cheat_cs_1_6_ahel_v2

– B: background color
– N: ambient lights
– T: main highlights
– L: background lights
– M: main lights
– E: shadow
– K: colorize
– S: adjust luminosity
– X: colorize edges
-.: include color mode in the name
– +: add to color mode

A:

If you are on Windows with Photoshop, check out some of the free (no-Adobe-subscription) stuff I found:
Elements:
And there are a few others which I can’t remember the URLs for right now but I’ll add them in later if I can find them.

A:

One that I’ve found really handy for the PSD editor is PixelateX. It gives you the most commonly used tools and a lot of them are pixel-centric.

Q:

How to get all $1$-forms of a given degree

Let $U \subseteq \mathbb{C}^n$ be an open set. Consider a closed form $\omega \in \Omega^1(U)$ of degree $k$. How can one get all the forms $\omega’$ of degree $k$ such that $\omega – \omega’$ is exact?
I can only think of applying the standard scalar multiplication to the equality $\omega = \omega’+d(u)$ with $u \in \Omega^0(U)$ and solving for $\omega’$. However, this seems quite cumbersome.

A:

Consider the surjective $\mathbb{C}$-linear map $$\Omega^{k}(U) \to \bigoplus_{p+q = k} \Omega^{p,q}(U) \;, \; \omega \mapsto \left(\omega \wedge \beta \mapsto \int_\beta \omega\right) \;.$$
If $\omega = d\beta$, then $\beta$ is of type $(p,q)$ if and only if the image of $\omega$ is not contained in $\Omega^{p+1,q}(U)$. Thus if 384a16bd22

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