46 +0200 edited question Checking whether a polynomial in unimodal Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say 2021-12-13 20:38:05 +0200 asked a question Checking whether a polynomial in unimodal Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say 2021-11-13 12:04:09 +0200 received badge ● Popular Question (source) 2021-10-25 23:07:06 +0200 received badge ● Nice Question (source) 2021-10-23 20:34:45 +0200 marked best answer Non-Symmetric Macdonald expansion I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a linear combination of Non-Symmetric Macdonald polynomials $E_{\alpha}$ where $\alpha$ varies over $\mathbb{Z}^n_{\geq 0}$ with $\sum \alpha_i = k$. Background: We know that these Macdonald polynomials do indeed form a basis of the vector space of homogeneous degree $k$ polynomials in $n$ variables. The Non-Symmetric Macdonald polynomials I am interested in is the type $GL_n$ kind. And their sage implementation can be found here: sage documentation Bottom line is that we have a basis of a vector space already implemented in sage. Now how do we use it to compute coefficients of any vector when written in terms of this basis? 2021-10-22 21:27:19 +0200 received badge ● Nice Question (source) 2021-10-22 15:24:57 +0200 commented answer Non-Symmetric Macdonald expansion Can you explain what is happening in the repM definition please? 2021-10-21 20:17:54 +0200 asked a question Non-Symmetric Macdonald expansion Non-Symmetric Macdonald expansion I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a l 2021-10-01 19:03:12 +0200 asked a question Running a search algorithm Running a search algorithm I want to write a program to check whether a given rational function $f(x,y)$ in two variable 2021-07-22 18:16:55 +0200 edited question Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v 2021-07-22 18:16:52 +0200 commented answer Defining vector partition functions in sage Edited post for clarity... please check. 2021-07-22 10:58:00 +0200 commented answer Defining vector partition functions in sage Understood. I wanted to get all partitions by somehow subtracting one part and knowing the smaller partitions. Do you ha 2021-07-21 15:33:26 +0200 received badge ● Editor (source) 2021-07-21 15:33:26 +0200 edited question Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v 2021-07-21 15:16:53 +0200 asked a question Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v 2021-06-30 01:57:39 +0200 received badge ● Nice Question (source) 2021-06-29 22:30:39 +0200 marked best answer Define matrix indexed by partitions I want to define the following matrix in sage: $J$ is of size Partitions(n), and $J_{\lambda, \mu} = 1$ if $\lambda'=\mu$ and $0$ else. Can someone please help? 2021-06-29 22:30:34 +0200 commented answer Define matrix indexed by partitions This was exactly what I was looking for. Thank you so much. 2021-06-29 21:00:56 +0200 asked a question Define matrix indexed by partitions Define matrix indexed by partitions I want to define the following matrix in sage: $J$ is of size Partitions(n), and $J_ 2021-06-02 18:58:11 +0200 commented answer plot not working in windows Thank you. I will try sage 9.1 2021-06-02 18:57:39 +0200 commented question plot not working in windows Nope. Doesn't work 2021-06-02 16:03:10 +0200 asked a question plot not working in windows plot not working in windows I am using sagemath on windows 10. If I do f(x)=x plot(f) my sagemath complete 2020-09-19 06:59:12 +0200 asked a question Functions in polynomials rings I want to define a function in a polynomial ring in several variables. R.=PolynomialRing(QQ) I am trying to define a function that takes$(i,j)$to$x_i^j\$. I tried def f(i,j): return xi^j This does not work. I tried replacing xi with x[i], that doesn't work. Can someone please tell me what I am doing wrong and how to fix it? If instead of taking 3 variables I take only 1 variable then the method works. 2020-09-19 06:09:36 +0200 received badge ● Scholar (source) 2020-09-06 10:42:42 +0200 commented answer Derivative in infinite polynomial ring Thanks a lot. 2020-09-06 10:42:16 +0200 received badge ● Supporter (source) 2020-09-05 20:12:00 +0200 received badge ● Student (source) 2020-09-05 19:50:05 +0200 asked a question Derivative in infinite polynomial ring I am defining my ring as R.=InfinitePolynomialRing(QQ), and this should give me ring with variables x[1],x[2],... etc. right? Now I want to differentiate a polynomial with respect to x[1] variable. So I defined f=x[1]^3 (for example). I am trying f.derivative(x[1]) but that does not work. It shows " 'typeerror': argument 'var' has incorrect type (expected sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular, got InfinitePolynomial_dense)." Can someone please explain what is wrong and what I should do to fix it?