diff --git a/fize.sh b/fize.sh index 6f20115..7bcd3a1 100755 --- a/fize.sh +++ b/fize.sh @@ -8,10 +8,14 @@ TREE="trees/$1.tree" sed -i '' -E 's/\$([^$]+)\$/#{\1}/g' $TREE # for the file $TREE, replace all string matching regrex \$\$\n([^$]+)\$\$ to ##{$1} where $1 is the first match using sed inplace cat $TREE | tr '\n' '\r' | sed -E 's/\$\$([^$]+)\$\$/##{\1}/g' > $TREE.tmp -# for the file $TREE.tmp, replace all string matching \r(.*)\r\r to \r\p{\1}\r\r where $1 is the first match using sed inplace -# sed -i '' -E 's/\r(.*)\r\r/\p{\r\1\r}\r\r/g' $TREE.tmp -cat $TREE.tmp | tr '\r' '\n' > $TREE -rm $TREE.tmp +# 1. \texdef{}{}{ -> \refdef{}{}{\r\\p{ +sed -i '' -E 's/\\texdef\{([^\}]*)\}\{([^\}]*)\}\{/\\refdef\{\1\}\{\2\}\{\n\\p\{/g' $TREE.tmp +# 2. before the line containing \refdef, skip; after the line, replace \r\r -> }\r\r\\p{ +awk 'BEGIN {skip=1} {if ($0 ~ /\\refdef/) {skip=0;print $0} else if (skip==1) {print $0} else { gsub(/\r\r/,"}\r\r\\p{", $0); print $0} }' $TREE.tmp > $TREE.tmp2 +# 3. }\s*$ -> }} +sed -i '' -E 's/\}\s*$/\}\}\r/g' $TREE.tmp2 +cat $TREE.tmp2 | tr '\r' '\n' > $TREE +rm $TREE.tmp* # for the file $TREE, replace all string \( to #{ using sed inplace sed -i '' -E 's/\\\(/#\{/g' $TREE # for the file $TREE, replace all string \) to } using sed inplace diff --git a/trees/hopf-0002.tree b/trees/hopf-0002.tree index c9e76ab..8768e4e 100644 --- a/trees/hopf-0002.tree +++ b/trees/hopf-0002.tree @@ -1,22 +1,24 @@ \import{macros} \tag{hopf} -\texdef{Peano space}{fauser2002treatise}{ -Let $V$ be a linear space of finite dimension $n$. Let lower case $x_i$ denote elements of $V$, which we will call also letters. We define a bracket as an alternating multilinear scalar valued function -$$ +\refdef{Peano space}{fauser2002treatise}{ +\p{ +Let #{V} be a linear space of finite dimension #{n}. Let lower case #{x_i} denote elements of #{V}, which we will call also letters. We define a bracket as an alternating multilinear scalar valued function +##{ \begin{gathered} {[, \ldots, .]: V \times \ldots \times V \rightarrow \mathbb{k}} \\ {\left[x_1, \ldots, x_n\right]=\operatorname{sign}(p)\left[x_{p(1)}, \ldots, x_{p(n)}\right]} \\ {\left[x_1, \ldots, \alpha x_r+\beta y_r, \ldots, x_n\right]=\alpha\left[x_1, \ldots, x_r, \ldots, x_n\right]+\beta\left[x_1, \ldots, y_r, \ldots, x_n\right]} \end{gathered} -$$ -$n$-factors -$$ +} +#{n}-factors +##{ \begin{aligned} {\left[x_1, \ldots, x_n\right] } & =\operatorname{sign}(p)\left[x_{p(1)}, \ldots, x_{p(n)}\right] \\ {\left[x_1, \ldots, \alpha x_r+\beta y_r, \ldots, x_n\right] } & =\alpha\left[x_1, \ldots, x_r, \ldots, x_n\right]+\beta\left[x_1, \ldots, y_r, \ldots, x_n\right] \end{aligned} -$$ +}} + +\p{The sign is due to the permutation #{p} on the arguments of the bracket. The pair #{\mathcal{P}=(V,[., \ldots,])}. is called a Peano space. +}} -The sign is due to the permutation $p$ on the arguments of the bracket. The pair $\mathcal{P}=(V,[., \ldots,])$. is called a Peano space. -} \ No newline at end of file diff --git a/trees/hopf-0003.tree b/trees/hopf-0003.tree index 7c2def9..3b7ec21 100644 --- a/trees/hopf-0003.tree +++ b/trees/hopf-0003.tree @@ -2,6 +2,7 @@ \tag{hopf} \taxon{remark} -\texnote{Peano space}{fauser2002treatise}{ -Of course, this structure is much weaker as e.g. a normed space or an inner product space. It does not allow to introduce the concept of length, distance or angle. Therefore it is clear that a geometry based on this structure cannot be metric. However, the bracket can be addressed as a volume form. Volume measurements are used e.g. in the analysis of chaotic systems and strange attractors. +\refnote{Peano space}{fauser2002treatise}{ +\p{Of course, this structure is much weaker as e.g. a normed space or an inner product space. It does not allow to introduce the concept of length, distance or angle. Therefore it is clear that a geometry based on this structure cannot be metric. However, the bracket can be addressed as a volume form. Volume measurements are used e.g. in the analysis of chaotic systems and strange attractors.} } + diff --git a/trees/hopf-0004.tree b/trees/hopf-0004.tree index 31c3ab2..2d0a4f2 100644 --- a/trees/hopf-0004.tree +++ b/trees/hopf-0004.tree @@ -1,11 +1,13 @@ \import{macros} \tag{hopf} -\texdef{standard Peano space}{fauser2002treatise}{ -A standard Peano space is a Peano space over the linear space $V$ of dimension $n$ whose bracket has the additional property that for every vector $x \in V$ there exist vectors $x_2, \ldots, x_n$ such that -$$ +\refdef{standard Peano space}{fauser2002treatise}{ +\p{ +A standard Peano space is a Peano space over the linear space #{V} of dimension #{n} whose bracket has the additional property that for every vector #{x \in V} there exist vectors #{x_2, \ldots, x_n} such that +##{ \left[x, x_2, \ldots, x_n\right] \neq 0 . -$$ +}} + +\p{In such a space the length of the bracket, i.e. the number of entries, equals the dimension of the space, and conversely. We will be concerned here with standard Peano spaces only. +}} -In such a space the length of the bracket, i.e. the number of entries, equals the dimension of the space, and conversely. We will be concerned here with standard Peano spaces only. -} \ No newline at end of file