diff options
Diffstat (limited to 'src/hyper/pages/DERHAM.pht')
-rw-r--r-- | src/hyper/pages/DERHAM.pht | 591 |
1 files changed, 591 insertions, 0 deletions
diff --git a/src/hyper/pages/DERHAM.pht b/src/hyper/pages/DERHAM.pht new file mode 100644 index 00000000..8342214e --- /dev/null +++ b/src/hyper/pages/DERHAM.pht @@ -0,0 +1,591 @@ +\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} + |