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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/XPR.pht | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/hyper/pages/XPR.pht')
-rw-r--r-- | src/hyper/pages/XPR.pht | 325 |
1 files changed, 325 insertions, 0 deletions
diff --git a/src/hyper/pages/XPR.pht b/src/hyper/pages/XPR.pht new file mode 100644 index 00000000..0d97a8f4 --- /dev/null +++ b/src/hyper/pages/XPR.pht @@ -0,0 +1,325 @@ +\begin{patch}{XPolynomialRingXmpPagePatch1} +\begin{paste}{XPolynomialRingXmpPageFull1}{XPolynomialRingXmpPageEmpty1} +\pastebutton{XPolynomialRingXmpPageFull1}{\hidepaste} +\tab{5}\spadcommand{Word := OrderedFreeMonoid(Symbol)\bound{Word }} +\indentrel{3}\begin{verbatim} + (1) OrderedFreeMonoid Symbol + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty1} +\begin{paste}{XPolynomialRingXmpPageEmpty1}{XPolynomialRingXmpPagePatch1} +\pastebutton{XPolynomialRingXmpPageEmpty1}{\showpaste} +\tab{5}\spadcommand{Word := OrderedFreeMonoid(Symbol)\bound{Word }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch2} +\begin{paste}{XPolynomialRingXmpPageFull2}{XPolynomialRingXmpPageEmpty2} +\pastebutton{XPolynomialRingXmpPageFull2}{\hidepaste} +\tab{5}\spadcommand{poly:= XPR(Integer,Word)\free{Word }\bound{poly }} +\indentrel{3}\begin{verbatim} + (2) + XPolynomialRing(Integer,OrderedFreeMonoid Symbol) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty2} +\begin{paste}{XPolynomialRingXmpPageEmpty2}{XPolynomialRingXmpPagePatch2} +\pastebutton{XPolynomialRingXmpPageEmpty2}{\showpaste} +\tab{5}\spadcommand{poly:= XPR(Integer,Word)\free{Word }\bound{poly }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch3} +\begin{paste}{XPolynomialRingXmpPageFull3}{XPolynomialRingXmpPageEmpty3} +\pastebutton{XPolynomialRingXmpPageFull3}{\hidepaste} +\tab{5}\spadcommand{p:poly := 2 * x - 3 * y + 1\free{poly }\bound{p }} +\indentrel{3}\begin{verbatim} + (3) 1 + 2x - 3y +Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty3} +\begin{paste}{XPolynomialRingXmpPageEmpty3}{XPolynomialRingXmpPagePatch3} +\pastebutton{XPolynomialRingXmpPageEmpty3}{\showpaste} +\tab{5}\spadcommand{p:poly := 2 * x - 3 * y + 1\free{poly }\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch4} +\begin{paste}{XPolynomialRingXmpPageFull4}{XPolynomialRingXmpPageEmpty4} +\pastebutton{XPolynomialRingXmpPageFull4}{\hidepaste} +\tab{5}\spadcommand{q:poly := 2 * x + 1\free{poly }\bound{q }} +\indentrel{3}\begin{verbatim} + (4) 1 + 2x +Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty4} +\begin{paste}{XPolynomialRingXmpPageEmpty4}{XPolynomialRingXmpPagePatch4} +\pastebutton{XPolynomialRingXmpPageEmpty4}{\showpaste} +\tab{5}\spadcommand{q:poly := 2 * x + 1\free{poly }\bound{q }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch5} +\begin{paste}{XPolynomialRingXmpPageFull5}{XPolynomialRingXmpPageEmpty5} +\pastebutton{XPolynomialRingXmpPageFull5}{\hidepaste} +\tab{5}\spadcommand{p + q\free{p }\free{q }} +\indentrel{3}\begin{verbatim} + (5) 2 + 4x - 3y +Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty5} +\begin{paste}{XPolynomialRingXmpPageEmpty5}{XPolynomialRingXmpPagePatch5} +\pastebutton{XPolynomialRingXmpPageEmpty5}{\showpaste} +\tab{5}\spadcommand{p + q\free{p }\free{q }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch6} +\begin{paste}{XPolynomialRingXmpPageFull6}{XPolynomialRingXmpPageEmpty6} +\pastebutton{XPolynomialRingXmpPageFull6}{\hidepaste} +\tab{5}\spadcommand{p * q\free{p }\free{q }} +\indentrel{3}\begin{verbatim} + 2 + (6) 1 + 4x - 3y + 4x - 6y x +Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty6} +\begin{paste}{XPolynomialRingXmpPageEmpty6}{XPolynomialRingXmpPagePatch6} +\pastebutton{XPolynomialRingXmpPageEmpty6}{\showpaste} +\tab{5}\spadcommand{p * q\free{p }\free{q }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch7} +\begin{paste}{XPolynomialRingXmpPageFull7}{XPolynomialRingXmpPageEmpty7} +\pastebutton{XPolynomialRingXmpPageFull7}{\hidepaste} +\tab{5}\spadcommand{(p +q)^2 -p^2 -q^2 - 2*p*q\free{p }\free{q }} +\indentrel{3}\begin{verbatim} + (7) - 6x y + 6y x +Type: XPolynomialRing(Integer,OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty7} +\begin{paste}{XPolynomialRingXmpPageEmpty7}{XPolynomialRingXmpPagePatch7} +\pastebutton{XPolynomialRingXmpPageEmpty7}{\showpaste} +\tab{5}\spadcommand{(p +q)^2 -p^2 -q^2 - 2*p*q\free{p }\free{q }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch8} +\begin{paste}{XPolynomialRingXmpPageFull8}{XPolynomialRingXmpPageEmpty8} +\pastebutton{XPolynomialRingXmpPageFull8}{\hidepaste} +\tab{5}\spadcommand{M := SquareMatrix(2,Fraction Integer)\bound{M }} +\indentrel{3}\begin{verbatim} + (8) SquareMatrix(2,Fraction Integer) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty8} +\begin{paste}{XPolynomialRingXmpPageEmpty8}{XPolynomialRingXmpPagePatch8} +\pastebutton{XPolynomialRingXmpPageEmpty8}{\showpaste} +\tab{5}\spadcommand{M := SquareMatrix(2,Fraction Integer)\bound{M }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch9} +\begin{paste}{XPolynomialRingXmpPageFull9}{XPolynomialRingXmpPageEmpty9} +\pastebutton{XPolynomialRingXmpPageFull9}{\hidepaste} +\tab{5}\spadcommand{poly1:= XPR(M,Word)\free{Word }\free{M }\bound{poly1 }} +\indentrel{3}\begin{verbatim} + (9) + XPolynomialRing(SquareMatrix(2,Fraction Integer),Ordere + dFreeMonoid Symbol) + Type: Domain +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty9} +\begin{paste}{XPolynomialRingXmpPageEmpty9}{XPolynomialRingXmpPagePatch9} +\pastebutton{XPolynomialRingXmpPageEmpty9}{\showpaste} +\tab{5}\spadcommand{poly1:= XPR(M,Word)\free{Word }\free{M }\bound{poly1 }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch10} +\begin{paste}{XPolynomialRingXmpPageFull10}{XPolynomialRingXmpPageEmpty10} +\pastebutton{XPolynomialRingXmpPageFull10}{\hidepaste} +\tab{5}\spadcommand{m1:M := matrix [[i*j**2 for i in 1..2] for j in 1..2]\free{M }\bound{m1 }} +\indentrel{3}\begin{verbatim} + Ú1 2¿ + (10) ³ ³ + À4 8Ù + Type: SquareMatrix(2,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty10} +\begin{paste}{XPolynomialRingXmpPageEmpty10}{XPolynomialRingXmpPagePatch10} +\pastebutton{XPolynomialRingXmpPageEmpty10}{\showpaste} +\tab{5}\spadcommand{m1:M := matrix [[i*j**2 for i in 1..2] for j in 1..2]\free{M }\bound{m1 }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch11} +\begin{paste}{XPolynomialRingXmpPageFull11}{XPolynomialRingXmpPageEmpty11} +\pastebutton{XPolynomialRingXmpPageFull11}{\hidepaste} +\tab{5}\spadcommand{m2:M := m1 - 5/4\free{M }\free{m1 }\bound{m2 }} +\indentrel{3}\begin{verbatim} + Ú 1 ¿ + ³- Ä 2 ³ + ³ 4 ³ + (11) ³ ³ + ³ 27³ + ³ 4 Äij + À 4Ù + Type: SquareMatrix(2,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty11} +\begin{paste}{XPolynomialRingXmpPageEmpty11}{XPolynomialRingXmpPagePatch11} +\pastebutton{XPolynomialRingXmpPageEmpty11}{\showpaste} +\tab{5}\spadcommand{m2:M := m1 - 5/4\free{M }\free{m1 }\bound{m2 }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch12} +\begin{paste}{XPolynomialRingXmpPageFull12}{XPolynomialRingXmpPageEmpty12} +\pastebutton{XPolynomialRingXmpPageFull12}{\hidepaste} +\tab{5}\spadcommand{m3: M := m2**2\free{M }\free{m2 }\bound{m3 }} +\indentrel{3}\begin{verbatim} + Ú129 ¿ + ³ÄÄÄ 13 ³ + ³ 16 ³ + (12) ³ ³ + ³ 857³ + ³26 ÄÄij + À 16Ù + Type: SquareMatrix(2,Fraction Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty12} +\begin{paste}{XPolynomialRingXmpPageEmpty12}{XPolynomialRingXmpPagePatch12} +\pastebutton{XPolynomialRingXmpPageEmpty12}{\showpaste} +\tab{5}\spadcommand{m3: M := m2**2\free{M }\free{m2 }\bound{m3 }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch13} +\begin{paste}{XPolynomialRingXmpPageFull13}{XPolynomialRingXmpPageEmpty13} +\pastebutton{XPolynomialRingXmpPageFull13}{\hidepaste} +\tab{5}\spadcommand{pm:poly1 := m1*x + m2*y + m3*z - 2/3\free{poly1 }\free{m1 }\free{m2 }\free{m3 }\bound{pm }} +\indentrel{3}\begin{verbatim} + Ú 2 ¿ Ú 1 ¿ Ú129 ¿ + ³- Ä 0 ³ ³- Ä 2 ³ ³ÄÄÄ 13 ³ + ³ 3 ³ Ú1 2¿ ³ 4 ³ ³ 16 ³ + (13) ³ ³ + ³ ³x + ³ ³y + ³ ³z + ³ 2³ À4 8Ù ³ 27³ ³ 857³ + ³ 0 - ij ³ 4 Äij ³26 ÄÄij + À 3Ù À 4Ù À 16Ù +Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty13} +\begin{paste}{XPolynomialRingXmpPageEmpty13}{XPolynomialRingXmpPagePatch13} +\pastebutton{XPolynomialRingXmpPageEmpty13}{\showpaste} +\tab{5}\spadcommand{pm:poly1 := m1*x + m2*y + m3*z - 2/3\free{poly1 }\free{m1 }\free{m2 }\free{m3 }\bound{pm }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch14} +\begin{paste}{XPolynomialRingXmpPageFull14}{XPolynomialRingXmpPageEmpty14} +\pastebutton{XPolynomialRingXmpPageFull14}{\hidepaste} +\tab{5}\spadcommand{qm:poly1 := pm - m1*x\free{m1 }\free{pm }\bound{qm }} +\indentrel{3}\begin{verbatim} + Ú 2 ¿ Ú 1 ¿ Ú129 ¿ + ³- Ä 0 ³ ³- Ä 2 ³ ³ÄÄÄ 13 ³ + ³ 3 ³ ³ 4 ³ ³ 16 ³ + (14) ³ ³ + ³ ³y + ³ ³z + ³ 2³ ³ 27³ ³ 857³ + ³ 0 - ij ³ 4 Äij ³26 ÄÄij + À 3Ù À 4Ù À 16Ù +Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty14} +\begin{paste}{XPolynomialRingXmpPageEmpty14}{XPolynomialRingXmpPagePatch14} +\pastebutton{XPolynomialRingXmpPageEmpty14}{\showpaste} +\tab{5}\spadcommand{qm:poly1 := pm - m1*x\free{m1 }\free{pm }\bound{qm }} +\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPagePatch15} +\begin{paste}{XPolynomialRingXmpPageFull15}{XPolynomialRingXmpPageEmpty15} +\pastebutton{XPolynomialRingXmpPageFull15}{\hidepaste} +\tab{5}\spadcommand{qm**3\bound{qm }} +\indentrel{3}\begin{verbatim} + (15) + Ú 8 ¿ Ú 1 8¿ Ú43 52 ¿ + ³- ÄÄ 0 ³ ³- Ä Ä³ ³ÄÄ ÄÄ ³ + ³ 27 ³ ³ 3 3³ ³ 4 3 ³ + ³ ³ + ³ ³y + ³ ³z + ³ 8³ ³16 ³ ³104 857³ + ³ 0 - Äij ³ÄÄ 9³ ³ÄÄÄ ÄÄij + À 27Ù À 3 Ù À 3 12Ù + + + Ú 129 ¿ Ú 3199 831 ¿ + ³- ÄÄÄ - 26 ³ ³- ÄÄÄÄ - ÄÄÄ ³ + ³ 8 ³ 2 ³ 32 4 ³ + ³ ³y + ³ ³y z + ³ 857³ ³ 831 26467³ + ³- 52 - ÄÄij ³- ÄÄÄ - ÄÄÄÄij + À 8 Ù À 2 32 Ù + + + Ú 3199 831 ¿ Ú 103169 6409 ¿ + ³- ÄÄÄÄ - ÄÄÄ ³ ³- ÄÄÄÄÄÄ - ÄÄÄÄ ³ + ³ 32 4 ³ ³ 128 4 ³ 2 + ³ ³z y + ³ ³z + ³ 831 26467³ ³ 6409 820977³ + ³- ÄÄÄ - ÄÄÄÄij ³ - ÄÄÄÄ - ÄÄÄÄÄij + À 2 32 Ù À 2 128 Ù + + + Ú3199 831 ¿ Ú103169 6409 ¿ + ³ÄÄÄÄ ÄÄÄ ³ ³ÄÄÄÄÄÄ ÄÄÄÄ ³ + ³ 64 8 ³ 3 ³ 256 8 ³ 2 + ³ ³y + ³ ³y z + ³831 26467³ ³ 6409 820977³ + ³ÄÄÄ ÄÄÄÄij ³ ÄÄÄÄ ÄÄÄÄÄij + À 4 64 Ù À 4 256 Ù + + + Ú103169 6409 ¿ Ú3178239 795341 ¿ + ³ÄÄÄÄÄÄ ÄÄÄÄ ³ ³ÄÄÄÄÄÄÄ ÄÄÄÄÄÄ ³ + ³ 256 8 ³ ³ 1024 128 ³ 2 + ³ ³y z y + ³ ³y z + ³ 6409 820977³ ³795341 25447787³ + ³ ÄÄÄÄ ÄÄÄÄÄij ³ÄÄÄÄÄÄ ÄÄÄÄÄÄÄij + À 4 256 Ù À 64 1024 Ù + + + Ú103169 6409 ¿ Ú3178239 795341 ¿ + ³ÄÄÄÄÄÄ ÄÄÄÄ ³ ³ÄÄÄÄÄÄÄ ÄÄÄÄÄÄ ³ + ³ 256 8 ³ 2 ³ 1024 128 ³ + ³ ³z y + ³ ³z y z + ³ 6409 820977³ ³795341 25447787³ + ³ ÄÄÄÄ ÄÄÄÄÄij ³ÄÄÄÄÄÄ ÄÄÄÄÄÄÄij + À 4 256 Ù À 64 1024 Ù + + + Ú3178239 795341 ¿ Ú98625409 12326223 ¿ + ³ÄÄÄÄÄÄÄ ÄÄÄÄÄÄ ³ ³ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ³ + ³ 1024 128 ³ 2 ³ 4096 256 ³ 3 + ³ ³z y + ³ ³z + ³795341 25447787³ ³12326223 788893897³ + ³ÄÄÄÄÄÄ ÄÄÄÄÄÄÄij ³ÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄij + À 64 1024 Ù À 128 4096 Ù +Type: XPolynomialRing(SquareMatrix(2,Fraction Integer),OrderedFreeMonoid Symbol) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{XPolynomialRingXmpPageEmpty15} +\begin{paste}{XPolynomialRingXmpPageEmpty15}{XPolynomialRingXmpPagePatch15} +\pastebutton{XPolynomialRingXmpPageEmpty15}{\showpaste} +\tab{5}\spadcommand{qm**3\bound{qm }} +\end{paste}\end{patch} + |