From ab8cc85adde879fb963c94d15675783f2cf4b183 Mon Sep 17 00:00:00 2001 From: dos-reis Date: Tue, 14 Aug 2007 05:14:52 +0000 Subject: Initial population. --- src/hyper/pages/coverex.pht | 1748 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1748 insertions(+) create mode 100644 src/hyper/pages/coverex.pht (limited to 'src/hyper/pages/coverex.pht') diff --git a/src/hyper/pages/coverex.pht b/src/hyper/pages/coverex.pht new file mode 100644 index 00000000..8b1a6db5 --- /dev/null +++ b/src/hyper/pages/coverex.pht @@ -0,0 +1,1748 @@ +\begin{patch}{MenuexdiffPatch1} +\begin{paste}{MenuexdiffFull1}{MenuexdiffEmpty1} +\pastebutton{MenuexdiffFull1}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + x x + (1) 2x %e sin(x) + cos(x)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty1} +\begin{paste}{MenuexdiffEmpty1}{MenuexdiffPatch1} +\pastebutton{MenuexdiffEmpty1}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * exp(x**2),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch2} +\begin{paste}{MenuexdiffFull2}{MenuexdiffEmpty2} +\pastebutton{MenuexdiffFull2}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\indentrel{3}\begin{verbatim} + 2 2 + (- 2x sin(x) + (y + x )cos(x))tan(y) + (2) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty2} +\begin{paste}{MenuexdiffEmpty2}{MenuexdiffPatch2} +\pastebutton{MenuexdiffEmpty2}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch3} +\begin{paste}{MenuexdiffFull3}{MenuexdiffEmpty3} +\pastebutton{MenuexdiffFull3}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\indentrel{3}\begin{verbatim} + (3) + 2 2 2 + (y + x )sin(x)tan(y) - 2y sin(x)tan(y) + + + 2 2 + (y + x )sin(x) + / + 4 2 2 4 + y + 2x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty3} +\begin{paste}{MenuexdiffEmpty3}{MenuexdiffPatch3} +\pastebutton{MenuexdiffEmpty3}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x) * tan(y)/(x**2 + y**2),y)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch4} +\begin{paste}{MenuexdiffFull4}{MenuexdiffEmpty4} +\pastebutton{MenuexdiffFull4}{\hidepaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\indentrel{3}\begin{verbatim} + 2 + 4 2 x + (4) (16x + 48x + 12)%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty4} +\begin{paste}{MenuexdiffEmpty4}{MenuexdiffPatch4} +\pastebutton{MenuexdiffEmpty4}{\showpaste} +\tab{5}\spadcommand{differentiate(exp(x**2),x,4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch5} +\begin{paste}{MenuexdiffFull5}{MenuexdiffEmpty5} +\pastebutton{MenuexdiffFull5}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\indentrel{3}\begin{verbatim} + 3 2 + 8x y sin(x) + (- 2y - 2x y)cos(x) + (5) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 + 6 2 4 4 2 6 + y + 3x y + 3x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty5} +\begin{paste}{MenuexdiffEmpty5}{MenuexdiffPatch5} +\pastebutton{MenuexdiffEmpty5}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch6} +\begin{paste}{MenuexdiffFull6}{MenuexdiffEmpty6} +\pastebutton{MenuexdiffFull6}{\hidepaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\indentrel{3}\begin{verbatim} + (6) + 2 3 4 2 2 4 + (- 40x y + 8x )sin(x) + (6y + 4x y - 2x )cos(x) + 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 + 8 2 6 4 4 6 2 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty6} +\begin{paste}{MenuexdiffEmpty6}{MenuexdiffPatch6} +\pastebutton{MenuexdiffEmpty6}{\showpaste} +\tab{5}\spadcommand{differentiate(sin(x)/(x**2 + y**2),[x,y,y])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch7} +\begin{paste}{MenuexdiffFull7}{MenuexdiffEmpty7} +\pastebutton{MenuexdiffFull7}{\hidepaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\indentrel{3}\begin{verbatim} + 4 3 + (- 84x y + 24x y)sin(z) + (7) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 + 12 2 9 4 6 6 3 8 + y + 4x y + 6x y + 4x y + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty7} +\begin{paste}{MenuexdiffEmpty7}{MenuexdiffPatch7} +\pastebutton{MenuexdiffEmpty7}{\showpaste} +\tab{5}\spadcommand{differentiate(cos(z)/(x**2 + y**3),[x,y,z],[1,2,3])} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch8} +\begin{paste}{MenuexdiffFull8}{MenuexdiffEmpty8} +\pastebutton{MenuexdiffFull8}{\hidepaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\indentrel{3}\begin{verbatim} + t 旼컴컴컴� + 悶 � 3 + (8) � \�%N + 1 d%N + 잎 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty8} +\begin{paste}{MenuexdiffEmpty8}{MenuexdiffPatch8} +\pastebutton{MenuexdiffEmpty8}{\showpaste} +\tab{5}\spadcommand{f := integrate(sqrt(1 + t**3),t)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch9} +\begin{paste}{MenuexdiffFull9}{MenuexdiffEmpty9} +\pastebutton{MenuexdiffFull9}{\hidepaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\indentrel{3}\begin{verbatim} + 旼컴컴커 + � 3 + (9) \퀃 + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty9} +\begin{paste}{MenuexdiffEmpty9}{MenuexdiffPatch9} +\pastebutton{MenuexdiffEmpty9}{\showpaste} +\tab{5}\spadcommand{differentiate(f,t)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexdiffPatch10} +\begin{paste}{MenuexdiffFull10}{MenuexdiffEmpty10} +\pastebutton{MenuexdiffFull10}{\hidepaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\indentrel{3}\begin{verbatim} + t 旼컴컴컴� 旼컴컴커 + 悶 � 3 2 � 3 + (10) 2t � \�%N + 1 d%N + t \퀃 + 1 + 잎 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexdiffEmpty10} +\begin{paste}{MenuexdiffEmpty10}{MenuexdiffPatch10} +\pastebutton{MenuexdiffEmpty10}{\showpaste} +\tab{5}\spadcommand{differentiate(f * t**2,t)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch1} +\begin{paste}{MenuexlimitFull1}{MenuexlimitEmpty1} +\pastebutton{MenuexlimitFull1}{\hidepaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\indentrel{3}\begin{verbatim} + 1 + (1) - � + 2 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty1} +\begin{paste}{MenuexlimitEmpty1}{MenuexlimitPatch1} +\pastebutton{MenuexlimitEmpty1}{\showpaste} +\tab{5}\spadcommand{limit((x**2 - 3*x + 2)/(x**2 - 1),x = 1)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch2} +\begin{paste}{MenuexlimitFull2}{MenuexlimitEmpty2} +\pastebutton{MenuexlimitFull2}{\hidepaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\indentrel{3}\begin{verbatim} + a + (2) � + b + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty2} +\begin{paste}{MenuexlimitEmpty2}{MenuexlimitPatch2} +\pastebutton{MenuexlimitEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(sinh(a*x)/tan(b*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch3} +\begin{paste}{MenuexlimitFull3}{MenuexlimitEmpty3} +\pastebutton{MenuexlimitFull3}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\indentrel{3}\begin{verbatim} + (3) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty3} +\begin{paste}{MenuexlimitEmpty3}{MenuexlimitPatch3} +\pastebutton{MenuexlimitEmpty3}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0,"right")} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch4} +\begin{paste}{MenuexlimitFull4}{MenuexlimitEmpty4} +\pastebutton{MenuexlimitFull4}{\hidepaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\indentrel{3}\begin{verbatim} + (4) [leftHandLimit= "failed",rightHandLimit= 0] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty4} +\begin{paste}{MenuexlimitEmpty4}{MenuexlimitPatch4} +\pastebutton{MenuexlimitEmpty4}{\showpaste} +\tab{5}\spadcommand{limit(x * log(x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch5} +\begin{paste}{MenuexlimitFull5}{MenuexlimitEmpty5} +\pastebutton{MenuexlimitFull5}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\indentrel{3}\begin{verbatim} + (5) [leftHandLimit= - 1,rightHandLimit= 1] +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty5} +\begin{paste}{MenuexlimitEmpty5}{MenuexlimitPatch5} +\pastebutton{MenuexlimitEmpty5}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch6} +\begin{paste}{MenuexlimitFull6}{MenuexlimitEmpty6} +\pastebutton{MenuexlimitFull6}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\indentrel{3}\begin{verbatim} + 1 1 + (6) [leftHandLimit= - 컴컴,rightHandLimit= 컴컴] + 旼� 旼� + \�2 \�2 +Type: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty6} +\begin{paste}{MenuexlimitEmpty6}{MenuexlimitPatch6} +\pastebutton{MenuexlimitEmpty6}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(1 - cos(t))/t,t = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch7} +\begin{paste}{MenuexlimitFull7}{MenuexlimitEmpty7} +\pastebutton{MenuexlimitFull7}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + 旼� + \�3 + (7) 컴컴 + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty7} +\begin{paste}{MenuexlimitEmpty7}{MenuexlimitPatch7} +\pastebutton{MenuexlimitEmpty7}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%plusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch8} +\begin{paste}{MenuexlimitFull8}{MenuexlimitEmpty8} +\pastebutton{MenuexlimitFull8}{\hidepaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\indentrel{3}\begin{verbatim} + 旼� + \�3 + (8) - 컴컴 + 5 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty8} +\begin{paste}{MenuexlimitEmpty8}{MenuexlimitPatch8} +\pastebutton{MenuexlimitEmpty8}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(3*x**2 + 1)/(5*x),x = \%minusInfinity)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlimitPatch9} +\begin{paste}{MenuexlimitFull9}{MenuexlimitEmpty9} +\pastebutton{MenuexlimitFull9}{\hidepaste} +\tab{5}\spadcommand{limit(z * sin(1/z),z = 0)} +\indentrel{3}\begin{verbatim} + (9) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + 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+\pastebutton{MenuexlimitFull13}{\hidepaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\indentrel{3}\begin{verbatim} + (13) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlimitEmpty13} +\begin{paste}{MenuexlimitEmpty13}{MenuexlimitPatch13} +\pastebutton{MenuexlimitEmpty13}{\showpaste} +\tab{5}\spadcommand{complexLimit(sin(x)/x,x = \%infinity)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch1} +\begin{paste}{Menuexplot2dFull1}{Menuexplot2dEmpty1} +\pastebutton{Menuexplot2dFull1}{\hidepaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot2d1.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot2d1}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty1} +\begin{paste}{Menuexplot2dEmpty1}{Menuexplot2dPatch1} +\pastebutton{Menuexplot2dEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(sin(tan(x)) - tan(sin(x)),x = 0..6)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch2} +\begin{paste}{Menuexplot2dFull2}{Menuexplot2dEmpty2} +\pastebutton{Menuexplot2dFull2}{\hidepaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot2d2.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot2d2}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty2} +\begin{paste}{Menuexplot2dEmpty2}{Menuexplot2dPatch2} +\pastebutton{Menuexplot2dEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(curve(9 * sin(3*t/4),8 * sin(t)),t = -4*\%pi..4*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch3} +\begin{paste}{Menuexplot2dFull3}{Menuexplot2dEmpty3} +\pastebutton{Menuexplot2dFull3}{\hidepaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot2d3.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot2d3}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty3} +\begin{paste}{Menuexplot2dEmpty3}{Menuexplot2dPatch3} +\pastebutton{Menuexplot2dEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(sin(4*t/7),t = 0..14*\%pi,coordinates == polar)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dPatch4} +\begin{paste}{Menuexplot2dFull4}{Menuexplot2dEmpty4} +\pastebutton{Menuexplot2dFull4}{\hidepaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot2d4.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot2d4}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot2dEmpty4} +\begin{paste}{Menuexplot2dEmpty4}{Menuexplot2dPatch4} +\pastebutton{Menuexplot2dEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(y**2 + y - (x**3 - x) = 0, x, y, range == [-2..2,-2..1])} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch1} +\begin{paste}{Menuexplot3dFull1}{Menuexplot3dEmpty1} +\pastebutton{Menuexplot3dFull1}{\hidepaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot3d1.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot3d1}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty1} +\begin{paste}{Menuexplot3dEmpty1}{Menuexplot3dPatch1} +\pastebutton{Menuexplot3dEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(cos(x*y),x = -3..3,y = -3..3)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch2} +\begin{paste}{Menuexplot3dFull2}{Menuexplot3dEmpty2} +\pastebutton{Menuexplot3dFull2}{\hidepaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot3d2.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot3d2}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty2} +\begin{paste}{Menuexplot3dEmpty2}{Menuexplot3dPatch2} +\pastebutton{Menuexplot3dEmpty2}{\showpaste} +\tab{5}\spadgraph{draw(surface(5*sin(u)*cos(v),4*sin(u)*sin(v),3*cos(u)),u=0..\%pi,v=0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch3} +\begin{paste}{Menuexplot3dFull3}{Menuexplot3dEmpty3} +\pastebutton{Menuexplot3dFull3}{\hidepaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot3d3.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot3d3}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty3} +\begin{paste}{Menuexplot3dEmpty3}{Menuexplot3dPatch3} +\pastebutton{Menuexplot3dEmpty3}{\showpaste} +\tab{5}\spadgraph{draw(surface(u*cos(v),u*sin(v),u),u=0..4,v=0..2*\%pi)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch4} +\begin{paste}{Menuexplot3dFull4}{Menuexplot3dEmpty4} +\pastebutton{Menuexplot3dFull4}{\hidepaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot3d4.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot3d4}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty4} +\begin{paste}{Menuexplot3dEmpty4}{Menuexplot3dPatch4} +\pastebutton{Menuexplot3dEmpty4}{\showpaste} +\tab{5}\spadgraph{draw(curve(cos(t),sin(t),t),t=0..6)} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dPatch5} +\begin{paste}{Menuexplot3dFull5}{Menuexplot3dEmpty5} +\pastebutton{Menuexplot3dFull5}{\hidepaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/Menuexplot3d5.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/Menuexplot3d5}} +\end{paste}\end{patch} + +\begin{patch}{Menuexplot3dEmpty5} +\begin{paste}{Menuexplot3dEmpty5}{Menuexplot3dPatch5} +\pastebutton{Menuexplot3dEmpty5}{\showpaste} +\tab{5}\spadgraph{draw(curve(t,t**2,t**3),t=-3..3)} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch1} +\begin{paste}{MenuexseriesFull1}{MenuexseriesEmpty1} +\pastebutton{MenuexseriesFull1}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\indentrel{3}\begin{verbatim} + (1) + 3 5 7 9 + a 3 a 5 a 7 a 9 + a x - 컴 x + 컴� x - 컴컴 x + 컴컴컴 x + 6 120 5040 362880 + + + 11 + a 11 12 + - 컴컴컴컴 x + O(x ) + 39916800 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty1} +\begin{paste}{MenuexseriesEmpty1}{MenuexseriesPatch1} +\pastebutton{MenuexseriesEmpty1}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch2} +\begin{paste}{MenuexseriesFull2}{MenuexseriesEmpty2} +\pastebutton{MenuexseriesFull2}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\indentrel{3}\begin{verbatim} + (2) + %pi x %pi x %pi + sin(컴컴�) + x cos(컴컴�)(a - 컴�) + 4 4 4 + + + 2 %pi x 3 %pi x + x sin(컴컴�) x cos(컴컴�) + 4 %pi 2 4 %pi 3 + - 컴컴컴컴컴컴 (a - 컴�) - 컴컴컴컴컴컴 (a - 컴�) + 2 4 6 4 + + + 4 %pi x 5 %pi x + x sin(컴컴�) x cos(컴컴�) + 4 %pi 4 4 %pi 5 + 컴컴컴컴컴컴 (a - 컴�) + 컴컴컴컴컴컴 (a - 컴�) + 24 4 120 4 + + + 6 %pi x 7 %pi x + x sin(컴컴�) x cos(컴컴�) + 4 %pi 6 4 %pi 7 + - 컴컴컴컴컴컴 (a - 컴�) - 컴컴컴컴컴컴 (a - 컴�) + 720 4 5040 4 + + + 8 %pi x 9 %pi x + x sin(컴컴�) x cos(컴컴�) + 4 %pi 8 4 %pi 9 + 컴컴컴컴컴컴 (a - 컴�) + 컴컴컴컴컴컴 (a - 컴�) + 40320 4 362880 4 + + + 10 %pi x + x sin(컴컴�) + 4 %pi 10 %pi 11 + - 컴컴컴컴컴컴� (a - 컴�) + O((a - 컴�) ) + 3628800 4 4 +Type: UnivariatePuiseuxSeries(Expression Integer,a,pi/4) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty2} +\begin{paste}{MenuexseriesEmpty2}{MenuexseriesPatch2} +\pastebutton{MenuexseriesEmpty2}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),a = \%pi/4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch3} +\begin{paste}{MenuexseriesFull3}{MenuexseriesEmpty3} +\pastebutton{MenuexseriesFull3}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\indentrel{3}\begin{verbatim} + (3) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty3} +\begin{paste}{MenuexseriesEmpty3}{MenuexseriesPatch3} +\pastebutton{MenuexseriesEmpty3}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch4} +\begin{paste}{MenuexseriesFull4}{MenuexseriesEmpty4} +\pastebutton{MenuexseriesFull4}{\hidepaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\indentrel{3}\begin{verbatim} + (4) + 2 3 4 5 6 7 8 + 1 + 2x + 3x + 4x + 5x + 6x + 7x + 8x + 9x + + + 9 10 11 + 10x + 11x + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty4} +\begin{paste}{MenuexseriesEmpty4}{MenuexseriesPatch4} +\pastebutton{MenuexseriesEmpty4}{\showpaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch5} +\begin{paste}{MenuexseriesFull5}{MenuexseriesEmpty5} +\pastebutton{MenuexseriesFull5}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\indentrel{3}\begin{verbatim} + (5) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty5} +\begin{paste}{MenuexseriesEmpty5}{MenuexseriesPatch5} +\pastebutton{MenuexseriesEmpty5}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch6} +\begin{paste}{MenuexseriesFull6}{MenuexseriesEmpty6} +\pastebutton{MenuexseriesFull6}{\hidepaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\indentrel{3}\begin{verbatim} + (6) + 1 2 1 3 1 4 1 5 1 6 1 7 1 8 + x + � x + � x + � x + � x + � x + � x + � x + 2 3 4 5 6 7 8 + + + 1 9 1 10 1 11 12 + � x + 컴 x + 컴 x + O(x ) + 9 10 11 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty6} +\begin{paste}{MenuexseriesEmpty6}{MenuexseriesPatch6} +\pastebutton{MenuexseriesEmpty6}{\showpaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch7} +\begin{paste}{MenuexseriesFull7}{MenuexseriesEmpty7} +\pastebutton{MenuexseriesFull7}{\hidepaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\indentrel{3}\begin{verbatim} + (7) + 2 3 4 5 6 7 8 9 10 + 1 + x + x + x + x + x + x + x + x + x + x + + + 11 + O(x ) + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty7} +\begin{paste}{MenuexseriesEmpty7}{MenuexseriesPatch7} +\pastebutton{MenuexseriesEmpty7}{\showpaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch8} +\begin{paste}{MenuexseriesFull8}{MenuexseriesEmpty8} +\pastebutton{MenuexseriesFull8}{\hidepaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\indentrel{3}\begin{verbatim} + (8) + 1 2 1 3 1 4 1 5 1 6 + 1 + x + � x + � x + 컴 x + 컴� x + 컴� x + 2 6 24 120 720 + + + 1 7 1 8 1 9 1 10 11 + 컴컴 x + 컴컴� x + 컴컴컴 x + 컴컴컴� x + O(x ) + 5040 40320 362880 3628800 + Type: UnivariateTaylorSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty8} +\begin{paste}{MenuexseriesEmpty8}{MenuexseriesPatch8} +\pastebutton{MenuexseriesEmpty8}{\showpaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexseriesPatch9} +\begin{paste}{MenuexseriesFull9}{MenuexseriesEmpty9} +\pastebutton{MenuexseriesFull9}{\hidepaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\indentrel{3}\begin{verbatim} + (9) + [1.0, 2.0, 2.5, 2.6666666666 666666667, + 2.7083333333 333333333, 2.7166666666 666666667, + 2.7180555555 555555556, 2.7182539682 53968254, + 2.7182787698 412698413, 2.7182815255 731922399, ...] + Type: Stream Expression Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexseriesEmpty9} +\begin{paste}{MenuexseriesEmpty9}{MenuexseriesPatch9} +\pastebutton{MenuexseriesEmpty9}{\showpaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch1} +\begin{paste}{MenuexmatrixFull1}{MenuexmatrixEmpty1} +\pastebutton{MenuexmatrixFull1}{\hidepaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\indentrel{3}\begin{verbatim} + �1 - 2 1 � + (1) � � + �4 2 - 4� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty1} +\begin{paste}{MenuexmatrixEmpty1}{MenuexmatrixPatch1} +\pastebutton{MenuexmatrixEmpty1}{\showpaste} +\tab{5}\spadcommand{m1 := matrix([[1,-2,1],[4,2,-4]])\bound{m1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch2} +\begin{paste}{MenuexmatrixFull2}{MenuexmatrixEmpty2} +\pastebutton{MenuexmatrixFull2}{\hidepaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\indentrel{3}\begin{verbatim} + �1 0 2 � + � � + (2) �20 30 10 � + � � + �0 200 100� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty2} +\begin{paste}{MenuexmatrixEmpty2}{MenuexmatrixPatch2} +\pastebutton{MenuexmatrixEmpty2}{\showpaste} +\tab{5}\spadcommand{m2 := matrix([[1,0,2],[20,30,10],[0,200,100]])\bound{m2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch3} +\begin{paste}{MenuexmatrixFull3}{MenuexmatrixEmpty3} +\pastebutton{MenuexmatrixFull3}{\hidepaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\indentrel{3}\begin{verbatim} + �1 2 3� + (3) � � + �2 4 6� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty3} +\begin{paste}{MenuexmatrixEmpty3}{MenuexmatrixPatch3} +\pastebutton{MenuexmatrixEmpty3}{\showpaste} +\tab{5}\spadcommand{m3 := matrix([[1,2,3],[2,4,6]])\bound{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch4} +\begin{paste}{MenuexmatrixFull4}{MenuexmatrixEmpty4} +\pastebutton{MenuexmatrixFull4}{\hidepaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\indentrel{3}\begin{verbatim} + �2 0 4� + (4) � � + �6 6 2� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty4} +\begin{paste}{MenuexmatrixEmpty4}{MenuexmatrixPatch4} +\pastebutton{MenuexmatrixEmpty4}{\showpaste} +\tab{5}\spadcommand{m1 + m3\free{m1 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch5} +\begin{paste}{MenuexmatrixFull5}{MenuexmatrixEmpty5} +\pastebutton{MenuexmatrixFull5}{\hidepaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\indentrel{3}\begin{verbatim} + �100 - 200 100 � + (5) � � + �400 200 - 400� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty5} +\begin{paste}{MenuexmatrixEmpty5}{MenuexmatrixPatch5} +\pastebutton{MenuexmatrixEmpty5}{\showpaste} +\tab{5}\spadcommand{100 * m1\free{m1 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch6} +\begin{paste}{MenuexmatrixFull6}{MenuexmatrixEmpty6} +\pastebutton{MenuexmatrixFull6}{\hidepaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\indentrel{3}\begin{verbatim} + �- 39 140 82 � + (6) � � + � 44 - 740 - 372� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty6} +\begin{paste}{MenuexmatrixEmpty6}{MenuexmatrixPatch6} +\pastebutton{MenuexmatrixEmpty6}{\showpaste} +\tab{5}\spadcommand{m1 * m2\free{m1 }\free{m2 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch7} +\begin{paste}{MenuexmatrixFull7}{MenuexmatrixEmpty7} +\pastebutton{MenuexmatrixFull7}{\hidepaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\indentrel{3}\begin{verbatim} + �40 662 321� + (7) � � + �78 1318 648� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty7} +\begin{paste}{MenuexmatrixEmpty7}{MenuexmatrixPatch7} +\pastebutton{MenuexmatrixEmpty7}{\showpaste} +\tab{5}\spadcommand{-m1 + m3 * m2\free{m1 }\free{m2 }\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch8} +\begin{paste}{MenuexmatrixFull8}{MenuexmatrixEmpty8} +\pastebutton{MenuexmatrixFull8}{\hidepaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\indentrel{3}\begin{verbatim} + (8) [4,8] + Type: Vector Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty8} +\begin{paste}{MenuexmatrixEmpty8}{MenuexmatrixPatch8} +\pastebutton{MenuexmatrixEmpty8}{\showpaste} +\tab{5}\spadcommand{m3 *vector([1,0,1])\free{m3 }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch9} +\begin{paste}{MenuexmatrixFull9}{MenuexmatrixEmpty9} +\pastebutton{MenuexmatrixFull9}{\hidepaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\indentrel{3}\begin{verbatim} + �1 0 0 0 0� + � � + �0 2 0 0 0� + � � + (9) �0 0 3 0 0� + � � + �0 0 0 2 0� + � � + �0 0 0 0 1� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty9} +\begin{paste}{MenuexmatrixEmpty9}{MenuexmatrixPatch9} +\pastebutton{MenuexmatrixEmpty9}{\showpaste} +\tab{5}\spadcommand{diagonalMatrix([1,2,3,2,1])} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch10} +\begin{paste}{MenuexmatrixFull10}{MenuexmatrixEmpty10} +\pastebutton{MenuexmatrixFull10}{\hidepaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\indentrel{3}\begin{verbatim} + �1 2 3 � + � � + (10) �6 7 8 � + � � + �11 12 13� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty10} +\begin{paste}{MenuexmatrixEmpty10}{MenuexmatrixPatch10} +\pastebutton{MenuexmatrixEmpty10}{\showpaste} +\tab{5}\spadcommand{subMatrix(matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]]), 1,3,2,4)} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch11} +\begin{paste}{MenuexmatrixFull11}{MenuexmatrixEmpty11} +\pastebutton{MenuexmatrixFull11}{\hidepaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + �1 2 3 11 12 13� + (11) � � + �6 7 8 55 77 88� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty11} +\begin{paste}{MenuexmatrixEmpty11}{MenuexmatrixPatch11} +\pastebutton{MenuexmatrixEmpty11}{\showpaste} +\tab{5}\spadcommand{horizConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch12} +\begin{paste}{MenuexmatrixFull12}{MenuexmatrixEmpty12} +\pastebutton{MenuexmatrixFull12}{\hidepaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\indentrel{3}\begin{verbatim} + �1 2 3 � + � � + �6 7 8 � + (12) � � + �11 12 13� + � � + �55 77 88� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty12} +\begin{paste}{MenuexmatrixEmpty12}{MenuexmatrixPatch12} +\pastebutton{MenuexmatrixEmpty12}{\showpaste} +\tab{5}\spadcommand{vertConcat(matrix([[1,2,3],[6,7,8]]),matrix([[11,12,13],[55,77,88]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch13} +\begin{paste}{MenuexmatrixFull13}{MenuexmatrixEmpty13} +\pastebutton{MenuexmatrixFull13}{\hidepaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\indentrel{3}\begin{verbatim} + �0 1 2 3 4 � + � � + (13) �5 6 7 8 9 � + � � + �10 11 12 13 14� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty13} +\begin{paste}{MenuexmatrixEmpty13}{MenuexmatrixPatch13} +\pastebutton{MenuexmatrixEmpty13}{\showpaste} +\tab{5}\spadcommand{b:=matrix([[0,1,2,3,4],[5,6,7,8,9],[10,11,12,13,14]])\bound{b }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch14} +\begin{paste}{MenuexmatrixFull14}{MenuexmatrixEmpty14} +\pastebutton{MenuexmatrixFull14}{\hidepaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\indentrel{3}\begin{verbatim} + �0 5 10 3 4 � + � � + (14) �1 6 11 8 9 � + � � + �2 7 12 13 14� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty14} +\begin{paste}{MenuexmatrixEmpty14}{MenuexmatrixPatch14} +\pastebutton{MenuexmatrixEmpty14}{\showpaste} +\tab{5}\spadcommand{setsubMatrix!(b,1,1,transpose(subMatrix(b,1,3,1,3)))\free{b }} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch15} +\begin{paste}{MenuexmatrixFull15}{MenuexmatrixEmpty15} +\pastebutton{MenuexmatrixFull15}{\hidepaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\indentrel{3}\begin{verbatim} + 2 3 + (15) z + y + u + 1 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty15} +\begin{paste}{MenuexmatrixEmpty15}{MenuexmatrixPatch15} +\pastebutton{MenuexmatrixEmpty15}{\showpaste} +\tab{5}\spadcommand{trace( matrix([[1,x,x**2,x**3],[1,y,y**2,y**3],[1,z,z**2,z**3],[1,u,u**2,u**3]]) )} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch16} +\begin{paste}{MenuexmatrixFull16}{MenuexmatrixEmpty16} +\pastebutton{MenuexmatrixFull16}{\hidepaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\indentrel{3}\begin{verbatim} + (16) - 48 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty16} +\begin{paste}{MenuexmatrixEmpty16}{MenuexmatrixPatch16} +\pastebutton{MenuexmatrixEmpty16}{\showpaste} +\tab{5}\spadcommand{determinant(matrix([[1,2,3,4],[2,3,2,5],[3,4,5,6],[4,1,6,7]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch17} +\begin{paste}{MenuexmatrixFull17}{MenuexmatrixEmpty17} +\pastebutton{MenuexmatrixFull17}{\hidepaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\indentrel{3}\begin{verbatim} + � 2 5 � + �- � - 1 � � + � 7 7 � + � � + (17) � 8 6� + � � 1 - 캐 + � 7 7� + � � + �- 1 - 1 1 � + Type: Union(Matrix Fraction Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty17} +\begin{paste}{MenuexmatrixEmpty17}{MenuexmatrixPatch17} +\pastebutton{MenuexmatrixEmpty17}{\showpaste} +\tab{5}\spadcommand{inverse(matrix([[1,2,1],[-2,3,4],[-1,5,6]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixPatch18} +\begin{paste}{MenuexmatrixFull18}{MenuexmatrixEmpty18} +\pastebutton{MenuexmatrixFull18}{\hidepaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\indentrel{3}\begin{verbatim} + (18) 2 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexmatrixEmpty18} +\begin{paste}{MenuexmatrixEmpty18}{MenuexmatrixPatch18} +\pastebutton{MenuexmatrixEmpty18}{\showpaste} +\tab{5}\spadcommand{rank(matrix([[0,4,1],[5,3,-7],[-5,5,9]]))} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch1} +\begin{paste}{MenuexlapFull1}{MenuexlapEmpty1} +\pastebutton{MenuexlapFull1}{\hidepaste} +\tab{5}\spadcommand{laplace(t**4 * exp(-a*t) / factorial(4), t, s)} +\indentrel{3}\begin{verbatim} + 1 + (1) 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+\begin{paste}{MenuexlapFull3}{MenuexlapEmpty3} +\pastebutton{MenuexlapFull3}{\hidepaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + (3) log(s + a ) - 2log(s) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty3} +\begin{paste}{MenuexlapEmpty3}{MenuexlapPatch3} +\pastebutton{MenuexlapEmpty3}{\showpaste} +\tab{5}\spadcommand{laplace(2/t * (1 - cos(a*t)), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch4} +\begin{paste}{MenuexlapFull4}{MenuexlapEmpty4} +\pastebutton{MenuexlapFull4}{\hidepaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\indentrel{3}\begin{verbatim} + (4) - log(s - a) + log(s - b) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty4} +\begin{paste}{MenuexlapEmpty4}{MenuexlapPatch4} +\pastebutton{MenuexlapEmpty4}{\showpaste} +\tab{5}\spadcommand{laplace((exp(a*t) - exp(b*t))/t, t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch5} +\begin{paste}{MenuexlapFull5}{MenuexlapEmpty5} +\pastebutton{MenuexlapFull5}{\hidepaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\indentrel{3}\begin{verbatim} + b s + c - a + %e log(컴컴컴컴�) + c + (5) 컴컴컴컴컴컴컴컴� + s - a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty5} +\begin{paste}{MenuexlapEmpty5}{MenuexlapPatch5} +\pastebutton{MenuexlapEmpty5}{\showpaste} +\tab{5}\spadcommand{laplace(exp(a*t+b)*Ei(c*t), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexlapPatch6} +\begin{paste}{MenuexlapFull6}{MenuexlapEmpty6} +\pastebutton{MenuexlapFull6}{\hidepaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\indentrel{3}\begin{verbatim} + 2 2 + s + b d + a log(컴컴컴�) + 2c atan(�) + 2 s + b + (6) 컴컴컴컴컴컴컴컴컴컴컴컴컴� + 2s + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexlapEmpty6} +\begin{paste}{MenuexlapEmpty6}{MenuexlapPatch6} +\pastebutton{MenuexlapEmpty6}{\showpaste} +\tab{5}\spadcommand{laplace(a*Ci(b*t) + c*Si(d*t), t, s)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch1} +\begin{paste}{MenuexintFull1}{MenuexintEmpty1} +\pastebutton{MenuexintFull1}{\hidepaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\indentrel{3}\begin{verbatim} + 3 2 + atan(x + 3x + 3x + 1) + (1) 컴컴컴컴컴컴컴컴컴컴컴� + 3 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty1} +\begin{paste}{MenuexintEmpty1}{MenuexintPatch1} +\pastebutton{MenuexintEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch2} +\begin{paste}{MenuexintFull2}{MenuexintEmpty2} +\pastebutton{MenuexintFull2}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\indentrel{3}\begin{verbatim} + (2) + 旼컴컴컴컴컴컴컴� + � 2 + �- 93%%CE0 + 12 + ( 냐컴컴컴컴컴컴컴 - %%CE0) + \� 31 + * + log + 旼컴컴컴컴컴컴컴� + � 2 + �- 93%%CE0 + 12 2 + (62%%CE0 + 31) 냐컴컴컴컴컴컴컴 + 62%%CE0 + \� 31 + + + - 31%%CE0 + 18x - 4 + + + 旼컴컴컴컴컴컴컴� + � 2 + �- 93%%CE0 + 12 + (- 냐컴컴컴컴컴컴컴 - %%CE0) + \� 31 + * + log + 旼컴컴컴컴컴컴컴� + � 2 + �- 93%%CE0 + 12 + (- 62%%CE0 - 31) 냐컴컴컴컴컴컴컴 + \� 31 + + + 2 + 62%%CE0 - 31%%CE0 + 18x - 4 + + + 2 + 2%%CE0 log(- 62%%CE0 + 31%%CE0 + 9x + 4) + / + 2 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty2} +\begin{paste}{MenuexintEmpty2}{MenuexintPatch2} +\pastebutton{MenuexintEmpty2}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**3+x+1),x)\bound{i }} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch3} +\begin{paste}{MenuexintFull3}{MenuexintEmpty3} +\pastebutton{MenuexintFull3}{\hidepaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\indentrel{3}\begin{verbatim} + 3 + 31%%CE0 - 3%%CE0 - 1 + (3) 컴컴컴컴컴컴컴컴컴컴� + 31 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty3} +\begin{paste}{MenuexintEmpty3}{MenuexintPatch3} +\pastebutton{MenuexintEmpty3}{\showpaste} +\tab{5}\spadcommand{definingPolynomial(tower(\%).2::EXPR INT)\free{i }} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch4} +\begin{paste}{MenuexintFull4}{MenuexintEmpty4} +\pastebutton{MenuexintFull4}{\hidepaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + 2 旼컴� + (x - a)\�- a + 2a x 旼� + log(컴컴컴컴컴컴컴컴컴컴�) x\쿪 + 2 atan(컴컴�) + x + a a + (4) [컴컴컴컴컴컴컴컴컴컴컴컴컴,컴컴컴컴컴�] + 旼컴� 旼� + 2\�- a \쿪 + Type: Union(List Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty4} +\begin{paste}{MenuexintEmpty4}{MenuexintPatch4} +\pastebutton{MenuexintEmpty4}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch5} +\begin{paste}{MenuexintFull5}{MenuexintEmpty5} +\pastebutton{MenuexintFull5}{\hidepaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\indentrel{3}\begin{verbatim} + 旼컴� 旼컴� + x\�- a + a x\�- a - a + log(컴컴컴컴컴�) - log(컴컴컴컴컴�) + 旼컴� 旼컴� + \�- a \�- a + (5) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 旼컴� + 2\�- a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty5} +\begin{paste}{MenuexintEmpty5}{MenuexintPatch5} +\pastebutton{MenuexintEmpty5}{\showpaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch6} +\begin{paste}{MenuexintFull6}{MenuexintEmpty6} +\pastebutton{MenuexintFull6}{\hidepaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\indentrel{3}\begin{verbatim} + (6) + 3 3 2 2 2 3 3旼컴컴컴�2 + (120b x - 135a b x + 162a b x - 243a )\쿫 x + a + 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 4 + 440b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty6} +\begin{paste}{MenuexintEmpty6}{MenuexintPatch6} +\pastebutton{MenuexintEmpty6}{\showpaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch7} +\begin{paste}{MenuexintFull7}{MenuexintEmpty7} +\pastebutton{MenuexintFull7}{\hidepaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\indentrel{3}\begin{verbatim} + (7) + - + 2 2 旼� + 2b x \�3 + * + 3旼�3旼컴컴컴�2 3旼�2 3旼컴컴컴� + log(\쿪 \쿫 x + a + \쿪 \쿫 x + a + a) + + + 2 2 旼� 3旼�2 3旼컴컴컴� + 4b x \�3 log(\쿪 \쿫 x + a - a) + + + 旼�3旼�2 3旼컴컴컴� 旼� + 2 2 2\�3 \쿪 \쿫 x + a + a\�3 + 12b x atan(컴컴컴컴컴컴컴컴컴컴컴컴컴컴) + 3a + + + 旼�3旼�3旼컴컴컴�2 + (12b x - 9a)\�3 \쿪 \쿫 x + a + / + 2 2 旼�3旼� + 18a x \�3 \쿪 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty7} +\begin{paste}{MenuexintEmpty7}{MenuexintPatch7} +\pastebutton{MenuexintEmpty7}{\showpaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch8} +\begin{paste}{MenuexintFull8}{MenuexintEmpty8} +\pastebutton{MenuexintFull8}{\hidepaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\indentrel{3}\begin{verbatim} + x 旼컴컴컴커 + 悶 log(\쿫 + %N a + 1) + (8) � 컴컴컴컴컴컴컴컴컴컴 d%N + 잎 %N + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexintEmpty8} +\begin{paste}{MenuexintEmpty8}{MenuexintPatch8} +\pastebutton{MenuexintEmpty8}{\showpaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\end{paste}\end{patch} + +\begin{patch}{MenuexintPatch9} +\begin{paste}{MenuexintFull9}{MenuexintEmpty9} +\pastebutton{MenuexintFull9}{\hidepaste} +\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b))/(sqrt(x+b)*(x+cosh(1+sqrt(x+b)))),x)} +\indentrel{3}\begin{verbatim} + (9) + 旼컴컴� + - 2cosh(\퀈 + b + 1) - 2x + 2log(컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴�) + 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+\pastebutton{MenuexsumFull2}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\indentrel{3}\begin{verbatim} + (2) 120 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty2} +\begin{paste}{MenuexsumEmpty2}{MenuexsumPatch2} +\pastebutton{MenuexsumEmpty2}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i for i in 1..15])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch3} +\begin{paste}{MenuexsumFull3}{MenuexsumEmpty3} +\pastebutton{MenuexsumFull3}{\hidepaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\indentrel{3}\begin{verbatim} + (3) + [25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, + 256, 289, 324, 361, 400] + Type: List PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty3} +\begin{paste}{MenuexsumEmpty3}{MenuexsumPatch3} +\pastebutton{MenuexsumEmpty3}{\showpaste} +\tab{5}\spadcommand{[n**2 for n in 5..20]} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch4} +\begin{paste}{MenuexsumFull4}{MenuexsumEmpty4} +\pastebutton{MenuexsumFull4}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\indentrel{3}\begin{verbatim} + (4) 2840 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty4} +\begin{paste}{MenuexsumEmpty4}{MenuexsumPatch4} +\pastebutton{MenuexsumEmpty4}{\showpaste} +\tab{5}\spadcommand{reduce(+,[n**2 for n in 5..20])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch5} +\begin{paste}{MenuexsumFull5}{MenuexsumEmpty5} +\pastebutton{MenuexsumFull5}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\indentrel{3}\begin{verbatim} + (5) 2.7182818284 590452354 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty5} +\begin{paste}{MenuexsumEmpty5}{MenuexsumPatch5} +\pastebutton{MenuexsumEmpty5}{\showpaste} +\tab{5}\spadcommand{reduce(+,[1.0/factorial(n) for n in 0..20])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch6} +\begin{paste}{MenuexsumFull6}{MenuexsumEmpty6} +\pastebutton{MenuexsumFull6}{\hidepaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\indentrel{3}\begin{verbatim} + 3 2 3 2 + 2b + 3b + b - 2a + 3a - a + (6) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 6 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty6} +\begin{paste}{MenuexsumEmpty6}{MenuexsumPatch6} +\pastebutton{MenuexsumEmpty6}{\showpaste} +\tab{5}\spadcommand{s := sum(k**2,k = a..b)\bound{s }} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch7} +\begin{paste}{MenuexsumFull7}{MenuexsumEmpty7} +\pastebutton{MenuexsumFull7}{\hidepaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\indentrel{3}\begin{verbatim} + (7) 5525 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty7} +\begin{paste}{MenuexsumEmpty7}{MenuexsumPatch7} +\pastebutton{MenuexsumEmpty7}{\showpaste} +\tab{5}\spadcommand{eval(s,[a,b],[1,25])\free{s }} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch8} +\begin{paste}{MenuexsumFull8}{MenuexsumEmpty8} +\pastebutton{MenuexsumFull8}{\hidepaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\indentrel{3}\begin{verbatim} + (8) 5525 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty8} +\begin{paste}{MenuexsumEmpty8}{MenuexsumPatch8} +\pastebutton{MenuexsumEmpty8}{\showpaste} +\tab{5}\spadcommand{reduce(+,[i**2 for i in 1..25])} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch9} +\begin{paste}{MenuexsumFull9}{MenuexsumEmpty9} +\pastebutton{MenuexsumFull9}{\hidepaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (9) 컴컴컴컴컴컴� + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty9} +\begin{paste}{MenuexsumEmpty9}{MenuexsumPatch9} +\pastebutton{MenuexsumEmpty9}{\showpaste} +\tab{5}\spadcommand{sum(k**3,k = 1..n)} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch10} +\begin{paste}{MenuexsumFull10}{MenuexsumEmpty10} +\pastebutton{MenuexsumFull10}{\hidepaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\indentrel{3}\begin{verbatim} + 4 3 2 + n + 2n + n + (10) 컴컴컴컴컴컴� + 4 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty10} +\begin{paste}{MenuexsumEmpty10}{MenuexsumPatch10} +\pastebutton{MenuexsumEmpty10}{\showpaste} +\tab{5}\spadcommand{sum(k,k = 1..n) ** 2} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch11} +\begin{paste}{MenuexsumFull11}{MenuexsumEmpty11} +\pastebutton{MenuexsumFull11}{\hidepaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\indentrel{3}\begin{verbatim} + (11) + 3 2 3 2 + (128b + 48b + 4b - 54a + 27a - 3a)d + + + 2 2 2 2 2 + (192b + 48b - 108a + 36a)c + 192b + 48b - 108a + + + 36a + / + 2 + (2c + 2)d + Type: Union(Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty11} +\begin{paste}{MenuexsumEmpty11}{MenuexsumPatch11} +\pastebutton{MenuexsumEmpty11}{\showpaste} +\tab{5}\spadcommand{sum(3*k**2/(c**2 + 1) + 12*k/d,k = (3*a)..(4*b))} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch12} +\begin{paste}{MenuexsumFull12}{MenuexsumEmpty12} +\pastebutton{MenuexsumFull12}{\hidepaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\indentrel{3}\begin{verbatim} + 2 n + (n x + (- n - 1)x)x + x + (12) 컴컴컴컴컴컴컴컴컴컴컴컴� + 2 + x - 2x + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty12} +\begin{paste}{MenuexsumEmpty12}{MenuexsumPatch12} +\pastebutton{MenuexsumEmpty12}{\showpaste} +\tab{5}\spadcommand{sum(k * x**k,k = 1..n)} +\end{paste}\end{patch} + +\begin{patch}{MenuexsumPatch13} +\begin{paste}{MenuexsumFull13}{MenuexsumEmpty13} +\pastebutton{MenuexsumFull13}{\hidepaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\indentrel{3}\begin{verbatim} + 3 + (13) � + 4 +Type: Union(OrderedCompletion Fraction Polynomial Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{MenuexsumEmpty13} +\begin{paste}{MenuexsumEmpty13}{MenuexsumPatch13} +\pastebutton{MenuexsumEmpty13}{\showpaste} +\tab{5}\spadcommand{limit( sum(1/(k * (k + 2)),k = 1..n) ,n = \%plusInfinity)} +\end{paste}\end{patch} + -- cgit v1.2.3