Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let’s call it $ f_\theta(t)$ , where $ \theta$ is a list of all parameters used in ParametricNDSolve.

For a given choice of the parameters $ \hat\theta$ , the ParametricFunction becomes a InterpolatingFunction object. I want to evaluate this function at multiple points $ \{t_1,t_2,…,t_n\}$ , which is, obtaining the value $ f_{\hat\theta}(t_i)$ .

Does Mathematica fully solve the system of equations each time I call $ f_{\hat\theta}(t_i)$ for a different $ i$ ? Or does it cache the InterpolatingFunction after the first call (let’s say, $ f_{\hat\theta}(t_1)$ ) and uses it to obtain the value of $ f_{\hat\theta}$ at $ t_2,…,t_n$ ?

Mathematica 12.0 returning a imaginary value for a real-valued improper integral

When I use MMA to solve this integral

Integrate[(1 - Cos[x])/( 2 - Cos[x] - Cos[y]), {x, -Pi, Pi}, {y, -Pi, Pi}] 

it returns 8I*Pi*Log[2], which is obviously wrong. If I iteratedly calculate it

Integrate[Integrate[(1 - Cos[x])/(2 - Cos[x] - Cos[y]), {y, -Pi, Pi}], {x, -Pi, Pi}] 

MMA gives 2Pi^2, which is correct. Can anybody give an explaination?

What is the status of using Mathematica under the new released windows 11?

I googled and could not find any information on this.

It is now possible to update from windows 10 to windows 11. I am using windows 10 now.

My question is: Has any one tried say Mathematica 12.3 on windows 11 yet? if so, were there any problems?

Will there be, any official announcement from WRI on if Mathematica will work as is on windows 11? or if there are any issues to worry about before upgrading to windows 11?

Of course, I could call Wolfram support and ask them. But I thought it will be more useful if this information is publicly available so not everyone has to call or email asking the same question.

What is the best source to learn how to use tensor operations (exterior algebra) in Mathematica?

I’m specifically interested in the TensorProduct,TensorWedge, HodgeDual and certain build in functions to do tensor arithmetic like TensorReduce, TensorExpand.

I would like to do exterior algebra calculations where I can choose to work with basis vectors as symbolic objects (and where I can choose to work without basis vectors).

To be explicit, I would like mathematica to do this input:

v = {v1, v2}; w = {w1, w2}; v\[TensorWedge]w  

desired output:

(v1 w2 - v2 v1) e1 \[TensorWedge] e2 

actual output (in normal form):

{{0, -v2 w1 + v1 w2}, {v2 w1 - v1 w2, 0}} 

If this is not possible what source gives the best advice on how to use mathematica to deal with exterior algebra related differential geometry topics ? A simple example code, video, guide or tutorial on the wolfram site would be optimal.

I want to change this matlab code to Mathematica? can you help me

my code have one matrix entry and works as QR decompose method by using Givens rotation and its outputs contain 2 matrix as Q and R I want to run this code in mathematica without using Matlink package…..can you help me by rewriting this code in mathematica Language eye is the IdentityMatrix and norm(a,b) is $ \sqrt{(a^2+b^2)}$ Thank you for HELP

function [Q,R] = my_givens_QR(A) n = size(A,1);  Q=eye(n); R=A; for j=1:n for i=n:(-1):j+1 x=R(:,j); if norm([x(i-1),x(i)])>0 c=x(i-1)/norm([x(i-1),x(i)]); s=-x(i)/norm([x(i-1),x(i)]); G=eye(n); G([i-1,i],[i-1,i])=[c,s;-s,c]; R=G'*R; Q=Q*G; end end end 

RegionPlot and ColorFunction strangely inaccurate in Mathematica 12.3

Here is a simple example of a RegionPlot of a disk with a user-defined ColorFunction that is supposed to be rendered with high quality according to my expectation. However, both the disk boundary is not rendered very precisely (polygon shape is recognizable despite PlotPoints -> 100 and PerformanceGoal -> "Quality") and the color function is very imprecisely reflected as well. Is this a problem with Mathematica 12.3 or is the problem in my formulation?

pts = Thread[RandomPoint[Disk[], 10] -> RandomColor[10]]; RegionPlot[   Disk[],   ColorFunction -> Function[{x, y}, Nearest[pts, {x, y}]],   ColorFunctionScaling -> False,   PerformanceGoal -> "Quality",   PlotPoints -> 100 ] 

Screenshot