diff options
author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/hyper/pages/CLIF.pht | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/hyper/pages/CLIF.pht')
-rw-r--r-- | src/hyper/pages/CLIF.pht | 622 |
1 files changed, 622 insertions, 0 deletions
diff --git a/src/hyper/pages/CLIF.pht b/src/hyper/pages/CLIF.pht new file mode 100644 index 00000000..1331d459 --- /dev/null +++ b/src/hyper/pages/CLIF.pht @@ -0,0 +1,622 @@ +\begin{patch}{ugxCliffordDiracPagePatch1} +\begin{paste}{ugxCliffordDiracPageFull1}{ugxCliffordDiracPageEmpty1} +\pastebutton{ugxCliffordDiracPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty1} +\begin{paste}{ugxCliffordDiracPageEmpty1}{ugxCliffordDiracPagePatch1} +\pastebutton{ugxCliffordDiracPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch2} +\begin{paste}{ugxCliffordDiracPageFull2}{ugxCliffordDiracPageEmpty2} +\pastebutton{ugxCliffordDiracPageFull2}{\hidepaste} +\tab{5}\spadcommand{g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]\bound{g }} +\indentrel{3}\begin{verbatim} + Ú1 0 0 0 ¿ + ³ ³ + ³0 - 1 0 0 ³ + (2) ³ ³ + ³0 0 - 1 0 ³ + ³ ³ + À0 0 0 - 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty2} +\begin{paste}{ugxCliffordDiracPageEmpty2}{ugxCliffordDiracPagePatch2} +\pastebutton{ugxCliffordDiracPageEmpty2}{\showpaste} +\tab{5}\spadcommand{g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch3} +\begin{paste}{ugxCliffordDiracPageFull3}{ugxCliffordDiracPageEmpty3} +\pastebutton{ugxCliffordDiracPageFull3}{\hidepaste} +\tab{5}\spadcommand{D := CliffordAlgebra(4,K, quadraticForm g)\free{K g }\bound{D }} +\indentrel{3}\begin{verbatim} + (3) CliffordAlgebra(4,Fraction Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty3} +\begin{paste}{ugxCliffordDiracPageEmpty3}{ugxCliffordDiracPagePatch3} +\pastebutton{ugxCliffordDiracPageEmpty3}{\showpaste} +\tab{5}\spadcommand{D := CliffordAlgebra(4,K, quadraticForm g)\free{K g }\bound{D }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch4} +\begin{paste}{ugxCliffordDiracPageFull4}{ugxCliffordDiracPageEmpty4} +\pastebutton{ugxCliffordDiracPageFull4}{\hidepaste} +\tab{5}\spadcommand{gam := [e(i)$D for i in 1..4]\free{D }\bound{gam }} +\indentrel{3}\begin{verbatim} + (4) [e ,e ,e ,e ] + 1 2 3 4 + Type: List CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty4} +\begin{paste}{ugxCliffordDiracPageEmpty4}{ugxCliffordDiracPagePatch4} +\pastebutton{ugxCliffordDiracPageEmpty4}{\showpaste} +\tab{5}\spadcommand{gam := [e(i)$D for i in 1..4]\free{D }\bound{gam }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch5} +\begin{paste}{ugxCliffordDiracPageFull5}{ugxCliffordDiracPageEmpty5} +\pastebutton{ugxCliffordDiracPageFull5}{\hidepaste} +\tab{5}\spadcommand{m := 1; n:= 2; r := 3; s := 4;\bound{m n r s }} +\indentrel{3}\begin{verbatim} + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty5} +\begin{paste}{ugxCliffordDiracPageEmpty5}{ugxCliffordDiracPagePatch5} +\pastebutton{ugxCliffordDiracPageEmpty5}{\showpaste} +\tab{5}\spadcommand{m := 1; n:= 2; r := 3; s := 4;\bound{m n r s }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch6} +\begin{paste}{ugxCliffordDiracPageFull6}{ugxCliffordDiracPageEmpty6} +\pastebutton{ugxCliffordDiracPageFull6}{\hidepaste} +\tab{5}\spadcommand{lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])\bound{lhs }\free{g gam m n r s }} +\indentrel{3}\begin{verbatim} + (6) - 4e e e e + 1 2 3 4 + Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty6} +\begin{paste}{ugxCliffordDiracPageEmpty6}{ugxCliffordDiracPagePatch6} +\pastebutton{ugxCliffordDiracPageEmpty6}{\showpaste} +\tab{5}\spadcommand{lhs := reduce(+, [reduce(+, [ g(l,t)*gam(l)*gam(m)*gam(n)*gam(r)*gam(s)*gam(t) for l in 1..4]) for t in 1..4])\bound{lhs }\free{g gam m n r s }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPagePatch7} +\begin{paste}{ugxCliffordDiracPageFull7}{ugxCliffordDiracPageEmpty7} +\pastebutton{ugxCliffordDiracPageFull7}{\hidepaste} +\tab{5}\spadcommand{rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)\bound{rhs }\free{lhs g gam m n r s }} +\indentrel{3}\begin{verbatim} + (7) - 4e e e e + 1 2 3 4 + Type: CliffordAlgebra(4,Fraction Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordDiracPageEmpty7} +\begin{paste}{ugxCliffordDiracPageEmpty7}{ugxCliffordDiracPagePatch7} +\pastebutton{ugxCliffordDiracPageEmpty7}{\showpaste} +\tab{5}\spadcommand{rhs := 2*(gam s * gam m*gam n*gam r + gam r*gam n*gam m*gam s)\bound{rhs }\free{lhs g gam m n r s }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch1} +\begin{paste}{ugxCliffordComplexPageFull1}{ugxCliffordComplexPageEmpty1} +\pastebutton{ugxCliffordComplexPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty1} +\begin{paste}{ugxCliffordComplexPageEmpty1}{ugxCliffordComplexPagePatch1} +\pastebutton{ugxCliffordComplexPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch2} +\begin{paste}{ugxCliffordComplexPageFull2}{ugxCliffordComplexPageEmpty2} +\pastebutton{ugxCliffordComplexPageFull2}{\hidepaste} +\tab{5}\spadcommand{m := matrix [[-1]]\bound{m }} +\indentrel{3}\begin{verbatim} + (2) [- 1] + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty2} +\begin{paste}{ugxCliffordComplexPageEmpty2}{ugxCliffordComplexPagePatch2} +\pastebutton{ugxCliffordComplexPageEmpty2}{\showpaste} +\tab{5}\spadcommand{m := matrix [[-1]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch3} +\begin{paste}{ugxCliffordComplexPageFull3}{ugxCliffordComplexPageEmpty3} +\pastebutton{ugxCliffordComplexPageFull3}{\hidepaste} +\tab{5}\spadcommand{C := CliffordAlgebra(1, K, quadraticForm m)\free{K m }\bound{C }} +\indentrel{3}\begin{verbatim} + (3) + CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty3} +\begin{paste}{ugxCliffordComplexPageEmpty3}{ugxCliffordComplexPagePatch3} +\pastebutton{ugxCliffordComplexPageEmpty3}{\showpaste} +\tab{5}\spadcommand{C := CliffordAlgebra(1, K, quadraticForm m)\free{K m }\bound{C }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch4} +\begin{paste}{ugxCliffordComplexPageFull4}{ugxCliffordComplexPageEmpty4} +\pastebutton{ugxCliffordComplexPageFull4}{\hidepaste} +\tab{5}\spadcommand{i: C := e(1)\bound{i }\free{C }} +\indentrel{3}\begin{verbatim} + (4) e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty4} +\begin{paste}{ugxCliffordComplexPageEmpty4}{ugxCliffordComplexPagePatch4} +\pastebutton{ugxCliffordComplexPageEmpty4}{\showpaste} +\tab{5}\spadcommand{i: C := e(1)\bound{i }\free{C }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch5} +\begin{paste}{ugxCliffordComplexPageFull5}{ugxCliffordComplexPageEmpty5} +\pastebutton{ugxCliffordComplexPageFull5}{\hidepaste} +\tab{5}\spadcommand{x := a + b * i\bound{x }\free{i }} +\indentrel{3}\begin{verbatim} + (5) a + b e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty5} +\begin{paste}{ugxCliffordComplexPageEmpty5}{ugxCliffordComplexPagePatch5} +\pastebutton{ugxCliffordComplexPageEmpty5}{\showpaste} +\tab{5}\spadcommand{x := a + b * i\bound{x }\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch6} +\begin{paste}{ugxCliffordComplexPageFull6}{ugxCliffordComplexPageEmpty6} +\pastebutton{ugxCliffordComplexPageFull6}{\hidepaste} +\tab{5}\spadcommand{y := c + d * i\bound{y }\free{i }} +\indentrel{3}\begin{verbatim} + (6) c + d e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty6} +\begin{paste}{ugxCliffordComplexPageEmpty6}{ugxCliffordComplexPagePatch6} +\pastebutton{ugxCliffordComplexPageEmpty6}{\showpaste} +\tab{5}\spadcommand{y := c + d * i\bound{y }\free{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPagePatch7} +\begin{paste}{ugxCliffordComplexPageFull7}{ugxCliffordComplexPageEmpty7} +\pastebutton{ugxCliffordComplexPageFull7}{\hidepaste} +\tab{5}\spadcommand{x * y\free{x y }} +\indentrel{3}\begin{verbatim} + (7) - b d + a c + (a d + b c)e + 1 +Type: CliffordAlgebra(1,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordComplexPageEmpty7} +\begin{paste}{ugxCliffordComplexPageEmpty7}{ugxCliffordComplexPagePatch7} +\pastebutton{ugxCliffordComplexPageEmpty7}{\showpaste} +\tab{5}\spadcommand{x * y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch1} +\begin{paste}{ugxCliffordQuaternPageFull1}{ugxCliffordQuaternPageEmpty1} +\pastebutton{ugxCliffordQuaternPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty1} +\begin{paste}{ugxCliffordQuaternPageEmpty1}{ugxCliffordQuaternPagePatch1} +\pastebutton{ugxCliffordQuaternPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch2} +\begin{paste}{ugxCliffordQuaternPageFull2}{ugxCliffordQuaternPageEmpty2} +\pastebutton{ugxCliffordQuaternPageFull2}{\hidepaste} +\tab{5}\spadcommand{m := matrix [[-1,0],[0,-1]]\bound{m }} +\indentrel{3}\begin{verbatim} + Ú- 1 0 ¿ + (2) ³ ³ + À 0 - 1Ù + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty2} +\begin{paste}{ugxCliffordQuaternPageEmpty2}{ugxCliffordQuaternPagePatch2} +\pastebutton{ugxCliffordQuaternPageEmpty2}{\showpaste} +\tab{5}\spadcommand{m := matrix [[-1,0],[0,-1]]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch3} +\begin{paste}{ugxCliffordQuaternPageFull3}{ugxCliffordQuaternPageEmpty3} +\pastebutton{ugxCliffordQuaternPageFull3}{\hidepaste} +\tab{5}\spadcommand{H := CliffordAlgebra(2, K, quadraticForm m)\free{K m }\bound{H }} +\indentrel{3}\begin{verbatim} + (3) + CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty3} +\begin{paste}{ugxCliffordQuaternPageEmpty3}{ugxCliffordQuaternPagePatch3} +\pastebutton{ugxCliffordQuaternPageEmpty3}{\showpaste} +\tab{5}\spadcommand{H := CliffordAlgebra(2, K, quadraticForm m)\free{K m }\bound{H }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch4} +\begin{paste}{ugxCliffordQuaternPageFull4}{ugxCliffordQuaternPageEmpty4} +\pastebutton{ugxCliffordQuaternPageFull4}{\hidepaste} +\tab{5}\spadcommand{i: H := e(1)\free{H }\bound{i }} +\indentrel{3}\begin{verbatim} + (4) e + 1 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty4} +\begin{paste}{ugxCliffordQuaternPageEmpty4}{ugxCliffordQuaternPagePatch4} +\pastebutton{ugxCliffordQuaternPageEmpty4}{\showpaste} +\tab{5}\spadcommand{i: H := e(1)\free{H }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch5} +\begin{paste}{ugxCliffordQuaternPageFull5}{ugxCliffordQuaternPageEmpty5} +\pastebutton{ugxCliffordQuaternPageFull5}{\hidepaste} +\tab{5}\spadcommand{j: H := e(2)\free{H }\bound{j }} +\indentrel{3}\begin{verbatim} + (5) e + 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty5} +\begin{paste}{ugxCliffordQuaternPageEmpty5}{ugxCliffordQuaternPagePatch5} +\pastebutton{ugxCliffordQuaternPageEmpty5}{\showpaste} +\tab{5}\spadcommand{j: H := e(2)\free{H }\bound{j }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch6} +\begin{paste}{ugxCliffordQuaternPageFull6}{ugxCliffordQuaternPageEmpty6} +\pastebutton{ugxCliffordQuaternPageFull6}{\hidepaste} +\tab{5}\spadcommand{k: H := i * j\free{H i j }\bound{k }} +\indentrel{3}\begin{verbatim} + (6) e e + 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty6} +\begin{paste}{ugxCliffordQuaternPageEmpty6}{ugxCliffordQuaternPagePatch6} +\pastebutton{ugxCliffordQuaternPageEmpty6}{\showpaste} +\tab{5}\spadcommand{k: H := i * j\free{H i j }\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch7} +\begin{paste}{ugxCliffordQuaternPageFull7}{ugxCliffordQuaternPageEmpty7} +\pastebutton{ugxCliffordQuaternPageFull7}{\hidepaste} +\tab{5}\spadcommand{x := a + b * i + c * j + d * k\free{i j k }\bound{x }} +\indentrel{3}\begin{verbatim} + (7) a + b e + c e + d e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty7} +\begin{paste}{ugxCliffordQuaternPageEmpty7}{ugxCliffordQuaternPagePatch7} +\pastebutton{ugxCliffordQuaternPageEmpty7}{\showpaste} +\tab{5}\spadcommand{x := a + b * i + c * j + d * k\free{i j k }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch8} +\begin{paste}{ugxCliffordQuaternPageFull8}{ugxCliffordQuaternPageEmpty8} +\pastebutton{ugxCliffordQuaternPageFull8}{\hidepaste} +\tab{5}\spadcommand{y := e + f * i + g * j + h * k\free{i j k }\bound{y }} +\indentrel{3}\begin{verbatim} + (8) e + f e + g e + h e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty8} +\begin{paste}{ugxCliffordQuaternPageEmpty8}{ugxCliffordQuaternPagePatch8} +\pastebutton{ugxCliffordQuaternPageEmpty8}{\showpaste} +\tab{5}\spadcommand{y := e + f * i + g * j + h * k\free{i j k }\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch9} +\begin{paste}{ugxCliffordQuaternPageFull9}{ugxCliffordQuaternPageEmpty9} +\pastebutton{ugxCliffordQuaternPageFull9}{\hidepaste} +\tab{5}\spadcommand{x + y\free{x y }} +\indentrel{3}\begin{verbatim} + (9) e + a + (f + b)e + (g + c)e + (h + d)e e + 1 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty9} +\begin{paste}{ugxCliffordQuaternPageEmpty9}{ugxCliffordQuaternPagePatch9} +\pastebutton{ugxCliffordQuaternPageEmpty9}{\showpaste} +\tab{5}\spadcommand{x + y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch10} +\begin{paste}{ugxCliffordQuaternPageFull10}{ugxCliffordQuaternPageEmpty10} +\pastebutton{ugxCliffordQuaternPageFull10}{\hidepaste} +\tab{5}\spadcommand{x * y\free{x y }} +\indentrel{3}\begin{verbatim} + (10) + - d h - c g - b f + a e + (c h - d g + a f + b e)e + 1 + + + (- b h + a g + d f + c e)e + 2 + + + (a h + b g - c f + d e)e e + 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty10} +\begin{paste}{ugxCliffordQuaternPageEmpty10}{ugxCliffordQuaternPagePatch10} +\pastebutton{ugxCliffordQuaternPageEmpty10}{\showpaste} +\tab{5}\spadcommand{x * y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPagePatch11} +\begin{paste}{ugxCliffordQuaternPageFull11}{ugxCliffordQuaternPageEmpty11} +\pastebutton{ugxCliffordQuaternPageFull11}{\hidepaste} +\tab{5}\spadcommand{y * x\free{x y }} +\indentrel{3}\begin{verbatim} + (11) + - d h - c g - b f + a e + (- c h + d g + a f + b e)e + 1 + + + (b h + a g - d f + c e)e + (a h - b g + c f + d e)e e + 2 1 2 +Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordQuaternPageEmpty11} +\begin{paste}{ugxCliffordQuaternPageEmpty11}{ugxCliffordQuaternPagePatch11} +\pastebutton{ugxCliffordQuaternPageEmpty11}{\showpaste} +\tab{5}\spadcommand{y * x\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch1} +\begin{paste}{ugxCliffordExteriorPageFull1}{ugxCliffordExteriorPageEmpty1} +\pastebutton{ugxCliffordExteriorPageFull1}{\hidepaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\indentrel{3}\begin{verbatim} + (1) Fraction Polynomial Integer + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty1} +\begin{paste}{ugxCliffordExteriorPageEmpty1}{ugxCliffordExteriorPagePatch1} +\pastebutton{ugxCliffordExteriorPageEmpty1}{\showpaste} +\tab{5}\spadcommand{K := Fraction Polynomial Integer\bound{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch2} +\begin{paste}{ugxCliffordExteriorPageFull2}{ugxCliffordExteriorPageEmpty2} +\pastebutton{ugxCliffordExteriorPageFull2}{\hidepaste} +\tab{5}\spadcommand{Ext := CliffordAlgebra(3, K, quadraticForm 0)\bound{Ext }\free{K }} +\indentrel{3}\begin{verbatim} + (2) + CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty2} +\begin{paste}{ugxCliffordExteriorPageEmpty2}{ugxCliffordExteriorPagePatch2} +\pastebutton{ugxCliffordExteriorPageEmpty2}{\showpaste} +\tab{5}\spadcommand{Ext := CliffordAlgebra(3, K, quadraticForm 0)\bound{Ext }\free{K }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch3} +\begin{paste}{ugxCliffordExteriorPageFull3}{ugxCliffordExteriorPageEmpty3} +\pastebutton{ugxCliffordExteriorPageFull3}{\hidepaste} +\tab{5}\spadcommand{i: Ext := e(1)\free{Ext }\bound{i }} +\indentrel{3}\begin{verbatim} + (3) e + 1 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty3} +\begin{paste}{ugxCliffordExteriorPageEmpty3}{ugxCliffordExteriorPagePatch3} +\pastebutton{ugxCliffordExteriorPageEmpty3}{\showpaste} +\tab{5}\spadcommand{i: Ext := e(1)\free{Ext }\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch4} +\begin{paste}{ugxCliffordExteriorPageFull4}{ugxCliffordExteriorPageEmpty4} +\pastebutton{ugxCliffordExteriorPageFull4}{\hidepaste} +\tab{5}\spadcommand{j: Ext := e(2)\free{Ext }\bound{j }} +\indentrel{3}\begin{verbatim} + (4) e + 2 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty4} +\begin{paste}{ugxCliffordExteriorPageEmpty4}{ugxCliffordExteriorPagePatch4} +\pastebutton{ugxCliffordExteriorPageEmpty4}{\showpaste} +\tab{5}\spadcommand{j: Ext := e(2)\free{Ext }\bound{j }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch5} +\begin{paste}{ugxCliffordExteriorPageFull5}{ugxCliffordExteriorPageEmpty5} +\pastebutton{ugxCliffordExteriorPageFull5}{\hidepaste} +\tab{5}\spadcommand{k: Ext := e(3)\free{Ext }\bound{k }} +\indentrel{3}\begin{verbatim} + (5) e + 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty5} +\begin{paste}{ugxCliffordExteriorPageEmpty5}{ugxCliffordExteriorPagePatch5} +\pastebutton{ugxCliffordExteriorPageEmpty5}{\showpaste} +\tab{5}\spadcommand{k: Ext := e(3)\free{Ext }\bound{k }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch6} +\begin{paste}{ugxCliffordExteriorPageFull6}{ugxCliffordExteriorPageEmpty6} +\pastebutton{ugxCliffordExteriorPageFull6}{\hidepaste} +\tab{5}\spadcommand{x := x1*i + x2*j + x3*k\free{i j k }\bound{x }} +\indentrel{3}\begin{verbatim} + (6) x1 e + x2 e + x3 e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty6} +\begin{paste}{ugxCliffordExteriorPageEmpty6}{ugxCliffordExteriorPagePatch6} +\pastebutton{ugxCliffordExteriorPageEmpty6}{\showpaste} +\tab{5}\spadcommand{x := x1*i + x2*j + x3*k\free{i j k }\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch7} +\begin{paste}{ugxCliffordExteriorPageFull7}{ugxCliffordExteriorPageEmpty7} +\pastebutton{ugxCliffordExteriorPageFull7}{\hidepaste} +\tab{5}\spadcommand{y := y1*i + y2*j + y3*k\free{i j k }\bound{y }} +\indentrel{3}\begin{verbatim} + (7) y1 e + y2 e + y3 e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty7} +\begin{paste}{ugxCliffordExteriorPageEmpty7}{ugxCliffordExteriorPagePatch7} +\pastebutton{ugxCliffordExteriorPageEmpty7}{\showpaste} +\tab{5}\spadcommand{y := y1*i + y2*j + y3*k\free{i j k }\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch8} +\begin{paste}{ugxCliffordExteriorPageFull8}{ugxCliffordExteriorPageEmpty8} +\pastebutton{ugxCliffordExteriorPageFull8}{\hidepaste} +\tab{5}\spadcommand{x + y\free{x y }} +\indentrel{3}\begin{verbatim} + (8) (y1 + x1)e + (y2 + x2)e + (y3 + x3)e + 1 2 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty8} +\begin{paste}{ugxCliffordExteriorPageEmpty8}{ugxCliffordExteriorPagePatch8} +\pastebutton{ugxCliffordExteriorPageEmpty8}{\showpaste} +\tab{5}\spadcommand{x + y\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch9} +\begin{paste}{ugxCliffordExteriorPageFull9}{ugxCliffordExteriorPageEmpty9} +\pastebutton{ugxCliffordExteriorPageFull9}{\hidepaste} +\tab{5}\spadcommand{x * y + y * x\free{x y }} +\indentrel{3}\begin{verbatim} + (9) 0 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty9} +\begin{paste}{ugxCliffordExteriorPageEmpty9}{ugxCliffordExteriorPagePatch9} +\pastebutton{ugxCliffordExteriorPageEmpty9}{\showpaste} +\tab{5}\spadcommand{x * y + y * x\free{x y }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch10} +\begin{paste}{ugxCliffordExteriorPageFull10}{ugxCliffordExteriorPageEmpty10} +\pastebutton{ugxCliffordExteriorPageFull10}{\hidepaste} +\tab{5}\spadcommand{dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k\free{i j k }\bound{dual2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty10} +\begin{paste}{ugxCliffordExteriorPageEmpty10}{ugxCliffordExteriorPagePatch10} +\pastebutton{ugxCliffordExteriorPageEmpty10}{\showpaste} +\tab{5}\spadcommand{dual2 a == coefficient(a,[2,3]) * i + coefficient(a,[3,1]) * j + coefficient(a,[1,2]) * k\free{i j k }\bound{dual2 }} +\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPagePatch11} +\begin{paste}{ugxCliffordExteriorPageFull11}{ugxCliffordExteriorPageEmpty11} +\pastebutton{ugxCliffordExteriorPageFull11}{\hidepaste} +\tab{5}\spadcommand{dual2(x*y)\free{x y dual2 }} +\indentrel{3}\begin{verbatim} + (11) + (x2 y3 - x3 y2)e + (- x1 y3 + x3 y1)e + 1 2 + + + (x1 y2 - x2 y1)e + 3 +Type: CliffordAlgebra(3,Fraction Polynomial Integer,MATRIX) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugxCliffordExteriorPageEmpty11} +\begin{paste}{ugxCliffordExteriorPageEmpty11}{ugxCliffordExteriorPagePatch11} +\pastebutton{ugxCliffordExteriorPageEmpty11}{\showpaste} +\tab{5}\spadcommand{dual2(x*y)\free{x y dual2 }} +\end{paste}\end{patch} + |