open-axiom repository from github
\begin{patch}{DeRhamComplexXmpPagePatch1}
\begin{paste}{DeRhamComplexXmpPageFull1}{DeRhamComplexXmpPageEmpty1}
\pastebutton{DeRhamComplexXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{coefRing := Integer\bound{coefRing }}
\indentrel{3}\begin{verbatim}
(1) Integer
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty1}
\begin{paste}{DeRhamComplexXmpPageEmpty1}{DeRhamComplexXmpPagePatch1}
\pastebutton{DeRhamComplexXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{coefRing := Integer\bound{coefRing }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch2}
\begin{paste}{DeRhamComplexXmpPageFull2}{DeRhamComplexXmpPageEmpty2}
\pastebutton{DeRhamComplexXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{lv : List Symbol := [x,y,z]\bound{lv }}
\indentrel{3}\begin{verbatim}
(2) [x,y,z]
Type: List Symbol
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty2}
\begin{paste}{DeRhamComplexXmpPageEmpty2}{DeRhamComplexXmpPagePatch2}
\pastebutton{DeRhamComplexXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{lv : List Symbol := [x,y,z]\bound{lv }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch3}
\begin{paste}{DeRhamComplexXmpPageFull3}{DeRhamComplexXmpPageEmpty3}
\pastebutton{DeRhamComplexXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{der := DERHAM(coefRing,lv)\free{coefRing }\free{lv }\bound{der }}
\indentrel{3}\begin{verbatim}
(3) DeRhamComplex(Integer,[x,y,z])
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty3}
\begin{paste}{DeRhamComplexXmpPageEmpty3}{DeRhamComplexXmpPagePatch3}
\pastebutton{DeRhamComplexXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{der := DERHAM(coefRing,lv)\free{coefRing }\free{lv }\bound{der }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch4}
\begin{paste}{DeRhamComplexXmpPageFull4}{DeRhamComplexXmpPageEmpty4}
\pastebutton{DeRhamComplexXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{R := Expression coefRing\free{coefRing }\bound{R }}
\indentrel{3}\begin{verbatim}
(4) Expression Integer
Type: Domain
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty4}
\begin{paste}{DeRhamComplexXmpPageEmpty4}{DeRhamComplexXmpPagePatch4}
\pastebutton{DeRhamComplexXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{R := Expression coefRing\free{coefRing }\bound{R }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch5}
\begin{paste}{DeRhamComplexXmpPageFull5}{DeRhamComplexXmpPageEmpty5}
\pastebutton{DeRhamComplexXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{f : R := x**2*y*z-5*x**3*y**2*z**5\free{R }\bound{f }}
\indentrel{3}\begin{verbatim}
3 2 5 2
(5) - 5x y z + x y z
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty5}
\begin{paste}{DeRhamComplexXmpPageEmpty5}{DeRhamComplexXmpPagePatch5}
\pastebutton{DeRhamComplexXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{f : R := x**2*y*z-5*x**3*y**2*z**5\free{R }\bound{f }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch6}
\begin{paste}{DeRhamComplexXmpPageFull6}{DeRhamComplexXmpPageEmpty6}
\pastebutton{DeRhamComplexXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2\free{R }\bound{g }}
\indentrel{3}\begin{verbatim}
2 3 2 2
(6) - 7z sin(x y ) + y z cos(z)
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty6}
\begin{paste}{DeRhamComplexXmpPageEmpty6}{DeRhamComplexXmpPagePatch6}
\pastebutton{DeRhamComplexXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2\free{R }\bound{g }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch7}
\begin{paste}{DeRhamComplexXmpPageFull7}{DeRhamComplexXmpPageEmpty7}
\pastebutton{DeRhamComplexXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{h : R :=x*y*z-2*x**3*y*z**2\free{R }\bound{h }}
\indentrel{3}\begin{verbatim}
3 2
(7) - 2x y z + x y z
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty7}
\begin{paste}{DeRhamComplexXmpPageEmpty7}{DeRhamComplexXmpPagePatch7}
\pastebutton{DeRhamComplexXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{h : R :=x*y*z-2*x**3*y*z**2\free{R }\bound{h }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch8}
\begin{paste}{DeRhamComplexXmpPageFull8}{DeRhamComplexXmpPageEmpty8}
\pastebutton{DeRhamComplexXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{dx : der := generator(1)\free{der }\bound{dx }}
\indentrel{3}\begin{verbatim}
(8) dx
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty8}
\begin{paste}{DeRhamComplexXmpPageEmpty8}{DeRhamComplexXmpPagePatch8}
\pastebutton{DeRhamComplexXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{dx : der := generator(1)\free{der }\bound{dx }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch9}
\begin{paste}{DeRhamComplexXmpPageFull9}{DeRhamComplexXmpPageEmpty9}
\pastebutton{DeRhamComplexXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{dy : der := generator(2)\free{der }\bound{dy }}
\indentrel{3}\begin{verbatim}
(9) dy
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty9}
\begin{paste}{DeRhamComplexXmpPageEmpty9}{DeRhamComplexXmpPagePatch9}
\pastebutton{DeRhamComplexXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{dy : der := generator(2)\free{der }\bound{dy }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch10}
\begin{paste}{DeRhamComplexXmpPageFull10}{DeRhamComplexXmpPageEmpty10}
\pastebutton{DeRhamComplexXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{dz : der := generator(3)\free{der }\bound{dz }}
\indentrel{3}\begin{verbatim}
(10) dz
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty10}
\begin{paste}{DeRhamComplexXmpPageEmpty10}{DeRhamComplexXmpPagePatch10}
\pastebutton{DeRhamComplexXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{dz : der := generator(3)\free{der }\bound{dz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch11}
\begin{paste}{DeRhamComplexXmpPageFull11}{DeRhamComplexXmpPageEmpty11}
\pastebutton{DeRhamComplexXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{[dx,dy,dz] := [generator(i)$der for i in 1..3]\free{der }\bound{dxyz }}
\indentrel{3}\begin{verbatim}
(11) [dx,dy,dz]
Type: List DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty11}
\begin{paste}{DeRhamComplexXmpPageEmpty11}{DeRhamComplexXmpPagePatch11}
\pastebutton{DeRhamComplexXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{[dx,dy,dz] := [generator(i)$der for i in 1..3]\free{der }\bound{dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch12}
\begin{paste}{DeRhamComplexXmpPageFull12}{DeRhamComplexXmpPageEmpty12}
\pastebutton{DeRhamComplexXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{alpha : der := f*dx + g*dy + h*dz\bound{alpha }\free{der f g h dxyz }}
\indentrel{3}\begin{verbatim}
(12)
3 2
(- 2x y z + x y z)dz
+
2 3 2 2 3 2 5 2
(- 7z sin(x y ) + y z cos(z))dy + (- 5x y z + x y z)dx
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty12}
\begin{paste}{DeRhamComplexXmpPageEmpty12}{DeRhamComplexXmpPagePatch12}
\pastebutton{DeRhamComplexXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{alpha : der := f*dx + g*dy + h*dz\bound{alpha }\free{der f g h dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch13}
\begin{paste}{DeRhamComplexXmpPageFull13}{DeRhamComplexXmpPageEmpty13}
\pastebutton{DeRhamComplexXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy\bound{beta }\free{der f g h dxyz }}
\indentrel{3}\begin{verbatim}
(13) x dy + cos(tan(x y z) + x y z)dx
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty13}
\begin{paste}{DeRhamComplexXmpPageEmpty13}{DeRhamComplexXmpPagePatch13}
\pastebutton{DeRhamComplexXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy\bound{beta }\free{der f g h dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch14}
\begin{paste}{DeRhamComplexXmpPageFull14}{DeRhamComplexXmpPageEmpty14}
\pastebutton{DeRhamComplexXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential alpha;\free{alpha }\bound{ed }}
\indentrel{3}\begin{verbatim}
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty14}
\begin{paste}{DeRhamComplexXmpPageEmpty14}{DeRhamComplexXmpPagePatch14}
\pastebutton{DeRhamComplexXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential alpha;\free{alpha }\bound{ed }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch15}
\begin{paste}{DeRhamComplexXmpPageFull15}{DeRhamComplexXmpPageEmpty15}
\pastebutton{DeRhamComplexXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential \%\free{ed }}
\indentrel{3}\begin{verbatim}
(15) 0
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty15}
\begin{paste}{DeRhamComplexXmpPageEmpty15}{DeRhamComplexXmpPagePatch15}
\pastebutton{DeRhamComplexXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential \%\free{ed }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch16}
\begin{paste}{DeRhamComplexXmpPageFull16}{DeRhamComplexXmpPageEmpty16}
\pastebutton{DeRhamComplexXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{gamma := alpha * beta\bound{gamma }\free{alpha }\free{beta }}
\indentrel{3}\begin{verbatim}
(16)
4 2 2
(2x y z - x y z)dy dz
+
3 2
(2x y z - x y z)cos(tan(x y z) + x y z)dx dz
+
2 3 2 2
(7z sin(x y ) - y z cos(z))
*
cos(tan(x y z) + x y z)
+
4 2 5 3
- 5x y z + x y z
*
dx dy
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty16}
\begin{paste}{DeRhamComplexXmpPageEmpty16}{DeRhamComplexXmpPagePatch16}
\pastebutton{DeRhamComplexXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{gamma := alpha * beta\bound{gamma }\free{alpha }\free{beta }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch17}
\begin{paste}{DeRhamComplexXmpPageFull17}{DeRhamComplexXmpPageEmpty17}
\pastebutton{DeRhamComplexXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))\free{alpha beta gamma }}
\indentrel{3}\begin{verbatim}
(17) 0
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty17}
\begin{paste}{DeRhamComplexXmpPageEmpty17}{DeRhamComplexXmpPagePatch17}
\pastebutton{DeRhamComplexXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - alpha * exteriorDifferential(beta))\free{alpha beta gamma }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch18}
\begin{paste}{DeRhamComplexXmpPageFull18}{DeRhamComplexXmpPageEmpty18}
\pastebutton{DeRhamComplexXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{a : BOP := operator('a)\bound{ao }}
\indentrel{3}\begin{verbatim}
(18) a
Type: BasicOperator
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty18}
\begin{paste}{DeRhamComplexXmpPageEmpty18}{DeRhamComplexXmpPagePatch18}
\pastebutton{DeRhamComplexXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{a : BOP := operator('a)\bound{ao }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch19}
\begin{paste}{DeRhamComplexXmpPageFull19}{DeRhamComplexXmpPageEmpty19}
\pastebutton{DeRhamComplexXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{b : BOP := operator('b)\bound{bo }}
\indentrel{3}\begin{verbatim}
(19) b
Type: BasicOperator
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty19}
\begin{paste}{DeRhamComplexXmpPageEmpty19}{DeRhamComplexXmpPagePatch19}
\pastebutton{DeRhamComplexXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{b : BOP := operator('b)\bound{bo }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch20}
\begin{paste}{DeRhamComplexXmpPageFull20}{DeRhamComplexXmpPageEmpty20}
\pastebutton{DeRhamComplexXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{c : BOP := operator('c)\bound{co }}
\indentrel{3}\begin{verbatim}
(20) c
Type: BasicOperator
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty20}
\begin{paste}{DeRhamComplexXmpPageEmpty20}{DeRhamComplexXmpPagePatch20}
\pastebutton{DeRhamComplexXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{c : BOP := operator('c)\bound{co }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch21}
\begin{paste}{DeRhamComplexXmpPageFull21}{DeRhamComplexXmpPageEmpty21}
\pastebutton{DeRhamComplexXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz\bound{sigma }\free{ao bo co dxyz }}
\indentrel{3}\begin{verbatim}
(21) c(x,y,z)dz + b(x,y,z)dy + a(x,y,z)dx
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty21}
\begin{paste}{DeRhamComplexXmpPageEmpty21}{DeRhamComplexXmpPagePatch21}
\pastebutton{DeRhamComplexXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz\bound{sigma }\free{ao bo co dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch22}
\begin{paste}{DeRhamComplexXmpPageFull22}{DeRhamComplexXmpPageEmpty22}
\pastebutton{DeRhamComplexXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz\bound{theta }\free{ao bo co dxyz }}
\indentrel{3}\begin{verbatim}
(22) c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty22}
\begin{paste}{DeRhamComplexXmpPageEmpty22}{DeRhamComplexXmpPagePatch22}
\pastebutton{DeRhamComplexXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz\bound{theta }\free{ao bo co dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch23}
\begin{paste}{DeRhamComplexXmpPageFull23}{DeRhamComplexXmpPageEmpty23}
\pastebutton{DeRhamComplexXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{totalDifferential(a(x,y,z))$der\free{ao der }}
\indentrel{3}\begin{verbatim}
(23) a (x,y,z)dz + a (x,y,z)dy + a (x,y,z)dx
,3 ,2 ,1
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty23}
\begin{paste}{DeRhamComplexXmpPageEmpty23}{DeRhamComplexXmpPagePatch23}
\pastebutton{DeRhamComplexXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{totalDifferential(a(x,y,z))$der\free{ao der }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch24}
\begin{paste}{DeRhamComplexXmpPageFull24}{DeRhamComplexXmpPageEmpty24}
\pastebutton{DeRhamComplexXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential sigma\free{sigma }}
\indentrel{3}\begin{verbatim}
(24)
(c (x,y,z) - b (x,y,z))dy dz
,2 ,3
+
(c (x,y,z) - a (x,y,z))dx dz
,1 ,3
+
(b (x,y,z) - a (x,y,z))dx dy
,1 ,2
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty24}
\begin{paste}{DeRhamComplexXmpPageEmpty24}{DeRhamComplexXmpPagePatch24}
\pastebutton{DeRhamComplexXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential sigma\free{sigma }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch25}
\begin{paste}{DeRhamComplexXmpPageFull25}{DeRhamComplexXmpPageEmpty25}
\pastebutton{DeRhamComplexXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential theta\free{theta }}
\indentrel{3}\begin{verbatim}
(25) (c (x,y,z) - b (x,y,z) + a (x,y,z))dx dy dz
,1 ,2 ,3
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty25}
\begin{paste}{DeRhamComplexXmpPageEmpty25}{DeRhamComplexXmpPagePatch25}
\pastebutton{DeRhamComplexXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential theta\free{theta }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch26}
\begin{paste}{DeRhamComplexXmpPageFull26}{DeRhamComplexXmpPageEmpty26}
\pastebutton{DeRhamComplexXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{one : der := 1\bound{one }\free{der }}
\indentrel{3}\begin{verbatim}
(26) 1
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty26}
\begin{paste}{DeRhamComplexXmpPageEmpty26}{DeRhamComplexXmpPagePatch26}
\pastebutton{DeRhamComplexXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{one : der := 1\bound{one }\free{der }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch27}
\begin{paste}{DeRhamComplexXmpPageFull27}{DeRhamComplexXmpPageEmpty27}
\pastebutton{DeRhamComplexXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{g1 : der := a([x,t,y,u,v,z,e]) * one\free{der one ao }\bound{g1 }}
\indentrel{3}\begin{verbatim}
(27) a(x,t,y,u,v,z,e)
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty27}
\begin{paste}{DeRhamComplexXmpPageEmpty27}{DeRhamComplexXmpPagePatch27}
\pastebutton{DeRhamComplexXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{g1 : der := a([x,t,y,u,v,z,e]) * one\free{der one ao }\bound{g1 }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch28}
\begin{paste}{DeRhamComplexXmpPageFull28}{DeRhamComplexXmpPageEmpty28}
\pastebutton{DeRhamComplexXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one\free{der one ao }\bound{h1 }}
\indentrel{3}\begin{verbatim}
(28) a(x,y,x,t,x,z,y,r,u,x)
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty28}
\begin{paste}{DeRhamComplexXmpPageEmpty28}{DeRhamComplexXmpPagePatch28}
\pastebutton{DeRhamComplexXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one\free{der one ao }\bound{h1 }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch29}
\begin{paste}{DeRhamComplexXmpPageFull29}{DeRhamComplexXmpPageEmpty29}
\pastebutton{DeRhamComplexXmpPageFull29}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential g1\free{g1 }}
\indentrel{3}\begin{verbatim}
(29)
a (x,t,y,u,v,z,e)dz + a (x,t,y,u,v,z,e)dy
,6 ,3
+
a (x,t,y,u,v,z,e)dx
,1
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty29}
\begin{paste}{DeRhamComplexXmpPageEmpty29}{DeRhamComplexXmpPagePatch29}
\pastebutton{DeRhamComplexXmpPageEmpty29}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential g1\free{g1 }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch30}
\begin{paste}{DeRhamComplexXmpPageFull30}{DeRhamComplexXmpPageEmpty30}
\pastebutton{DeRhamComplexXmpPageFull30}{\hidepaste}
\tab{5}\spadcommand{exteriorDifferential h1\free{h1 }}
\indentrel{3}\begin{verbatim}
(30)
a (x,y,x,t,x,z,y,r,u,x)dz
,6
+
a (x,y,x,t,x,z,y,r,u,x)
,7
+
a (x,y,x,t,x,z,y,r,u,x)
,2
*
dy
+
a (x,y,x,t,x,z,y,r,u,x)
,10
+
a (x,y,x,t,x,z,y,r,u,x)
,5
+
a (x,y,x,t,x,z,y,r,u,x) + a (x,y,x,t,x,z,y,r,u,x)
,3 ,1
*
dx
Type: DeRhamComplex(Integer,[x,y,z])
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty30}
\begin{paste}{DeRhamComplexXmpPageEmpty30}{DeRhamComplexXmpPagePatch30}
\pastebutton{DeRhamComplexXmpPageEmpty30}{\showpaste}
\tab{5}\spadcommand{exteriorDifferential h1\free{h1 }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch31}
\begin{paste}{DeRhamComplexXmpPageFull31}{DeRhamComplexXmpPageEmpty31}
\pastebutton{DeRhamComplexXmpPageFull31}{\hidepaste}
\tab{5}\spadcommand{coefficient(gamma, dx*dy)\free{gamma dxyz }}
\indentrel{3}\begin{verbatim}
(31)
2 3 2 2
(7z sin(x y ) - y z cos(z))cos(tan(x y z) + x y z)
+
4 2 5 3
- 5x y z + x y z
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty31}
\begin{paste}{DeRhamComplexXmpPageEmpty31}{DeRhamComplexXmpPagePatch31}
\pastebutton{DeRhamComplexXmpPageEmpty31}{\showpaste}
\tab{5}\spadcommand{coefficient(gamma, dx*dy)\free{gamma dxyz }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch32}
\begin{paste}{DeRhamComplexXmpPageFull32}{DeRhamComplexXmpPageEmpty32}
\pastebutton{DeRhamComplexXmpPageFull32}{\hidepaste}
\tab{5}\spadcommand{coefficient(gamma, one)\free{gamma one }}
\indentrel{3}\begin{verbatim}
(32) 0
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty32}
\begin{paste}{DeRhamComplexXmpPageEmpty32}{DeRhamComplexXmpPagePatch32}
\pastebutton{DeRhamComplexXmpPageEmpty32}{\showpaste}
\tab{5}\spadcommand{coefficient(gamma, one)\free{gamma one }}
\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPagePatch33}
\begin{paste}{DeRhamComplexXmpPageFull33}{DeRhamComplexXmpPageEmpty33}
\pastebutton{DeRhamComplexXmpPageFull33}{\hidepaste}
\tab{5}\spadcommand{coefficient(g1,one)\free{g1 one }}
\indentrel{3}\begin{verbatim}
(33) a(x,t,y,u,v,z,e)
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{DeRhamComplexXmpPageEmpty33}
\begin{paste}{DeRhamComplexXmpPageEmpty33}{DeRhamComplexXmpPagePatch33}
\pastebutton{DeRhamComplexXmpPageEmpty33}{\showpaste}
\tab{5}\spadcommand{coefficient(g1,one)\free{g1 one }}
\end{paste}\end{patch}