diff -r 7f3760f39bdc -r f8845fc8f38d doc-isac/jrocnik/wn-notes.txt
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-isac/jrocnik/wn-notes.txt	Tue Sep 17 09:50:52 2013 +0200
@@ -0,0 +1,76 @@
+WN110711
+HOL/Multivariate_Analysis/
+######################### _multi_variate ... nothing else found
+
+src$ grep -r "interior " *
+==========================
+HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+definition "interior S = {x. \<exists>T. open T \<and> x \<in> T \<and> T \<subseteq> S}"
+
+grep -r "definition \"interval" *
+=================================
+HOL/Multivariate_Analysis/Brouwer_Fixpoint.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+definition "interval_bij = (\<lambda> (a::'a,b::'a) (u::'a,v::'a) (x::'a::ordered_euclidean_space).
+    (\<chi>\<chi> i. u$$i + (x$$i - a$$i) / (b$$i - a$$i) * (v$$i - u$$i))::'a)"
+
+
+??? "{a<..<b} \<subseteq> {c..d} \<union> s" ?definition interval?
+
+src$ grep -r ".nti.eriv" *
+=========================
+1 file except isac:
+# HOL/Multivariate_Analysis/Derivative.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+header {* Kurzweil-Henstock Gauge Integration in many dimensions. *}
+definition differentiable :: "('a::real_normed_vector \<Rightarrow> 'b::real_normed_vector) \<Rightarrow> 'a net \<Rightarrow> bool" (infixr "differentiable" 30) where
+  "f differentiable net \<equiv> (\<exists>f'. (f has_derivative f') net)"
+
+definition differentiable_on :: "('a::real_normed_vector \<Rightarrow> 'b::real_normed_vector) \<Rightarrow> 'a set \<Rightarrow> bool" (infixr "differentiable'_on" 30) where
+  "f differentiable_on s \<equiv> (\<forall>x\<in>s. f differentiable (at x within s))"
+
+definition "frechet_derivative f net = (SOME f'. (f has_derivative f') net)"
+
+/
+=========================
+HOL/Multivariate_Analysis/Integration.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+header {* Kurzweil-Henstock Gauge Integration in many dimensions. *}
+definition "integral i f \<equiv> SOME y. (f has_integral y) i"
+
+/
+=========================
+HOL/Multivariate_Analysis/Real_Integration.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+text{*We follow John Harrison in formalizing the Gauge integral.*}
+
+definition Integral :: "real set \<Rightarrow> (real \<Rightarrow> real) \<Rightarrow> real \<Rightarrow> bool" where
+  "Integral s f k = (f o dest_vec1 has_integral k) (vec1 ` s)"
+
+Multivariate_Analysis/L2_Norm.thy:header {* Square root of sum of squares *}
+
+
+################################################################################
+### sum
+################################################################################
+src/HOL$ grep -r " sum " *
+==========================
+ex/Summation.thy:text {* The formal sum operator. *}
+ex/Termination.thy:function sum :: "nat \<Rightarrow> nat \<Rightarrow> nat"
+ex/Termination.thy:  "sum i N = (if i > N then 0 else i + sum (Suc i) N)"
+Isar_Examples/Summation.thy
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+text {* The sum of natural numbers $0 + \cdots + n$ equals $n \times
+
+Series.thy
+~~~~~~~~~~
+header{*Finite Summation and Infinite Series*}
+
+Deriv.thy
+~~~~~~~~~
+definition
+  deriv :: "['a::real_normed_field \<Rightarrow> 'a, 'a, 'a] \<Rightarrow> bool"
+    --{*Differentiation: D is derivative of function f at x*}
+          ("(DERIV (_)/ (_)/ :> (_))" [1000, 1000, 60] 60) where
+  "DERIV f x :> D = ((%h. (f(x + h) - f x) / h) -- 0 --> D)"