From e8fcbfb46f9d7badd043b9daca9659bbd45f84ee Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Andreas=20M=C3=BCller?= Date: Sat, 10 Apr 2021 22:56:28 +0200 Subject: new images --- vorlesungen/slides/7/Makefile.inc | 1 + vorlesungen/slides/7/chapter.tex | 1 + vorlesungen/slides/7/images/Makefile | 9 +- vorlesungen/slides/7/images/c/c01.jpg | Bin 0 -> 89652 bytes vorlesungen/slides/7/images/c/c02.jpg | Bin 0 -> 91977 bytes vorlesungen/slides/7/images/c/c03.jpg | Bin 0 -> 92274 bytes vorlesungen/slides/7/images/c/c04.jpg | Bin 0 -> 90229 bytes vorlesungen/slides/7/images/c/c05.jpg | Bin 0 -> 91184 bytes vorlesungen/slides/7/images/c/c06.jpg | Bin 0 -> 91815 bytes vorlesungen/slides/7/images/c/c07.jpg | Bin 0 -> 93209 bytes vorlesungen/slides/7/images/c/c08.jpg | Bin 0 -> 94763 bytes vorlesungen/slides/7/images/c/c09.jpg | Bin 0 -> 96009 bytes vorlesungen/slides/7/images/c/c10.jpg | Bin 0 -> 97027 bytes vorlesungen/slides/7/images/c/c11.jpg | Bin 0 -> 98137 bytes vorlesungen/slides/7/images/c/c12.jpg | Bin 0 -> 99295 bytes vorlesungen/slides/7/images/c/c13.jpg | Bin 0 -> 100147 bytes vorlesungen/slides/7/images/c/c14.jpg | Bin 0 -> 101194 bytes vorlesungen/slides/7/images/c/c15.jpg | Bin 0 -> 101868 bytes vorlesungen/slides/7/images/c/c16.jpg | Bin 0 -> 102544 bytes vorlesungen/slides/7/images/c/c17.jpg | Bin 0 -> 104255 bytes vorlesungen/slides/7/images/c/c18.jpg | Bin 0 -> 105202 bytes vorlesungen/slides/7/images/c/c19.jpg | Bin 0 -> 106230 bytes vorlesungen/slides/7/images/c/c20.jpg | Bin 0 -> 106768 bytes vorlesungen/slides/7/images/c/c21.jpg | Bin 0 -> 107806 bytes vorlesungen/slides/7/images/c/c22.jpg | Bin 0 -> 108712 bytes vorlesungen/slides/7/images/c/c23.jpg | Bin 0 -> 110159 bytes vorlesungen/slides/7/images/c/c24.jpg | Bin 0 -> 111085 bytes vorlesungen/slides/7/images/c/c25.jpg | Bin 0 -> 111563 bytes vorlesungen/slides/7/images/c/c26.jpg | Bin 0 -> 113074 bytes vorlesungen/slides/7/images/c/c27.jpg | Bin 0 -> 114026 bytes vorlesungen/slides/7/images/c/c28.jpg | Bin 0 -> 114945 bytes vorlesungen/slides/7/images/c/c29.jpg | Bin 0 -> 115822 bytes vorlesungen/slides/7/images/c/c30.jpg | Bin 0 -> 117059 bytes vorlesungen/slides/7/images/c/c31.jpg | Bin 0 -> 118367 bytes vorlesungen/slides/7/images/c/c32.jpg | Bin 0 -> 118665 bytes vorlesungen/slides/7/images/c/c33.jpg | Bin 0 -> 120098 bytes vorlesungen/slides/7/images/c/c34.jpg | Bin 0 -> 121217 bytes vorlesungen/slides/7/images/c/c35.jpg | Bin 0 -> 122325 bytes vorlesungen/slides/7/images/c/c36.jpg | Bin 0 -> 122812 bytes vorlesungen/slides/7/images/c/c37.jpg | Bin 0 -> 123804 bytes vorlesungen/slides/7/images/c/c38.jpg | Bin 0 -> 124962 bytes vorlesungen/slides/7/images/c/c39.jpg | Bin 0 -> 125724 bytes vorlesungen/slides/7/images/c/c40.jpg | Bin 0 -> 126927 bytes vorlesungen/slides/7/images/c/c41.jpg | Bin 0 -> 127858 bytes vorlesungen/slides/7/images/c/c42.jpg | Bin 0 -> 128953 bytes vorlesungen/slides/7/images/c/c43.jpg | Bin 0 -> 129970 bytes vorlesungen/slides/7/images/c/c44.jpg | Bin 0 -> 130975 bytes vorlesungen/slides/7/images/c/c45.jpg | Bin 0 -> 131873 bytes vorlesungen/slides/7/images/c/c46.jpg | Bin 0 -> 132818 bytes vorlesungen/slides/7/images/c/c47.jpg | Bin 0 -> 133829 bytes vorlesungen/slides/7/images/c/c48.jpg | Bin 0 -> 134665 bytes vorlesungen/slides/7/images/c/c49.jpg | Bin 0 -> 135442 bytes vorlesungen/slides/7/images/c/c50.jpg | Bin 0 -> 136606 bytes vorlesungen/slides/7/images/c/c51.jpg | Bin 0 -> 136916 bytes vorlesungen/slides/7/images/c/c52.jpg | Bin 0 -> 137866 bytes vorlesungen/slides/7/images/c/c53.jpg | Bin 0 -> 138695 bytes vorlesungen/slides/7/images/c/c54.jpg | Bin 0 -> 139282 bytes vorlesungen/slides/7/images/c/c55.jpg | Bin 0 -> 140090 bytes vorlesungen/slides/7/images/c/c56.jpg | Bin 0 -> 140469 bytes vorlesungen/slides/7/images/c/c57.jpg | Bin 0 -> 141408 bytes vorlesungen/slides/7/images/c/c58.jpg | Bin 0 -> 141554 bytes vorlesungen/slides/7/images/c/c59.jpg | Bin 0 -> 142018 bytes vorlesungen/slides/7/images/c/c60.jpg | Bin 0 -> 142174 bytes vorlesungen/slides/7/images/common.inc | 70 +++++++++++++++ vorlesungen/slides/7/images/commutator.ini | 8 ++ vorlesungen/slides/7/images/commutator.m | 111 +++++++++++++++++++++++ vorlesungen/slides/7/images/commutator.pov | 59 ++++++++++++ vorlesungen/slides/7/kommutator.tex | 139 +++++++++++++++++++++++++++++ vorlesungen/slides/7/sl2.tex | 26 ++++++ vorlesungen/slides/test.tex | 8 +- 70 files changed, 427 insertions(+), 5 deletions(-) create mode 100644 vorlesungen/slides/7/images/c/c01.jpg create mode 100644 vorlesungen/slides/7/images/c/c02.jpg create mode 100644 vorlesungen/slides/7/images/c/c03.jpg create mode 100644 vorlesungen/slides/7/images/c/c04.jpg create mode 100644 vorlesungen/slides/7/images/c/c05.jpg create mode 100644 vorlesungen/slides/7/images/c/c06.jpg create mode 100644 vorlesungen/slides/7/images/c/c07.jpg create mode 100644 vorlesungen/slides/7/images/c/c08.jpg create mode 100644 vorlesungen/slides/7/images/c/c09.jpg create mode 100644 vorlesungen/slides/7/images/c/c10.jpg create mode 100644 vorlesungen/slides/7/images/c/c11.jpg create mode 100644 vorlesungen/slides/7/images/c/c12.jpg create mode 100644 vorlesungen/slides/7/images/c/c13.jpg create mode 100644 vorlesungen/slides/7/images/c/c14.jpg create mode 100644 vorlesungen/slides/7/images/c/c15.jpg create mode 100644 vorlesungen/slides/7/images/c/c16.jpg create mode 100644 vorlesungen/slides/7/images/c/c17.jpg create mode 100644 vorlesungen/slides/7/images/c/c18.jpg create mode 100644 vorlesungen/slides/7/images/c/c19.jpg create mode 100644 vorlesungen/slides/7/images/c/c20.jpg create mode 100644 vorlesungen/slides/7/images/c/c21.jpg create mode 100644 vorlesungen/slides/7/images/c/c22.jpg create mode 100644 vorlesungen/slides/7/images/c/c23.jpg create mode 100644 vorlesungen/slides/7/images/c/c24.jpg create mode 100644 vorlesungen/slides/7/images/c/c25.jpg create mode 100644 vorlesungen/slides/7/images/c/c26.jpg create mode 100644 vorlesungen/slides/7/images/c/c27.jpg create mode 100644 vorlesungen/slides/7/images/c/c28.jpg create mode 100644 vorlesungen/slides/7/images/c/c29.jpg create mode 100644 vorlesungen/slides/7/images/c/c30.jpg create mode 100644 vorlesungen/slides/7/images/c/c31.jpg create mode 100644 vorlesungen/slides/7/images/c/c32.jpg create mode 100644 vorlesungen/slides/7/images/c/c33.jpg create mode 100644 vorlesungen/slides/7/images/c/c34.jpg create mode 100644 vorlesungen/slides/7/images/c/c35.jpg create mode 100644 vorlesungen/slides/7/images/c/c36.jpg create mode 100644 vorlesungen/slides/7/images/c/c37.jpg create mode 100644 vorlesungen/slides/7/images/c/c38.jpg create mode 100644 vorlesungen/slides/7/images/c/c39.jpg create mode 100644 vorlesungen/slides/7/images/c/c40.jpg create mode 100644 vorlesungen/slides/7/images/c/c41.jpg create mode 100644 vorlesungen/slides/7/images/c/c42.jpg create mode 100644 vorlesungen/slides/7/images/c/c43.jpg create mode 100644 vorlesungen/slides/7/images/c/c44.jpg create mode 100644 vorlesungen/slides/7/images/c/c45.jpg create mode 100644 vorlesungen/slides/7/images/c/c46.jpg create mode 100644 vorlesungen/slides/7/images/c/c47.jpg create mode 100644 vorlesungen/slides/7/images/c/c48.jpg create mode 100644 vorlesungen/slides/7/images/c/c49.jpg create mode 100644 vorlesungen/slides/7/images/c/c50.jpg create mode 100644 vorlesungen/slides/7/images/c/c51.jpg create mode 100644 vorlesungen/slides/7/images/c/c52.jpg create mode 100644 vorlesungen/slides/7/images/c/c53.jpg create mode 100644 vorlesungen/slides/7/images/c/c54.jpg create mode 100644 vorlesungen/slides/7/images/c/c55.jpg create mode 100644 vorlesungen/slides/7/images/c/c56.jpg create mode 100644 vorlesungen/slides/7/images/c/c57.jpg create mode 100644 vorlesungen/slides/7/images/c/c58.jpg create mode 100644 vorlesungen/slides/7/images/c/c59.jpg create mode 100644 vorlesungen/slides/7/images/c/c60.jpg create mode 100644 vorlesungen/slides/7/images/common.inc create mode 100644 vorlesungen/slides/7/images/commutator.ini create mode 100644 vorlesungen/slides/7/images/commutator.m create mode 100644 vorlesungen/slides/7/images/commutator.pov create mode 100644 vorlesungen/slides/7/kommutator.tex (limited to 'vorlesungen') diff --git a/vorlesungen/slides/7/Makefile.inc b/vorlesungen/slides/7/Makefile.inc index ef004ca..540b080 100644 --- a/vorlesungen/slides/7/Makefile.inc +++ b/vorlesungen/slides/7/Makefile.inc @@ -15,6 +15,7 @@ chapter5 = \ ../slides/7/einparameter.tex \ ../slides/7/ableitung.tex \ ../slides/7/liealgebra.tex \ + ../slides/7/kommutator.tex \ ../slides/7/dg.tex \ ../slides/7/chapter.tex diff --git a/vorlesungen/slides/7/chapter.tex b/vorlesungen/slides/7/chapter.tex index 44d46a6..5878164 100644 --- a/vorlesungen/slides/7/chapter.tex +++ b/vorlesungen/slides/7/chapter.tex @@ -14,4 +14,5 @@ \folie{7/einparameter.tex} \folie{7/ableitung.tex} \folie{7/liealgebra.tex} +\folie{7/kommutator.tex} \folie{7/dg.tex} diff --git a/vorlesungen/slides/7/images/Makefile b/vorlesungen/slides/7/images/Makefile index 1b9590d..cc67c8a 100644 --- a/vorlesungen/slides/7/images/Makefile +++ b/vorlesungen/slides/7/images/Makefile @@ -3,10 +3,17 @@ # # (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule #  -all: rodriguez.jpg +all: rodriguez.jpg rodriguez.png: rodriguez.pov povray +A0.1 -W1920 -H1080 -Orodriguez.png rodriguez.pov rodriguez.jpg: rodriguez.png convert -extract 1740x1070+135+10 rodriguez.png rodriguez.jpg + +commutator: commutator.ini commutator.pov common.inc + povray +A0.1 -W1920 -H1080 -Oc/c.png commutator.ini +jpg: + for f in c/c*.png; do convert $${f} c/`basename $${f} .png`.jpg; done + + diff --git a/vorlesungen/slides/7/images/c/c01.jpg b/vorlesungen/slides/7/images/c/c01.jpg new file mode 100644 index 0000000..b2dbdb2 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c01.jpg differ diff --git a/vorlesungen/slides/7/images/c/c02.jpg b/vorlesungen/slides/7/images/c/c02.jpg new file mode 100644 index 0000000..9b45ba3 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c02.jpg differ diff --git a/vorlesungen/slides/7/images/c/c03.jpg b/vorlesungen/slides/7/images/c/c03.jpg new file mode 100644 index 0000000..882be40 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c03.jpg differ diff --git a/vorlesungen/slides/7/images/c/c04.jpg b/vorlesungen/slides/7/images/c/c04.jpg new file mode 100644 index 0000000..5d26572 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c04.jpg differ diff --git a/vorlesungen/slides/7/images/c/c05.jpg b/vorlesungen/slides/7/images/c/c05.jpg new file mode 100644 index 0000000..458f565 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c05.jpg differ diff --git a/vorlesungen/slides/7/images/c/c06.jpg b/vorlesungen/slides/7/images/c/c06.jpg new file mode 100644 index 0000000..cd40cda Binary files /dev/null and b/vorlesungen/slides/7/images/c/c06.jpg differ diff --git a/vorlesungen/slides/7/images/c/c07.jpg b/vorlesungen/slides/7/images/c/c07.jpg new file mode 100644 index 0000000..3349795 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c07.jpg differ diff --git a/vorlesungen/slides/7/images/c/c08.jpg b/vorlesungen/slides/7/images/c/c08.jpg new file mode 100644 index 0000000..65048cf Binary files /dev/null and b/vorlesungen/slides/7/images/c/c08.jpg differ diff --git a/vorlesungen/slides/7/images/c/c09.jpg b/vorlesungen/slides/7/images/c/c09.jpg new file mode 100644 index 0000000..000d502 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c09.jpg differ diff --git a/vorlesungen/slides/7/images/c/c10.jpg b/vorlesungen/slides/7/images/c/c10.jpg new file mode 100644 index 0000000..064c96b Binary files /dev/null and b/vorlesungen/slides/7/images/c/c10.jpg differ diff --git a/vorlesungen/slides/7/images/c/c11.jpg b/vorlesungen/slides/7/images/c/c11.jpg new file mode 100644 index 0000000..c67bc5d Binary files /dev/null and b/vorlesungen/slides/7/images/c/c11.jpg differ diff --git a/vorlesungen/slides/7/images/c/c12.jpg b/vorlesungen/slides/7/images/c/c12.jpg new file mode 100644 index 0000000..f2174de Binary files /dev/null and b/vorlesungen/slides/7/images/c/c12.jpg differ diff --git a/vorlesungen/slides/7/images/c/c13.jpg b/vorlesungen/slides/7/images/c/c13.jpg new file mode 100644 index 0000000..3cb5ae6 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c13.jpg differ diff --git a/vorlesungen/slides/7/images/c/c14.jpg b/vorlesungen/slides/7/images/c/c14.jpg new file mode 100644 index 0000000..6985e4f Binary files /dev/null and b/vorlesungen/slides/7/images/c/c14.jpg differ diff --git a/vorlesungen/slides/7/images/c/c15.jpg b/vorlesungen/slides/7/images/c/c15.jpg new file mode 100644 index 0000000..5bb5aed Binary files /dev/null and b/vorlesungen/slides/7/images/c/c15.jpg differ diff --git a/vorlesungen/slides/7/images/c/c16.jpg b/vorlesungen/slides/7/images/c/c16.jpg new file mode 100644 index 0000000..cc77fa1 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c16.jpg differ diff --git a/vorlesungen/slides/7/images/c/c17.jpg b/vorlesungen/slides/7/images/c/c17.jpg new file mode 100644 index 0000000..a60e2e9 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c17.jpg differ diff --git a/vorlesungen/slides/7/images/c/c18.jpg b/vorlesungen/slides/7/images/c/c18.jpg new file mode 100644 index 0000000..1d08c29 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c18.jpg differ diff --git a/vorlesungen/slides/7/images/c/c19.jpg b/vorlesungen/slides/7/images/c/c19.jpg new file mode 100644 index 0000000..9210c60 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c19.jpg differ diff --git a/vorlesungen/slides/7/images/c/c20.jpg b/vorlesungen/slides/7/images/c/c20.jpg new file mode 100644 index 0000000..8951883 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c20.jpg differ diff --git a/vorlesungen/slides/7/images/c/c21.jpg b/vorlesungen/slides/7/images/c/c21.jpg new file mode 100644 index 0000000..5169c7e Binary files /dev/null and b/vorlesungen/slides/7/images/c/c21.jpg differ diff --git a/vorlesungen/slides/7/images/c/c22.jpg b/vorlesungen/slides/7/images/c/c22.jpg new file mode 100644 index 0000000..bdeb90b Binary files /dev/null and b/vorlesungen/slides/7/images/c/c22.jpg differ diff --git a/vorlesungen/slides/7/images/c/c23.jpg b/vorlesungen/slides/7/images/c/c23.jpg new file mode 100644 index 0000000..fa3eac7 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c23.jpg differ diff --git a/vorlesungen/slides/7/images/c/c24.jpg b/vorlesungen/slides/7/images/c/c24.jpg new file mode 100644 index 0000000..52adc13 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c24.jpg differ diff --git a/vorlesungen/slides/7/images/c/c25.jpg b/vorlesungen/slides/7/images/c/c25.jpg new file mode 100644 index 0000000..d557497 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c25.jpg differ diff --git a/vorlesungen/slides/7/images/c/c26.jpg b/vorlesungen/slides/7/images/c/c26.jpg new file mode 100644 index 0000000..f825f49 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c26.jpg differ diff --git a/vorlesungen/slides/7/images/c/c27.jpg b/vorlesungen/slides/7/images/c/c27.jpg new file mode 100644 index 0000000..0de6c3e Binary files /dev/null and b/vorlesungen/slides/7/images/c/c27.jpg differ diff --git a/vorlesungen/slides/7/images/c/c28.jpg b/vorlesungen/slides/7/images/c/c28.jpg new file mode 100644 index 0000000..d9f89a4 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c28.jpg differ diff --git a/vorlesungen/slides/7/images/c/c29.jpg b/vorlesungen/slides/7/images/c/c29.jpg new file mode 100644 index 0000000..937f692 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c29.jpg differ diff --git a/vorlesungen/slides/7/images/c/c30.jpg b/vorlesungen/slides/7/images/c/c30.jpg new file mode 100644 index 0000000..45901cc Binary files /dev/null and b/vorlesungen/slides/7/images/c/c30.jpg differ diff --git a/vorlesungen/slides/7/images/c/c31.jpg b/vorlesungen/slides/7/images/c/c31.jpg new file mode 100644 index 0000000..eb52bec Binary files /dev/null and b/vorlesungen/slides/7/images/c/c31.jpg differ diff --git a/vorlesungen/slides/7/images/c/c32.jpg b/vorlesungen/slides/7/images/c/c32.jpg new file mode 100644 index 0000000..a011640 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c32.jpg differ diff --git a/vorlesungen/slides/7/images/c/c33.jpg b/vorlesungen/slides/7/images/c/c33.jpg new file mode 100644 index 0000000..ecbb8bd Binary files /dev/null and b/vorlesungen/slides/7/images/c/c33.jpg differ diff --git a/vorlesungen/slides/7/images/c/c34.jpg b/vorlesungen/slides/7/images/c/c34.jpg new file mode 100644 index 0000000..8a624d1 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c34.jpg differ diff --git a/vorlesungen/slides/7/images/c/c35.jpg b/vorlesungen/slides/7/images/c/c35.jpg new file mode 100644 index 0000000..33765a1 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c35.jpg differ diff --git a/vorlesungen/slides/7/images/c/c36.jpg b/vorlesungen/slides/7/images/c/c36.jpg new file mode 100644 index 0000000..e38a448 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c36.jpg differ diff --git a/vorlesungen/slides/7/images/c/c37.jpg b/vorlesungen/slides/7/images/c/c37.jpg new file mode 100644 index 0000000..9f823f4 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c37.jpg differ diff --git a/vorlesungen/slides/7/images/c/c38.jpg b/vorlesungen/slides/7/images/c/c38.jpg new file mode 100644 index 0000000..19c96fc Binary files /dev/null and b/vorlesungen/slides/7/images/c/c38.jpg differ diff --git a/vorlesungen/slides/7/images/c/c39.jpg b/vorlesungen/slides/7/images/c/c39.jpg new file mode 100644 index 0000000..c00482b Binary files /dev/null and b/vorlesungen/slides/7/images/c/c39.jpg differ diff --git a/vorlesungen/slides/7/images/c/c40.jpg b/vorlesungen/slides/7/images/c/c40.jpg new file mode 100644 index 0000000..de9fca4 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c40.jpg differ diff --git a/vorlesungen/slides/7/images/c/c41.jpg b/vorlesungen/slides/7/images/c/c41.jpg new file mode 100644 index 0000000..1b8a3d1 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c41.jpg differ diff --git a/vorlesungen/slides/7/images/c/c42.jpg b/vorlesungen/slides/7/images/c/c42.jpg new file mode 100644 index 0000000..6d4e5bc Binary files /dev/null and b/vorlesungen/slides/7/images/c/c42.jpg differ diff --git a/vorlesungen/slides/7/images/c/c43.jpg b/vorlesungen/slides/7/images/c/c43.jpg new file mode 100644 index 0000000..b39551f Binary files /dev/null and b/vorlesungen/slides/7/images/c/c43.jpg differ diff --git a/vorlesungen/slides/7/images/c/c44.jpg b/vorlesungen/slides/7/images/c/c44.jpg new file mode 100644 index 0000000..0fe56f6 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c44.jpg differ diff --git a/vorlesungen/slides/7/images/c/c45.jpg b/vorlesungen/slides/7/images/c/c45.jpg new file mode 100644 index 0000000..9196ad3 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c45.jpg differ diff --git a/vorlesungen/slides/7/images/c/c46.jpg b/vorlesungen/slides/7/images/c/c46.jpg new file mode 100644 index 0000000..a4f5823 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c46.jpg differ diff --git a/vorlesungen/slides/7/images/c/c47.jpg b/vorlesungen/slides/7/images/c/c47.jpg new file mode 100644 index 0000000..18474dd Binary files /dev/null and b/vorlesungen/slides/7/images/c/c47.jpg differ diff --git a/vorlesungen/slides/7/images/c/c48.jpg b/vorlesungen/slides/7/images/c/c48.jpg new file mode 100644 index 0000000..d839014 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c48.jpg differ diff --git a/vorlesungen/slides/7/images/c/c49.jpg b/vorlesungen/slides/7/images/c/c49.jpg new file mode 100644 index 0000000..3cb5cb0 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c49.jpg differ diff --git a/vorlesungen/slides/7/images/c/c50.jpg b/vorlesungen/slides/7/images/c/c50.jpg new file mode 100644 index 0000000..de32f8b Binary files /dev/null and b/vorlesungen/slides/7/images/c/c50.jpg differ diff --git a/vorlesungen/slides/7/images/c/c51.jpg b/vorlesungen/slides/7/images/c/c51.jpg new file mode 100644 index 0000000..4bbc224 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c51.jpg differ diff --git a/vorlesungen/slides/7/images/c/c52.jpg b/vorlesungen/slides/7/images/c/c52.jpg new file mode 100644 index 0000000..ebf1db6 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c52.jpg differ diff --git a/vorlesungen/slides/7/images/c/c53.jpg b/vorlesungen/slides/7/images/c/c53.jpg new file mode 100644 index 0000000..2ece537 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c53.jpg differ diff --git a/vorlesungen/slides/7/images/c/c54.jpg b/vorlesungen/slides/7/images/c/c54.jpg new file mode 100644 index 0000000..0ffbac2 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c54.jpg differ diff --git a/vorlesungen/slides/7/images/c/c55.jpg b/vorlesungen/slides/7/images/c/c55.jpg new file mode 100644 index 0000000..5f75419 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c55.jpg differ diff --git a/vorlesungen/slides/7/images/c/c56.jpg b/vorlesungen/slides/7/images/c/c56.jpg new file mode 100644 index 0000000..5c0f9ae Binary files /dev/null and b/vorlesungen/slides/7/images/c/c56.jpg differ diff --git a/vorlesungen/slides/7/images/c/c57.jpg b/vorlesungen/slides/7/images/c/c57.jpg new file mode 100644 index 0000000..9b61179 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c57.jpg differ diff --git a/vorlesungen/slides/7/images/c/c58.jpg b/vorlesungen/slides/7/images/c/c58.jpg new file mode 100644 index 0000000..81d2173 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c58.jpg differ diff --git a/vorlesungen/slides/7/images/c/c59.jpg b/vorlesungen/slides/7/images/c/c59.jpg new file mode 100644 index 0000000..0ae9bac Binary files /dev/null and b/vorlesungen/slides/7/images/c/c59.jpg differ diff --git a/vorlesungen/slides/7/images/c/c60.jpg b/vorlesungen/slides/7/images/c/c60.jpg new file mode 100644 index 0000000..2bc77e7 Binary files /dev/null and b/vorlesungen/slides/7/images/c/c60.jpg differ diff --git a/vorlesungen/slides/7/images/common.inc b/vorlesungen/slides/7/images/common.inc new file mode 100644 index 0000000..0e27c9a --- /dev/null +++ b/vorlesungen/slides/7/images/common.inc @@ -0,0 +1,70 @@ +// +// common.inc +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.025; +#declare O = <0, 0, 0>; +#declare at = 0.015; + +camera { + location <18, 15, -50> + look_at <0.0, 0.5, 0> + right 16/9 * x * imagescale + up y * imagescale +} + +light_source { + <-40, 30, -50> color White + area_light <1,0,0> <0,0,1>, 10, 10 + adaptive 1 + jitter +} + +sky_sphere { + pigment { + color rgb<1,1,1> + } +} + +#macro arrow(from, to, arrowthickness, c) +#declare arrowdirection = vnormalize(to - from); +#declare arrowlength = vlength(to - from); +union { + sphere { + from, 1.1 * arrowthickness + } + cylinder { + from, + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + arrowthickness + } + cone { + from + (arrowlength - 5 * arrowthickness) * arrowdirection, + 2 * arrowthickness, + to, + 0 + } + pigment { + color c + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare l = 1.2; + +arrow(< -l, 0, 0 >, < l, 0, 0 >, at, White) +arrow(< 0, 0, -l >, < 0, 0, l >, at, White) +arrow(< 0, -l, 0 >, < 0, l, 0 >, at, White) + diff --git a/vorlesungen/slides/7/images/commutator.ini b/vorlesungen/slides/7/images/commutator.ini new file mode 100644 index 0000000..8c2211e --- /dev/null +++ b/vorlesungen/slides/7/images/commutator.ini @@ -0,0 +1,8 @@ +Input_File_Name=commutator.pov +Initial_Frame=1 +Final_Frame=60 +Initial_Clock=1 +Final_Clock=60 +Cyclic_Animation=off +Pause_when_Done=off + diff --git a/vorlesungen/slides/7/images/commutator.m b/vorlesungen/slides/7/images/commutator.m new file mode 100644 index 0000000..5a448db --- /dev/null +++ b/vorlesungen/slides/7/images/commutator.m @@ -0,0 +1,111 @@ +# +# commutator.m +# +# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +# + +X = [ + 0, 0, 0; + 0, 0, -1; + 0, 1, 0 +]; + +Y = [ + 0, 0, 1; + 0, 0, 0; + -1, 0, 0 +]; + +Z = [ + 0, -1, 0; + 1, 0, 0; + 0, 0, 0 +]; + +function retval = Dx(alpha) + retval = [ + 1, 0, 0 ; + 0, cos(alpha), -sin(alpha); + 0, sin(alpha), cos(alpha) + ]; +end + +function retval = Dy(beta) + retval = [ + cos(beta), 0, sin(beta); + 0, 1, 0 ; + -sin(beta), 0, cos(beta) + ]; +end + +t = 0.9; +P = Dx(t) * Dy(t) +Q = Dy(t) * Dx(t) +P - Q +(P - Q) * [0;0;1] + +function retval = kurven(filename, t) + retval = -1; + N = 20; + fn = fopen(filename, "w"); + fprintf(fn, "//\n"); + fprintf(fn, "// %s\n", filename); + fprintf(fn, "//\n"); + fprintf(fn, "#macro XYkurve()\n"); + for i = (0:N-1) + v1 = Dx(t * i / N) * [0;0;1]; + v2 = Dx(t * (i+1) / N) * [0;0;1]; + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1)); + fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1)); + end + for i = (0:N-1) + v1 = Dx(t) * Dy(t * i / N) * [0;0;1]; + v2 = Dx(t) * Dy(t * (i+1) / N) * [0;0;1]; + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1)); + fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1)); + end + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v2(1,1), v2(3,1), v2(2,1)); + fprintf(fn, "#end\n"); + fprintf(fn, "#declare finalXY = <%.4f, %.4f, %.4f>;\n", + v2(1,1), v2(3,1), v2(2,1)); + fprintf(fn, "#macro YXkurve()\n"); + for i = (0:N-1) + v1 = Dy(t * i / N) * [0;0;1]; + v2 = Dy(t * (i+1) / N) * [0;0;1]; + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1)); + fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1)); + end + for i = (0:N-1) + v1 = Dy(t) * Dx(t * i / N) * [0;0;1]; + v2 = Dy(t) * Dx(t * (i+1) / N) * [0;0;1]; + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1)); + fprintf(fn, "cylinder { <%.4f,%.4f,%.4f>, <%.4f, %.4f, %.4f>, at }\n", + v1(1,1), v1(3,1), v1(2,1), v2(1,1), v2(3,1), v2(2,1)); + end + fprintf(fn, "sphere { <%.4f,%.4f,%.4f>, at }\n", + v2(1,1), v2(3,1), v2(2,1)); + fprintf(fn, "#end\n"); + fprintf(fn, "#declare finalYX = <%.4f, %.4f, %.4f>;\n", + v2(1,1), v2(3,1), v2(2,1)); + + fclose(fn); + retval = 0; +end + +function retval = kurve(i) + n = pi / 180; + filename = sprintf("f/%04d.inc", i); + kurven(filename, n * i); +end + +for i = (1:60) + kurve(i); +end diff --git a/vorlesungen/slides/7/images/commutator.pov b/vorlesungen/slides/7/images/commutator.pov new file mode 100644 index 0000000..9ae11b9 --- /dev/null +++ b/vorlesungen/slides/7/images/commutator.pov @@ -0,0 +1,59 @@ +// +// commutator.pov +// +// (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#include "common.inc" + +sphere { O, 0.99 + pigment { + color rgbt<1,1,1,0.5> + } + finish { + specular 0.9 + metallic + } +} + +#declare filename = concat("f/", str(clock, -4, 0), ".inc"); + +#include filename + +#declare n1 = vcross(<0,1,0>, finalXY); +#declare n2 = vcross(<0,1,0>, finalYX); + +intersection { + sphere { O, 1 } + plane { -n1, 0 } + plane { n2, 0 } + pigment { + color rgb<0,0.4,0.1> + } + finish { + specular 0.9 + metallic + } +} + +union { + XYkurve() + pigment { + color Red + } + finish { + specular 0.9 + metallic + } +} + +union { + YXkurve() + pigment { + color Blue + } + finish { + specular 0.9 + metallic + } +} + diff --git a/vorlesungen/slides/7/kommutator.tex b/vorlesungen/slides/7/kommutator.tex new file mode 100644 index 0000000..f01debe --- /dev/null +++ b/vorlesungen/slides/7/kommutator.tex @@ -0,0 +1,139 @@ +% +% template.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Kommutator in $\operatorname{SO}(3)$} +\vspace{-20pt} +\begin{center} +\begin{tikzpicture}[>=latex,thick] +\ifthenelse{\boolean{presentation}}{ +\only<1>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c01.jpg}};} +\only<2>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c02.jpg}};} +\only<3>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c03.jpg}};} +\only<4>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c04.jpg}};} +\only<5>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c05.jpg}};} +\only<6>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c06.jpg}};} +\only<7>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c07.jpg}};} +\only<8>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c08.jpg}};} +\only<9>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c09.jpg}};} +\only<10>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c10.jpg}};} +\only<11>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c11.jpg}};} +\only<12>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c12.jpg}};} +\only<13>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c13.jpg}};} +\only<14>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c14.jpg}};} +\only<15>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c15.jpg}};} +\only<16>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c16.jpg}};} +\only<17>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c17.jpg}};} +\only<18>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c18.jpg}};} +\only<19>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c19.jpg}};} +\only<20>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c20.jpg}};} +\only<21>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c21.jpg}};} +\only<22>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c22.jpg}};} +\only<23>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c23.jpg}};} +\only<24>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c24.jpg}};} +\only<25>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c25.jpg}};} +\only<26>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c26.jpg}};} +\only<27>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c27.jpg}};} +\only<28>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c28.jpg}};} +\only<29>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c29.jpg}};} +\only<30>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c30.jpg}};} +\only<31>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c31.jpg}};} +\only<32>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c32.jpg}};} +\only<33>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c33.jpg}};} +\only<34>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c34.jpg}};} +\only<35>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c35.jpg}};} +\only<36>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c36.jpg}};} +\only<37>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c37.jpg}};} +\only<38>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c38.jpg}};} +\only<39>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c39.jpg}};} +\only<40>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c40.jpg}};} +\only<41>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c41.jpg}};} +\only<42>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c42.jpg}};} +\only<43>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c43.jpg}};} +\only<44>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c44.jpg}};} +\only<45>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c45.jpg}};} +\only<46>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c46.jpg}};} +\only<47>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c47.jpg}};} +\only<48>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c48.jpg}};} +\only<49>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c49.jpg}};} +\only<50>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c50.jpg}};} +\only<51>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c51.jpg}};} +\only<52>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c52.jpg}};} +\only<53>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c53.jpg}};} +\only<54>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c54.jpg}};} +\only<55>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c55.jpg}};} +\only<56>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c56.jpg}};} +\only<57>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c57.jpg}};} +\only<58>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c58.jpg}};} +\only<59>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c59.jpg}};} +\only<60>{\node at (0,0) { +\includegraphics[width=\textwidth]{../slides/7/images/c/c60.jpg}};} +}{} +\end{tikzpicture} +\end{center} +\end{frame} +\egroup diff --git a/vorlesungen/slides/7/sl2.tex b/vorlesungen/slides/7/sl2.tex index 3480460..a65b4f6 100644 --- a/vorlesungen/slides/7/sl2.tex +++ b/vorlesungen/slides/7/sl2.tex @@ -50,6 +50,7 @@ c&d \foreach \y in {-2,...,2}{ \draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y); } + \ifthenelse{\boolean{presentation}}{ \foreach \d in {4,...,10}{ \only<\d>{ \pgfmathparse{1+(\d-4)/10} @@ -66,6 +67,7 @@ c&d } } } + }{} \uncover<11->{ \xdef\t{1.6} \fill[color=red!40,opacity=0.5] @@ -105,6 +107,7 @@ c&d \foreach \y in {-2,...,2}{ \draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y); } + \ifthenelse{\boolean{presentation}}{ \foreach \d in {11,...,17}{ \only<\d>{ \pgfmathparse{(\d-11)/10} @@ -128,6 +131,7 @@ c&d } } } + }{} \uncover<18->{ \xdef\t{0.6} \fill[color=red!40,opacity=0.5] @@ -174,6 +178,7 @@ c&d \foreach \y in {-2,...,2}{ \draw[color=blue,line width=0.3pt] (-3,\y) -- (3,\y); } + \ifthenelse{\boolean{presentation}}{ \foreach \d in {18,...,24}{ \only<\d>{ \pgfmathparse{(\d-18)/10} @@ -197,6 +202,27 @@ c&d } } } + }{} + \uncover<25->{ + \xdef\t{0.6} + \fill[color=red!40,opacity=0.5] + (-1,{\t*(-1)-1}) + -- + (1,{\t*1-1}) + -- + (1,{\t*1+1}) + -- + (-1,{\t*(-1)+1}) + -- cycle; + \foreach \x in {-3,...,3}{ + \draw[color=red,line width=0.3pt] + (\x,{\x*\t-3}) -- (\x,{\x*\t+3}); + } + \foreach \y in {-3,...,3}{ + \draw[color=red,line width=0.3pt] + (-3,{-3*\t+\y}) -- (3,{3*\t+\y}); + } + } \end{scope} \draw[->] (-2.1,0) -- (2.3,0) coordinate[label={$x$}]; \draw[->] (0,-2.1) -- (0,2.3) coordinate[label={right:$y$}]; diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex index 7062509..ee6829e 100644 --- a/vorlesungen/slides/test.tex +++ b/vorlesungen/slides/test.tex @@ -15,8 +15,8 @@ \folie{7/mannigfaltigkeit.tex} % Weitere Beispiele % SL_2(R) -%\folie{7/sl2.tex} -%\folie{7/drehung.tex} +\folie{7/sl2.tex} +\folie{7/drehung.tex} % Semidirekte Produkte SO(2) x R^2, R^+ x R \folie{7/semi.tex} @@ -29,10 +29,10 @@ \folie{7/ableitung.tex} % Lie-Algebra \folie{7/liealgebra.tex} +% Kommutator +\folie{7/kommutator.tex} \section{Exponentialabbildung} % Differentialgleichung für die Exponentialabbildung \folie{7/dg.tex} -% Exponentialabbilung -%\folie{7/exponential.tex} -- cgit v1.2.1