mixing related objects django I have something like this in my models.py:  class Section(models.Model):     title = models.CharField(max_length=50)  class Lesson1(models.Model):     section = models.ForeignKey(Section)     title = models.CharField(max_length=50)     ...     sort_index = models.IntegerField()  class Lesson2(models.Model):     section = models.ForeignKey(Section)     title = models.CharField(max_length=50)     ....     sort_index = models.IntegerField()   And I need to display them mixed, like this:  section title: -lesson1 title -lesson2 title -lesson1 title  next section title: -lesson2 title -lesson2 title -lesson1 title   Is there a nice way to do this?
How can I combine two or more querysets in a Django view? I am trying to build the search for a Django site I am building, and in that search, I am searching in three different models. And to get pagination on the search result list, I would like to use a generic object_list view to display the results. But to do that, I have to merge three querysets into one. How can I do that? I've tried this: result_list = [] page_list = Page.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term)) article_list = Article.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term) |     Q(tags__icontains=cleaned_search_term)) post_list = Post.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term) |     Q(tags__icontains=cleaned_search_term))  for x in page_list:     result_list.append(x) for x in article_list:     result_list.append(x) for x in post_list:     result_list.append(x)  return object_list(     request,     queryset=result_list,     template_object_name='result',     paginate_by=10,     extra_context={         'search_term': search_term},     template_name=&quot;search/result_list.html&quot;)  But this doesn't work. I get an error when I try to use that list in the generic view. The list is missing the clone attribute. How can I merge the three lists, page_list, article_list and post_list?
Blade of the Ruined King Vs. The Bloodthirster Effects:  +25 attack damage +15% life steal +40% attack speed Passive  Unique: Your attacks deal 5% of the target's current health in physical damage (60 max vs minions and monsters). Active   Unique: Drains target champion, dealing 15% of the champion's maximum Health in physical damage and healing you by the same amount. Additionally you steal 30% of their movement speed for 4 seconds - 60 second cooldown. (500 range)  Cost: 3200g VS.   Effects:  +70 attack damage +12% life steal Passive: Gain +1 attack damage and +0.2% life steal per kill (maximum +30 attack damage and +6% life steal). Half of the bonuses are lost upon death.  Cost: 3200g What is better for what situations, and when should you build BT instead of BotRK and Vice Versa. Which provides more lifesteal, the only variable being the stats of the weapon? I find myself constantly questioning my decision on which weapon to get and would really love some in depth answers. Would be great if any examples given were given from the ADC side of the house. Can a legendary creature use a legendary resistance to pass a concentration check? As I was looking through some legendary creatures, I had a thought. Most legendary creatures get three Legendary Resistances per day, which they can use to automatically succeed on a saving throw.  A Concentration check is technically a Constitution saving throw, so does that mean that a creature can use a Legendary Resistance to automatically pass a Concentration check, or is it not considered a saving throw? For a given class I would like to have tracing functionality i.e. I would like to log every method call (method signature and actual parameter values) and every method exit (just the method signature).      How do I accomplish this assuming that:     I don't want to use any 3rd party AOP libraries for C#, I don't want to add duplicate code to all the methods that I want to trace,   I don't want to change the public API of the class - users of the class should be able to call all the methods in exactly the same way.     To make the question more concrete let's assume there are 3 classes:     public class Caller   {      public static void Call()       {          Traced traced = new Traced();          traced.Method1();          traced.Method2();       }  }   public class Traced   {      public void Method1(String name, Int32 value) { }       public void Method2(Object object) { }  }   public class Logger  {      public static void LogStart(MethodInfo method, Object[] parameterValues);       public static void LogEnd(MethodInfo method);  }   How do I invoke Logger.LogStart and Logger.LogEnd for every call to Method1 and Method2 without modifying the Caller.Call method and without adding the calls explicitly to Traced.Method1 and Traced.Method2?  Edit:  What would be the solution if I'm allowed to slightly change the Call method? What library do I have to use such that the document can render \lt and \gt as less than and greater than signs, respectively? \documentclass{article} %\usepackage{amsmath} It does Not work ! \begin{document} \[ x\lt y \gt z \] \end{document}  What library do I have to use such that the document can render \lt and \gt as less than and greater than signs, respectively? Edit I am using MathJax library in my site under Asp.net Mvc 3. Web application is vulnerable to XSS and XSRF attacks so &lt; and &gt; should be avoided as the input from the users. My database will save LaTeX commands that can be rendered by both LaTeX compiler and MathJax. Therefore, I need \gt and \lt that already work in MathJax. Source:  Rendered: Here is the problem setup  \begin{equation} \begin{array}{c} \text{min} \hspace{4mm}  \mathbf{b}^{T}_{}\mathbf{A}^{}_{}\mathbf{b}^{}_{} \\ s.t \hspace{5mm} \mathbf{b} \in \mathbb{R}^{N} \\ \hspace{9mm}b_0=1\\ \hspace{62mm}b_i=b_{i-2}b_{i-1} \hspace{5mm} \forall \hspace{5mm} 2&lt;i\leq N-1 \end{array} \end{equation}  where $\mathbf{A}$ is a $N\times N$ positive semi-definite matrix  To handle $b_0=1$ constrain, I know I can introduce Lagrange multiplier in objective function  \begin{equation} \begin{array}{c} \text{min} \hspace{4mm}  \mathbf{b}^{T}_{}\mathbf{A}^{}_{}\mathbf{b}^{}_{} + \lambda(\mathbf{b}^{T}_{}\mathbf{u}^{}_{}-1) \end{array} \end{equation}  where $\mathbf{u}_{}^{}$ is a $N\times 1$ column vector and $u_0=1$ and $u_i=0 \forall 1&lt;i\leq N-1$.  But I dont know how to handle second set of constraints?   EDIT: Example  Let $N=4$. Therefore I am looking for $\mathbf{b}=[b_0 \quad b_1 \quad b_2 \quad b_3]^T = [1 \quad b_1 \quad b_2 \quad b_1b_2]^T$. How do I include $b_3=b_1b_2$ constraint in objective function Say I have the titanic kaggle competition, but I'm not interested in the competition for predicting survival for each individual. Instead I want the most accurate estimate of total survivors on the titanic. Would this be achieved by using a probabilistic model, then adding the probabilities for each individual? For example, if I have 3 people and 1 survived, but my model produced 0.4, 0.4, and 0.4 probabilities for each person to survive, I calculate 0 survived. But if I add 0.4 for each person, I get 1.2, which is closer to the actual. Does this make sense? Prove that the equation $x^2-y^2 = 2002$ has no integer solution Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$ I'm not sure how to go about this. Does it involve using MVT?  I got as far as saying $e = \frac{e^x - e^y}{x-y}$. Var[A+B+C] = Var [A] + Var [B] + Var [C] I know that this relationship is correct when A,B and C are pairwise independent. However, I'm finding it difficult to calculate it.  Let's say that: Var [A] = Var [B] = Var [C] = 0.25. How can I prove that Var[A+B+C] = 0.75?  I started to work with the formula: Var[A+B+C] =E[(A+B+C)^2]−(E[A+B+C])^2 but I got stuck.  Thanks! You can't see the question owner's special color When the owner of a question comments on their question or an answer to their question or self-answers their question, they get a special color for the box around their username.  The problem is, you can't see the box:        Can you please make this not white on white? Is it okay to keep flour in the freezer? Years ago I noticed I was getting little bugs in the flour that I kept in the pantry.  To prevent this, I started keeping my flour in the freezer.  I don't do a lot of baking, but I was wondering what effects this might have on anything I do bake.  Do baked goods turn out any differently when flour is kept in the freezer vs flour kept at room temperature?  Also, if it's okay to freeze flour, how long will it last this way? Characterization of weak convergence in $\ell_\infty$ Is there some simple characterization of weak convergence of sequences in the space $\ell_\infty$? If yes, is there some similar claim for nets?   I was only able to come up with a characterization of sequential weak convergence using limit along ultrafilters, which I will describe below. I wonder whether there is some insight into this characterization. (E.g. whether there is some simple reformulations which does not use ultralimits.) Moreover, I do not know whether at least this characterization works for nets, too.  We have the following result describing weak convergence in $C(K)$, see e.g. Corollary 3.138,  in Banach Space Theory by Fabian, Habala et al. (It is a consequence of Rainwater theorem and characterization of extreme points of unit ball in $C(K)^*$.)     Let $K$ be a compact topological space. Let $\{f_n\}$ be a bounded sequence in $C(K)$ and $f\in C(K)$. Then, if $f_n\to f$ pointwise, we have $f_n\overset{w}\to f$.   Moreover we have isometric isomorphism between $\ell_\infty$ and $C(\beta\mathbb N)$, which is described e.g. in the Wikipedia article on  or in  of Carothers' book A short course on Banach space theory. This isomorphism assigns to each bounded sequence $(x_n)$ the continuous function $\overline x$ on $\beta\mathbb N$ defined by $$\overline x(\mathscr U) = \operatorname{\mathscr U-lim} x_n,$$ where $\operatorname{\mathscr U-lim} x_n$ denotes the  of $x_n$ w.r.t the ultrafilter $\mathscr U$.  Combining the above results we get the following characterization:      Let $f^{(n)},f\in\ell_\infty$. The sequence $f^{(n)}$ converges to $f$ weakly if and only if for every ultrafilter $\mathscr U$    $$\lim_{n\to\infty} \operatorname{\mathscr U-lim} f^{(n)}= \operatorname{\mathscr U-lim} f.$$   (The above claim for principal ultrafilters is just a pointwise convergence. But in the above claim the equality is required for free ultrafilters, too.) How to determine exact contrast ratio Because of the recent Web accessibility Law in my region, I need to ensure I'm designing with an appropriate contrast ratio.  WCAG says the value of this ratio is 4.5:1    How do I figure this out in in Photoshop and Illustrator? I'm not sure how to remove the line that represents the 180th meridian (international dateline) on my polygon. I have the "Russia Country Boundary 2017" feature layer added from the Living Atlas. My Projected Coordinate System is set to "Asia North Albers Equal Area Conic". I've tried to google this question, but I haven't come across an answer I can fully understand. I'm a student and very new to all this!  The line is actually a gap between the polygons.   Using ArcGIS Pro 2.3.1  ANSWER:  It turns out I was not projecting correctly, which was creating issues down the line when editing polygons. Here's what I did...  1. Start a blank project in ArcGIS. Insert new map, go into its     properties, change the Coordinate System to "Asia North Albers Equal     Area Conic".  2. Add "World Countries (Generalized)" from the Living     Atlas. Select Russia and Export Features to new feature class layer.  3. Search and select the Project tool from Analysis>Geoprocessing>Tools.   4. Select the Russia layer for input. Select "Current Map" for Output Coordinate System. Run.  5.Now edit the polygons to close the gap and merge to remove any lines. All done!  The only thing that bothers me with this fix is the addition of shape area (484,914.49674 m²) and shape length (4.59 m) to the original Russia polygon. These numbers could be different depending on how you close the gap, and possibly affect data projections depending on your use of this map? On some Microsoft Access queries, I get the following message:  Operation must use an updatable query. (Error 3073).  I work around it by using temporary tables, but I'm wondering if there's a better way.  All the tables involved have a primary key. Here's the code:  UPDATE CLOG SET CLOG.NEXTDUE = (     SELECT H1.paidthru      FROM CTRHIST as H1     WHERE H1.ACCT = clog.ACCT AND     H1.SEQNO = (         SELECT MAX(SEQNO)          FROM CTRHIST          WHERE CTRHIST.ACCT = Clog.ACCT AND          CTRHIST.AMTPAID &gt; 0 AND         CTRHIST.DATEPAID &lt; CLOG.UPDATED_ON     ) ) WHERE CLOG.NEXTDUE IS NULL; Here is my candidate for  the most elementary proof that $\lim_{n \to \infty}(1+1/n)^n $ exists. I would be interested in seeing others.  $***$ Added after some comments: I prove here by very elementary means that the limit exists. Calling the limit "$e$" names it. $***$  It only needs Bernoulli's inequality (BI) in the form $(1+x)^n \ge 1+nx$ for $x &gt; -1$ and $n$ a positive integer, with equality only if $x = 0$ or $n = 1$. This is easily proved by induction: It is true for $n=1$, and $(1+x)^{n+1} = (1+x)(1+x)^n \ge (1+x)(1+nx) = 1+(n+1)x+nx^2 \ge 1+(n+1)x $. (If $-1 &lt; x &lt; 0$, if $1+nx \ge 0$, the above proof goes through, and if $1+nx &lt; 0$, $1+mx &lt; 0$ for all $m \ge n$ so certainly $(1+x)^m &gt; 1+mx$.)  This proof originally appeared in N.S Mendelsohn, An application of a famous inequality, Amer. Math. Monthly 58 (1951), 563 and uses the arithmetic-geometric mean inequality (AGMI) in the form $\big(\sum_{i=1}^n v_i/n\big)^n \ge \prod_{i=1}^n v_i$  (all $v_i$ positive) with equality if and only if all the $v_i$ are equal.  Let $a_n = (1+1/n)^n$ and $b_n = (1+1/n)^{n+1}$.  We will prove that $a_n$ is an increasing sequence  and $b_n$ is an decreasing sequence.  Since $a_n &lt; b_n$, this implies,  for any positive integers $n$ and $m$ with $m &lt; n$  that $a_m &lt; a_n &lt; b_n &lt; b_m$.  For $a_n$, consider n values of $1+1/n$ and $1$ value of $1$.  Since their sum is $n+2$ and their product is $(1+1/n)^n$, by the AGMI,  $((n+2)/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $(1+1/(n+1))^{n+1} &gt; (1+1/n)^n$,  or $a_{n+1} &gt; a_n$.  For $b_n$, consider $n$ values of $1-1/n$ and $1$ value of $1$.  Since their sum is $n$ and their product is $(1-1/n)^n$, by the AGMI,  $(n/(n+1))^{n+1} &gt; (1-1/n)^n$  or $(1+1/n)^{n+1} &lt; (1+1/(n-1))^n$,  or $b_n &gt; b_{n+1}$.  Since $b_n-a_n  = (1+1/n)^{n+1} - (1+1/n)^n = (1+1/n)^n(1/n) =a_n/n $ and every $a_n$ is less than any $b_n$ and $b_3 = (1+1/3)^4 = 256/81 &lt; 4$, $b_n-a_n &lt; 4/n$, so $b_n$ and $a_n$ converge to a common limit.  These proofs do not seem to be really elementary,  since they use the AGMI.  However, they use a special form of the AGMI,  where all but one of the values are the same,  and this will now be shown to be implied by BI,  and thus be truly elementary.   Suppose we have $n-1$ values of $u$ and $1$ value of $v$ with $u$ and $v$ positive.  The AGMI for these values is  $(((n-1)u+v)/n)^n \ge u^{n-1}v$  with equality if and only if $u = v$.  We will now show that this is implied by BI: $(((n-1)u+v)/n)^n \ge u^{n-1}v$  is the same as  $(u+(v-u)/n)^n \ge u^n(v/u)$.  Dividing by $u^n$,  this is equivalent to  $(1+(v/u-1)/n)^n \ge v/u$.  By BI,  since $(v/u-1)/n &gt; -1/n &gt; -1$, $(1+(v/u-1)/n)^n \ge 1+n((v/u-1)/n) = v/u$  with equality only if $n=1$ or $v/u-1 = 0$. Thus BI implies this version of the AGMI. Scaling vs Offsetting in Quasi-Poisson GLM I  modeled insurance claim frequency assuming a Quasi-Poisson distribution in R. My frequency dependent variable was calculated, in advance of modeling, as the number of claims per underlying exposure. Someone  that it would be incorrect to do this, and that the correct method was to model the observed claim counts and use the underlying exposure as an offset.   Can someone explain the theoretical and practical differences between scaling and offsetting? I ran the code both ways and noticed that the deviance residuals are significantly smaller when using offsets, but otherwise there were no material differences in variable selection.   P.S. Note the similar but still different question . How to deal with high correlation among predictors in multiple regression? I found a reference in an article that goes like:     According to Tabachnick &amp; Fidell (1996) the independent variables with   a bivariate correlation more than .70 should not be included in   multiple regression analysis.   Problem: I used in a multiple regression design 3 variables correlated >.80, VIF's at about .2 - .3, Tolerance ~ 4- 5. I cannot exclude any of them (important predictors and outcome). When I regressed the outcome on the 2 predictors which correlated at .80, they remained both significant, each predicted important variances, and these same two variables have   the largest part and semipartial correlation coefficients amongst all 10 variables included (5 controls).   Question: Is my model valid despite high correlations? Any references greatly welcomed!    Thank you for the answers!  I did not use Tabachnick and Fidell as a guideline, I found this reference in an article dealing with high collinearity amongst predictors.   So, basically, I have too few cases for the number of predictors in the model (many categorical, dummy coded control variables- age, tenure, gender, etc) - 13 variables for 72 cases. The Condition Index is ~ 29 with all the controls in and ~23 without them (5 variables).   I cannot drop any variable or use factorial analysis to combine them because theoretically they have sense on their own. It is too late to get more data. Since I am conducting the analysis in SPSS perhaps it would be best to find a syntax for ridge regression (although I haven't done this before and interpreting the results would be new to me).   If it matters, when I conducted stepwise regression, the same 2 highly correlated variables remained the single significant predictors of the outcome.  And I still do not understand if the partial correlations which are high for each of these variables matter as an explanation for why I have kept them in the model (in case ridge regression can't be performed).   Would you say the "Regression diagnostic: identifying influential data and sources of collinearity / David A. Belsley, Edwin Kuh and Roy E. Welsch, 1980" would be helpful in understanding multicollinearity? Or might other references be useful? Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition I have the following data structure (a list of lists)  [  ['4', '21', '1', '14', '2008-10-24 15:42:58'],   ['3', '22', '4', '2somename', '2008-10-24 15:22:03'],   ['5', '21', '3', '19', '2008-10-24 15:45:45'],   ['6', '21', '1', '1somename', '2008-10-24 15:45:49'],   ['7', '22', '3', '2somename', '2008-10-24 15:45:51'] ]   I would like to be able to   Use a function to reorder the list so that I can group by each item in the list. For example I'd like to be able to group by the second column (so that all the 21's are together)  Use a function to only display certain values from each inner list. For example i'd like to reduce this list to only contain the 4th field value of '2somename'    so the list would look like this   [      ['3', '22', '4', '2somename', '2008-10-24 15:22:03'],       ['7', '22', '3', '2somename', '2008-10-24 15:45:51'] ]