C Point Version July 2003 By Andrea Kohlhase, The Course Capsules Project (CCaps),CMU Look at our website CCaps for latest news!CCaps C ategorize Objects to add value C ontent For marking up objects C onvert To other formats C o nn ect To other applications

My test axiom My  axiom This is an inserted symbol  And   and  Infinity This is a character with a special font R RealR TestSymbol Plus Definitions: Text Sections With use of Symbols (defined in the Definitions) Math Text

Theory test2 My test2 axiom My test2 assertion My test2 conclusion

My R axiom For all α, β in R, we have  α * β in R My  claim My next test Andreas Test QMath 2

Annotation Details Forms Theory Example Question Counter Example Answer Rhetorical Question CommentNote ExerciseSolutionHint Assertion Proof Step Remark CodeGraphics Moti- vation Warning Intro- duction No OMDoc DefinitionAxiom Each object on this slide is annotated! QMath 1  

Mein Lieblingstitel Theory for the rest of the world Liste mit Symbolen: Liste1  1. Liste11  2.Liste12  3.Liste13  Liste 2 My ordered list21 My unordered sublist212

Not Uniform list with linked image Uniform 1 Uniform2 Uniform Bonus: Uniform 12

Time bounds Variables –M operations.N elements. Algorithms –Simple forest representation in arrays Worst: find O(N). mixed operations O(MN). Average: tricky –Union by height; Union by size Worst: find O(log N). mixed operations O(M log N). Average: mixed operations O(M) [see text] –Path compression in find Worst: mixed operations: “nearly linear” [analysis forthcoming]

Group tests Groupelement with text T  es  t1 T  e  st2 Test3 This is a nested group (=group in group) These are simple groups

Character entities? This is a character entity ¼. This is another one Ŵ. Ƣ –Symbols(inserted by Insert Symbol):ÐǼ, – SymbolFont: 

Table 1a1B1D 2A2B2C 3A3B 4a

find flattens trees Redirect nodes to point directly to the root Graphics? a d e b f c This is a group  This is not a group, but may be annotated as graphics! In fact: it is with “image only”-property. That means the ovals and arrows are not considered independent objects any more in terms of CPoint. Do this whenever traversing a path from node to root.

find flattens trees Redirect nodes to point directly to the root Graphics? (II) a d e b f c This is a group  This is not a group, but may be annotated as graphics! In fact: it is with “disregard underlying structure”-property. That means the ovals and arrows are not considered independent objects any more in terms of CCaps. This is annotated as graphics! (Disregarding underlying structure) This is annotated as graphics. (Regarding underlying structure)

All the code in Java (annotated as Code) class UnionFind { int[] u; UnionFind(int n) { u = new int[n]; for (int i = 0; i < n; i++) u[i] = -1; } int find(int i) { int j,root; for (j = i; u[j] >= 0; j = u[j]) ; root = j; while (u[i] >= 0) { j = u[i]; u[i] = root; i = j; } return root; } void union(int i,int j) { i = find(i); j = find(j); if (i !=j) { if (u[i] < u[j]) { u[i] += u[j]; u[j] = i; } else { u[j] += u[i]; u[i] = j; } }

Some Proofs First we state the theorem Then comes the first proof step And now the second one This concludes the proof QED My Proofstep for this theorem

My TexPoint Test As LaTex isn’t working on H: (or I can’t find it), it is just an error, but the source of this error in LaTex should be outputted in the OMDoc document

My OLEObjects This chart was inserted as an embedded OLE Object ….

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