When a Microbot Alpha has been played, it gives an ongoing action of     [...] All of your minions are considered Microbots.   Does this include minions in your discard pile?  The question came up in a game where a subsequent Microbot Reclaimer was played, which states:     [...] Shuffle any number of Microbots from your discard pile into your deck.   Does this combination allow for reclaiming minions "considered" as Microbots, even when they are in the discard pile as well as from another faction?
Microbot Alpha says "All of your minions are considered Microbots."  Does this mean while this card is in play, every single minion in play and in discard and in my hand are considered Microbots?   For every Microbot Fixer in play, does every single minion I have in play now get +1 because they are all microbots? If Microbot Archive is in play, does every single minion I have now cause me to draw a card when destroyed? If I play Microbot Reclaimer, can I shuffle any minions from my discard pile into my deck (by considering them all microbots)?   It looks like this link addresses the first item above:   And it looks like this link addresses the 3rd item, implying that minions in the discard are not minions because they are out of play:
Primary decomposition of a monomial ideal Can anyone give me an idea about the primary decomposition of the ideal $I=(x^3y,xy^4)$ of the ring $R=k[x,y]$?    I am trying to connect the primary decomposition with the set Ass(R/I) which i have find before.. Behave as if it was or it were You can place the script in the head or body as you like. The   script will behave as if it was located exactly where you put the   script tag in the document.   The sentences above are taken from  (at the very bottom). I think they made a grammatical mistake here: it should be behave as if it were rather than it was. I'm not 100% sure, so want to confirm it. Is StringBuilder really faster than Aggreggate? Which process scheduler is my linux system using? I'm not quite sure if stackoverflow or serverfault is the forum to use for this question, but ill try here.  Is there some command I can use or a file I can check in order to find out which process scheduler I'm using on my Linux system? I am not looking for the I/O scheduler, but the process scheduler, and please, do not refer to guides or howtos for what a scheduler is, what I'm simply asking is if there is a command or file I can run/check to see this. I could check the doc for my kernel but again I'm just wondering if there is a command or file i can check.  I might have been a little redundant above but that's because the posts I've seen people seem to confuse process scheduler with the i/o scheduler, and they don't seem to answer the actual question, just provide links to what a scheduler is which is not what I'm after here, so apologies if the above comments sounded rude. Screen goes white when posting a comment Is Unit Testing worth the effort? I am working to integrate unit testing into the development process on the team I work on and there are some sceptics. What are some good ways to convince the sceptical developers on the team of the value of Unit Testing? In my specific case we would be adding Unit Tests as we add functionality or fixed bugs. Unfortunately our code base does not lend itself to easy testing. Show that a continuous function has a fixed point Question: Let $a, b \in \mathbb{R}$ with $a &lt; b$ and let $f: [a,b] \rightarrow [a,b]$ continuous. Show: $f$ has a fixed point, that is, there is an $x \in [a,b]$ with $f(x)=x$.  I suppose this has to do with the basic definition of continuity. The definition I am using is that $f$ is continuous at $a$ if $\displaystyle \lim_{x \to a} f(x)$ exists and if $\displaystyle \lim_{x \to a} f(x) = f(a)$. I must not be understanding it, since I am not sure how to begin showing this... Should I be trying to show that $x$ is both greater than or equal to and less than or equal to $\displaystyle \lim_{x \to a} f(x)$ ? What Lagrangian counterterms might be needed in a $\phi^ 6$ theory in 3D? Two-Weapon Fighting & Bonus Actions During the latest gaming session our level 3 Rogue was Two-Weapon fighting with a Rapier in the main-hand and a scimitar in the off-hand.  At the completion of our gaming session I contested the application of the Two-Weapon fighting rules as it seemed unbalanced.  Once I got home I reviewed the PHB and various RPGStack and Reddit but couldn't find a concrete answer.  My interpretation of the PHB Reference rules below is that although any class/character can technically wield a weapon in their off-hand, only those who have been granted a Bonus Action for which no explicit bonus action have been defined would be allowed to actually attack.  So in the case of a Rogue the Bonus Actions granted under Cunning Action allow for specific actions (none of which are attack).  The alternate interpretation would be the rules under Two-Weapon Fighting, perhaps it should be written      you receive a bonus action to attack with a different light melee weapon that you’re holding in the other hand.   This would, in my opinion, explicitly grant the Bonus Action to any character/class who is Two-Weapon Fighting.  After thorough review does it boil down to application of the rules-as-written and determining a house-rule to apply in our campaign?    References  Page 189 of PHB : Bonus Actions  Various class features, spells, and other abilities let you take an additional action on your turn called a bonus action. The Cunning Action feature, for example, allows a rogue to take a bonus action.      You can take a bonus action only when a special ability, spell, or other feature of the game states that you can do something as a bonus   action. You otherwise don’t have a bonus action to take.   You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available. You choose when to take a bonus action during your turn, unless the bonus action’s timing is specified, and anything that deprives you of your ability to take actions also prevents you from taking a bonus action.  Page 96 of PHB  A Rogue receives cunning action at level 2, You can take a bonus action on each of your turns in combat.      This action can be used only to take the Dash, Disengage, or Hide action.   Page 195 of PHB  Two-Weapon Fighting (Combat Rules)  When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.  Page 165 of PHB  Dual Wielder  (Feat)  You master fighting with two weapons, gaining the following benefits:   You gain a +1 bonus to AC while you are wielding a separate melee weapon in each hand. You can use two-weapon fighting even when the one-handed melee weapons you are wielding aren't light. You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one. The question asks to prove that -  $$\frac {\sin x} {\cos 3x} + \frac {\sin 3x} {\cos 9x} + \frac {\sin 9x} {\cos 27x}  = \frac 12 (\tan 27x - \tan x) $$  I tried combining the first two or the last two fractions on the L.H.S to allow me to use the double angle formula and get $\sin 6x$ or $\sin 18x$ but that did not help at all.   I'm pretty sure that if I express everything in terms of $x$, the answer will ultimately appear but I'm also certain that there must be another simpler way. When do we double the consonant before '-ing' affix? My son is learning how to spell. He is doing a good job listening to sounds and working out spelling that way (which doesn't work for many words, but at least a lot of common ones), but although he's gotten the -ing chunk, he frequently misses doubling letters in these words.  Is there a guideline for when the end consonant is doubled? He's working on these sorts of words:        riding   sitting   skating   writing   getting Splitting a large document into several files javax.faces.application.ViewExpiredException: View could not be restored Using one group separator for integer part and another for decimal part (siunitx) I thought I was able to do something like this before, but I can't find my solution.  I would like to format my large numbers as follows:   12,504.3124 2359 3   I know I can use siunitx to partially set this up, but I'm not getting the results I want:  \documentclass{article} \usepackage{siunitx}  \newcommand\aenumA[1][4]{%%   \num[group-separator={,},        group-digits=integer,        ]}  \newcommand\aenumB[1][4]{%%   \num[group-digits=decimal,        ]}  \pagestyle{empty} \begin{document}    \aenumA{12504.312423593}    \aenumB{12504.312423593}  \end{document}   I would like a hybrid solution (commas in the integer part and spaces in the decimal).  I would actually also like to be able to group differently between the two: every three digits in the integer part, every four digits in the decimal part.  Is there a straight-forward way to do this with siunitx?  Or, do I need to split the number at the decimal and treat the two parts separately and then glue them back together? What exactly is "base ISO" and how do I find what is base ISO on my camera? If I understood correctly, base ISO is in full stop steps from the lowest possible ISO setting on my camera. For example if the lowest setting on my camera is ISO 100, than the following table would be base ISO:    100, 200, 400, 800, 1600, 3200, 6400   While steps in between like   125, 160, 250, 320, 500, 640, 1000, 1300, 2000, 2500, 4000, 5000   would be third-stop "pulled" values, which result more noise than perhaps higher base ISO values (for example 2500 is worse than 3200).   Did I get this right or missed by a mile, what did I miss? Do non-base ISO values generate more noise than next higher base-value ISO stop? How do I find what are my base-value ISO stops (is it the lowest ISO value multiplied by 2n)? When does the amount of skew or prevalence of outliers make the median preferable to the mean? I know that "deviations in the data are devil", and when the distribution is highly skewed, it is better to consider median as average rather than mean, but how to decide these hard-limits.  For example:   CASE 1:   Assume X = 10,20,30,40,50,60,70 In this case, I think that it is better to use mean and that it will give very accurate results.  CASE 2:   Assume X = 10,20,30,40,50,60,70,7000 In this case, I think that it is better to use median instead of using the mean.  CASE 3:    Assume X = 10,20,30,400,500,600,700 In this case, I think it is better to use IQR (Inter Quartile Range)    But I'm stuck with how to decide these hard-limits i.e. which to use in which condition, in general.   I've found a tool working on subjected principle, which takes context-less sample-distribution as input and determines whether mean is close/moderate or against the null-hypothesis.  Find References:-     (For Mean Test)  (For Median Test)   What I'm really looking is a good answer which states how to derive these conclusions. If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$. Standard error of a ratio I have a linear regression and two estimates, say A and B and their standard errors. I need to find the standard error of a ratio A/B [or A/(1-B)].  I guess the main problem is that I don't know the correlation between A and B. I also guess that makes this unsolvable, since the correlation plays a major role. Is this correct?  If I knew it, what would be the way to calculate the standard error? I've seen plots of test/training error suddenly dropping at certain epoch(s) a few times during the neural network training, and I wonder what causes these performance jumps:    This image is taken from Kaiming He's Github, but similar plots show up in many papers. How can I modify my hot sauce to make it Shelf Stable? I would like to be able to can and then sell my own hot sauce. The hot sauce I make is a low acid meat (ground beef) and tomato based sauce. I had sent it in to get a shelf life expectancy, and was advised the acidity level was too low and the only way I could make the sauce in a way that it was shelf stable was if I used a retort or sold it as a frozen product. Neither of these are options I can consider at this time.