Gee Law’s Blog
Sharing data among apps is a common task in modern operating system. Both iOS and Windows Runtime provides central means of transmitting data from one app to another beyond the clipboard. In this entry, I will look at the sharing functionalities in both systems.
Group presentation is a method to express groups as a quotient of a free group and a normal subgroup. In a presentation, there are generators and relators, and the presentation yields a ‘minimalist implementation’ of these generators and relations. Some cases of special interests are finitely generated/related/presented groups. From the definition, finite generation + finite relation is not linguistically equivalent to finite presentation. There has been some discussion on the relation of the three properties for several other algebraic structures. This entry proves that finite generation + finite relation imples finite presentation for groups.
What goes wrong when arrows are reversed in the diagrams for direct product/sum universal properties?
I’m taking an algebra course and regaining my algebra sense (non-sense?). Familiar to us is that direct products [resp. sums] of groups [resp. abelian groups] possess their versions of universal properties. When reviewing these things, I went curious on what would go wrong if the arrows were reversed. Let’s try and see.
PowerShell 6.1.0 (preview) messes verbs of directories, causing Previous Versions to open previous verions of a directory in PowerShell
Issue #6799 in PowerShell repository on GitHub raises the question why Previous Versions is opening previous versions of a directory in PowerShell, instead of File Explorer as expected. The reason is that PowerShell 6.1.0 (preview) installer creates a context menu to open the shell on any folder. However, it unfortunately names the verbs as open/runas, which is very dangerous since they are canonical and do not make much sense for a folder. Related is issue #7815, where shortcuts to a folder are opened in PowerShell.