MaplePrimes - Newest Comments

something is wrong in whole idea...

salim-barzani — Thu, 25 Jun 2026 17:30:16 Z

@dharr really i am stuck bad and i have to pass this topic not becuase we can't find it is becuase in this way and shape is not true if sigma be zero it seems there is no any effect of stocastic or maybe we can't find true derivative of the term which can have winer process term, i asked a lot specially my supervisor which his student did a lot paper on this topic but he use the ready ode he say we have same issue too and they show the effect also my supervisor told me the winerprocess take derivative from it is so different is not normal but how i really i can't go looking for that becuase i have a lot sequncing paper which have to finish , really aprciate of your work and you did the best job in this topic if be like that as we think all paper will retrack in this topic

Hi @Hullzie16I am busy with other stuff but ...

ecterrab — Thu, 25 Jun 2026 15:10:51 Z

Hi @Hullzie16
I am busy with other stuff but here is the gist. First a screenshot of the relevant part of the worksheet you attached:

The relevant comments:

In this derivation found in your worksheet, no matter that in your mind (5) is an approximation, for the computer, g is the Minkowski metric (you didn't set it to something else). But in (5) eta is also the Minkowski metric (you set it as such in (4)). Therefore, for (5) to be true, h = 0 and in (11) you get delta = delta.
In general, exactly, not an approximation, if A, B and C are tensors and you have A = B + C, that is true with the + sign regardless of whether the indices are covariant or contravariant. So if g = eta + h when their indices are covariant, the + sign remains + when you raise the indices.
One consequence is that if spacetime is curved and eta[mu, nu] has the matrix form corresponding to (-1, 1, 1, 1) then, exactly (not approximately) eta[~mu, ~nu] does not have that form.

To avoid these subtleties and be able to compute with "approximations" and "exact" tensor equations at the same time, as we do when working with "linearized" gravity, you can use Physics:-Library:-Linearize with exact tensor equations, and all it does is as explained in its (mini) help page within the large Physics:-Library help page: "Linearize receives a tensorial expression "T" that depends on a perturbation "h" and discards all terms quadratic or of higher order in "h" and its derivatives." That is why the computations shown there work as expected; also what you noticed when saying "Now, this does not give any invalid results for the Ricci tensor as displayed in the worksheet, since we are only going to linear order".

Note as well that the section on Linearized Gravity in the help page Physics,Tensors goes beyond the linearized Ricci tensor, deriving also correct linearized Einstein equations in different gauges.

Edgardo S. Cheb-Terrab
ExaktAI
Research Fellow Emeritus at Maplesoft.

sigma=0

dharr — Thu, 25 Jun 2026 00:22:06 Z

See https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma#Motivation

where the term with sigma is not involved in the expectation. But then I'm not sure why sigma would remain in the phase factor.

adjustments

dharr — Thu, 25 Jun 2026 00:11:23 Z

@salim-barzani Notice that there is a u on the rhs side of the pde, so I expect to be able to cancel the exp parts, and this does work out.

You forgot to differentiate zeta(t) in the pde. And the paper had missing parentheses - if the exp bit is supposed to be the phase factor, then it must be exp(I*(X+Y)) not exp(I*X+Y).

But you still have to set sigma to zero, so I think this has to be part of the way to deal with stochastic pdes. Sigma still appears in the phase factor, so the solution has randomness still.

F-ode-Fpaper.mw

memoization

acer — Wed, 24 Jun 2026 11:19:24 Z

@C_R Some of the internals of dsolve utilize remember tables or a cache, which avoids duplicate re-computation if the call to the command is repeated.

Some of that affects some of the userinfo messages (since some of those userinfo calls are made underneath such an internal entry point).

Note that your Document doesn't begin with a restart, so if you re-run it without restarting via the ribbon then some or the computations are memoized.

something is wrong cancelation

salim-barzani — Wed, 24 Jun 2026 07:56:36 Z

@dharr in a lot of paper if focus on it is clear a term must be appear in the first derivative of (G_t) which must remove that term including the (tau) or any variable with t appear i changed a lot of other pde but all of them is like that so something is wrong we do

F-ode-Fpaper.mw

link