derivate

I new with Python and much more with Sympy, I'm trying to solve an equation; the user introduces the equation and the value of 'x'. Example: eq: x**2+x*3+1, x = 4, so the 4 should be replaced on the 'x' of the equation and calculate the result.

This is what I have been trying:

So, my issue concerns vectors, I don't know where I'm going with that case. I'm building a pandemic simulation (using Javascript and the library p5.js), and I'm trying to add a lockdown feature.

Here is an image to make everything clearer:

Essentially, at the moment, when two molecules collide, their velocity vector change appropriately by switching their former velocity.

I've reached a wall in publishing my paper due to the issue of two platonic solids I'm coding for their SA:V: The cube and octahedron.

Normally, when one derivates the SA:V ratio for a cube and octahedron, it will come out to 6/a and (3*sqrt(6))/a, respectively.

When you take those ratios as a ratio, you get a constant non 1:1 ratio for all size regimes so, how is my output a 1:1 relationship?

Output (click link):

Graph of Ratios:

Table

Relevant code for both shapes in all instances for user request, tabulation, and graphing (ignore icosahedron code): First Instance:

I was reading the chapter "Object-Oriented Programming" in "Programming in Lua" on https://www.lua.org/pil/16.html.

In that example, they create this "constructor":

I was looking through the Spatial Transformer Network paper, and I am trying to implement a custom grid_sample function (inheriting the autograd.Function class) in PyTorch for the Integer Sampling Kernel.

While defining the backward function, I have come across the following conundrum.

Given that the integer sampling works as the following:

I think that the gradients w.r.t the input map and the transformed grid (x_i^s, y_i^s) should be like the following:

Gradient w.r.t. input map:

Gradient w.r.t transformed grid (x_i^s):

Gradient w.r.t transformed grid (y_i^s):

as the derivative of the Kronecker delta function is zero (I'm unsure about this!! - HELP)

Derivative of the Kronecker delta?

Thus I am reaching a conclusion that the gradient w.r.t to the input should be: a tensor of the same size as the input filled with ones if the pixel was sampled and 0 if it wasn't sampled, and the gradient w.r.t the transformed grid should be a tensor full of zeros.

However, if the gradient of the transformed grid is 0, then due to the chain rule, no information will be passed on to the layers before the integer sampler. Therefore I think the derivate with respect to the grid should be something else. Could anybody point out what I'm doing wrong?

Many thanks in advance!

Let's say I have a WorkBank DB with words for a particular language. For example, Russian. Russian words have different endings due to quantity and cases (Nominative, Accusative, etc.)

So, Student may be:

студент студента

and whatnot...

There are other languages, like for example English where a verb can have different forms based on its tense (speak, spoke, spoken, etc). Also, other languages like Italian and French where words may be joined with another one:

hôtel = hotel l'hôtel = the hotel

anatra = duck l'anatra = the duck

I would like to store all words in the WorkBank, however, I would like link them to their parent word and to differentiate unique words vs derivated words, so all forms of студент and all forms of "speak" would count only one.

I know this is a very broad subject and I am not asking for a solution. I would really appreciate if someone could point me the right direction or any documentation I could read to start implementing this.

I'm working with some bezier curves. I get my position at parameter using directly matrices, no decasteljau involved, I find it more elegant:

I'm quite new to linux shell scripting and have a question:

1.) why does the command

test1="leafpad" && coproc exec "$test1"

work in bash (commandline, GNU bash 4.4.12 on a debian derivate linux), but the command

test1="coproc" && exec "$test1" leafpad

does not? Error messages: bash: exec: coproc: Not found.

whereas coproc leafpad does work as expected.

How this command must be correct quouted to make it work? I've tried already

test1=`coproc` && exec "$test1" leafpad

test1='coproc' && exec "$test1" leafpad

test1="'coproc'" && exec "$test1" leafpad

test1=`coproc` && exec '$test1' leafpad

test1=`coproc` && exec `$test1` leafpad

test1="coproc" && exec $test1 leafpad

test1=`coproc` && exec $test1 leafpad

and some more variations, but none of them works.

2.) This was the test on commandline only. But what I rather need is to do this within a script: So I'm sure there are to be done some additional quotations or masquerading of special characters.

Background: I have to execute a command, containing many arguments, some of them replaced by variables. Think of something like yad with all its possible arguments in a couple of lines, but let's create an easier example:

I'm trying to make a Blazor component that I will then specialize and override some methods.

Base Component "ZoomList":