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/ug01.pht | 3673 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 3673 insertions(+) create mode 100644 src/hyper/pages/ug01.pht (limited to 'src/hyper/pages/ug01.pht') diff --git a/src/hyper/pages/ug01.pht b/src/hyper/pages/ug01.pht new file mode 100644 index 00000000..0ef9c533 --- /dev/null +++ b/src/hyper/pages/ug01.pht @@ -0,0 +1,3673 @@ +\begin{patch}{ugIntroCalcDerivPagePatch1} +\begin{paste}{ugIntroCalcDerivPageFull1}{ugIntroCalcDerivPageEmpty1} +\pastebutton{ugIntroCalcDerivPageFull1}{\hidepaste} +\tab{5}\spadcommand{f := exp exp x\bound{f }} +\indentrel{3}\begin{verbatim} + x + %e + (1) %e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty1} +\begin{paste}{ugIntroCalcDerivPageEmpty1}{ugIntroCalcDerivPagePatch1} +\pastebutton{ugIntroCalcDerivPageEmpty1}{\showpaste} +\tab{5}\spadcommand{f := exp exp x\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch2} +\begin{paste}{ugIntroCalcDerivPageFull2}{ugIntroCalcDerivPageEmpty2} +\pastebutton{ugIntroCalcDerivPageFull2}{\hidepaste} +\tab{5}\spadcommand{D(f, x)\free{f }} +\indentrel{3}\begin{verbatim} + x + x %e + (2) %e %e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty2} +\begin{paste}{ugIntroCalcDerivPageEmpty2}{ugIntroCalcDerivPagePatch2} +\pastebutton{ugIntroCalcDerivPageEmpty2}{\showpaste} +\tab{5}\spadcommand{D(f, x)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch3} +\begin{paste}{ugIntroCalcDerivPageFull3}{ugIntroCalcDerivPageEmpty3} +\pastebutton{ugIntroCalcDerivPageFull3}{\hidepaste} +\tab{5}\spadcommand{D(f, x, 4)\free{f }} +\indentrel{3}\begin{verbatim} + x + x 4 x 3 x 2 x %e + (3) ((%e ) + 6(%e ) + 7(%e ) + %e )%e + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty3} +\begin{paste}{ugIntroCalcDerivPageEmpty3}{ugIntroCalcDerivPagePatch3} +\pastebutton{ugIntroCalcDerivPageEmpty3}{\showpaste} +\tab{5}\spadcommand{D(f, x, 4)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch4} +\begin{paste}{ugIntroCalcDerivPageFull4}{ugIntroCalcDerivPageEmpty4} +\pastebutton{ugIntroCalcDerivPageFull4}{\hidepaste} +\tab{5}\spadcommand{g := sin(x**2 + y)\bound{g }} +\indentrel{3}\begin{verbatim} + 2 + (4) sin(y + x ) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty4} +\begin{paste}{ugIntroCalcDerivPageEmpty4}{ugIntroCalcDerivPagePatch4} +\pastebutton{ugIntroCalcDerivPageEmpty4}{\showpaste} +\tab{5}\spadcommand{g := sin(x**2 + y)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch5} +\begin{paste}{ugIntroCalcDerivPageFull5}{ugIntroCalcDerivPageEmpty5} +\pastebutton{ugIntroCalcDerivPageFull5}{\hidepaste} +\tab{5}\spadcommand{D(g, y)\free{g }} +\indentrel{3}\begin{verbatim} + 2 + (5) cos(y + x ) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty5} +\begin{paste}{ugIntroCalcDerivPageEmpty5}{ugIntroCalcDerivPagePatch5} +\pastebutton{ugIntroCalcDerivPageEmpty5}{\showpaste} +\tab{5}\spadcommand{D(g, y)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch6} +\begin{paste}{ugIntroCalcDerivPageFull6}{ugIntroCalcDerivPageEmpty6} +\pastebutton{ugIntroCalcDerivPageFull6}{\hidepaste} +\tab{5}\spadcommand{D(g, [y, y, x, x])\free{g }} +\indentrel{3}\begin{verbatim} + 2 2 2 + (6) 4x sin(y + x ) - 2cos(y + x ) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty6} +\begin{paste}{ugIntroCalcDerivPageEmpty6}{ugIntroCalcDerivPagePatch6} +\pastebutton{ugIntroCalcDerivPageEmpty6}{\showpaste} +\tab{5}\spadcommand{D(g, [y, y, x, x])\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch7} +\begin{paste}{ugIntroCalcDerivPageFull7}{ugIntroCalcDerivPageEmpty7} +\pastebutton{ugIntroCalcDerivPageFull7}{\hidepaste} +\tab{5}\spadcommand{D(F,x)} +\indentrel{3}\begin{verbatim} + (7) 0 + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty7} +\begin{paste}{ugIntroCalcDerivPageEmpty7}{ugIntroCalcDerivPagePatch7} +\pastebutton{ugIntroCalcDerivPageEmpty7}{\showpaste} +\tab{5}\spadcommand{D(F,x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch8} +\begin{paste}{ugIntroCalcDerivPageFull8}{ugIntroCalcDerivPageEmpty8} +\pastebutton{ugIntroCalcDerivPageFull8}{\hidepaste} +\tab{5}\spadcommand{F := operator 'F; x := operator 'x; y := operator 'y\bound{F x y }} +\indentrel{3}\begin{verbatim} + (8) y + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty8} +\begin{paste}{ugIntroCalcDerivPageEmpty8}{ugIntroCalcDerivPagePatch8} +\pastebutton{ugIntroCalcDerivPageEmpty8}{\showpaste} +\tab{5}\spadcommand{F := operator 'F; x := operator 'x; y := operator 'y\bound{F x y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch9} +\begin{paste}{ugIntroCalcDerivPageFull9}{ugIntroCalcDerivPageEmpty9} +\pastebutton{ugIntroCalcDerivPageFull9}{\hidepaste} +\tab{5}\spadcommand{a := F(x z, y z, z**2) + x y(z+1)\bound{a }\free{F }\free{x }\free{y }} +\indentrel{3}\begin{verbatim} + 2 + (9) x(y(z + 1)) + F(x(z),y(z),z ) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty9} +\begin{paste}{ugIntroCalcDerivPageEmpty9}{ugIntroCalcDerivPagePatch9} +\pastebutton{ugIntroCalcDerivPageEmpty9}{\showpaste} +\tab{5}\spadcommand{a := F(x z, y z, z**2) + x y(z+1)\bound{a }\free{F }\free{x }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch10} +\begin{paste}{ugIntroCalcDerivPageFull10}{ugIntroCalcDerivPageEmpty10} +\pastebutton{ugIntroCalcDerivPageFull10}{\hidepaste} +\tab{5}\spadcommand{dadz := D(a, z)\bound{da }\free{a }} +\indentrel{3}\begin{verbatim} + (10) + 2 , 2 + 2zF (x(z),y(z),z ) + y (z)F (x(z),y(z),z ) + ,3 ,2 + + + , 2 , , + x (z)F (x(z),y(z),z ) + x (y(z + 1))y (z + 1) + ,1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty10} +\begin{paste}{ugIntroCalcDerivPageEmpty10}{ugIntroCalcDerivPagePatch10} +\pastebutton{ugIntroCalcDerivPageEmpty10}{\showpaste} +\tab{5}\spadcommand{dadz := D(a, z)\bound{da }\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch11} +\begin{paste}{ugIntroCalcDerivPageFull11}{ugIntroCalcDerivPageEmpty11} +\pastebutton{ugIntroCalcDerivPageFull11}{\hidepaste} +\tab{5}\spadcommand{eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))\free{da }} +\indentrel{3}\begin{verbatim} + (11) + 2 z 2 + (2z + 2z)F (%e ,log(z + 1),z ) + ,3 + + + z 2 + F (%e ,log(z + 1),z ) + ,2 + + + z z 2 + (z + 1)%e F (%e ,log(z + 1),z ) + z + 1 + ,1 + / + z + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty11} +\begin{paste}{ugIntroCalcDerivPageEmpty11}{ugIntroCalcDerivPagePatch11} +\pastebutton{ugIntroCalcDerivPageEmpty11}{\showpaste} +\tab{5}\spadcommand{eval(eval(dadz, 'x, z +-> exp z), 'y, z +-> log(z+1))\free{da }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch12} +\begin{paste}{ugIntroCalcDerivPageFull12}{ugIntroCalcDerivPageEmpty12} +\pastebutton{ugIntroCalcDerivPageFull12}{\hidepaste} +\tab{5}\spadcommand{eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))\free{a }\bound{eva }} +\indentrel{3}\begin{verbatim} + z 2 + (12) F(%e ,log(z + 1),z ) + z + 2 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty12} +\begin{paste}{ugIntroCalcDerivPageEmpty12}{ugIntroCalcDerivPagePatch12} +\pastebutton{ugIntroCalcDerivPageEmpty12}{\showpaste} +\tab{5}\spadcommand{eval(eval(a, 'x, z +-> exp z), 'y, z +-> log(z+1))\free{a }\bound{eva }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPagePatch13} +\begin{paste}{ugIntroCalcDerivPageFull13}{ugIntroCalcDerivPageEmpty13} +\pastebutton{ugIntroCalcDerivPageFull13}{\hidepaste} +\tab{5}\spadcommand{D(\%, z)\free{eva }} +\indentrel{3}\begin{verbatim} + (13) + 2 z 2 + (2z + 2z)F (%e ,log(z + 1),z ) + ,3 + + + z 2 + F (%e ,log(z + 1),z ) + ,2 + + + z z 2 + (z + 1)%e F (%e ,log(z + 1),z ) + z + 1 + ,1 + / + z + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcDerivPageEmpty13} +\begin{paste}{ugIntroCalcDerivPageEmpty13}{ugIntroCalcDerivPagePatch13} +\pastebutton{ugIntroCalcDerivPageEmpty13}{\showpaste} +\tab{5}\spadcommand{D(\%, z)\free{eva }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch1} +\begin{paste}{ugIntroVariablesPageFull1}{ugIntroVariablesPageEmpty1} +\pastebutton{ugIntroVariablesPageFull1}{\hidepaste} +\tab{5}\spadcommand{(x**2 - x*y**3 +3*y)**2} +\indentrel{3}\begin{verbatim} + 2 6 4 3 3 2 2 4 + (1) x y - 6x y - 2x y + 9y + 6x y + x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty1} +\begin{paste}{ugIntroVariablesPageEmpty1}{ugIntroVariablesPagePatch1} +\pastebutton{ugIntroVariablesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{(x**2 - x*y**3 +3*y)**2} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch2} +\begin{paste}{ugIntroVariablesPageFull2}{ugIntroVariablesPageEmpty2} +\pastebutton{ugIntroVariablesPageFull2}{\hidepaste} +\tab{5}\spadcommand{p: UP(x,INT) := (3*x-1)**2 * (2*x + 8)} +\indentrel{3}\begin{verbatim} + 3 2 + (2) 18x + 60x - 46x + 8 + Type: UnivariatePolynomial(x,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty2} +\begin{paste}{ugIntroVariablesPageEmpty2}{ugIntroVariablesPagePatch2} +\pastebutton{ugIntroVariablesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{p: UP(x,INT) := (3*x-1)**2 * (2*x + 8)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch3} +\begin{paste}{ugIntroVariablesPageFull3}{ugIntroVariablesPageEmpty3} +\pastebutton{ugIntroVariablesPageFull3}{\hidepaste} +\tab{5}\spadcommand{m: MPOLY([x,y],INT) := (x**2-x*y**3+3*y)**2\bound{m }} +\indentrel{3}\begin{verbatim} + 4 3 3 6 2 4 2 + (3) x - 2y x + (y + 6y)x - 6y x + 9y + Type: MultivariatePolynomial([x,y],Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty3} +\begin{paste}{ugIntroVariablesPageEmpty3}{ugIntroVariablesPagePatch3} +\pastebutton{ugIntroVariablesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{m: MPOLY([x,y],INT) := (x**2-x*y**3+3*y)**2\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch4} +\begin{paste}{ugIntroVariablesPageFull4}{ugIntroVariablesPageEmpty4} +\pastebutton{ugIntroVariablesPageFull4}{\hidepaste} +\tab{5}\spadcommand{m :: MPOLY([y,x],INT)\free{m }} +\indentrel{3}\begin{verbatim} + 2 6 4 3 3 2 2 4 + (4) x y - 6x y - 2x y + 9y + 6x y + x + Type: MultivariatePolynomial([y,x],Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty4} +\begin{paste}{ugIntroVariablesPageEmpty4}{ugIntroVariablesPagePatch4} +\pastebutton{ugIntroVariablesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{m :: MPOLY([y,x],INT)\free{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch5} +\begin{paste}{ugIntroVariablesPageFull5}{ugIntroVariablesPageEmpty5} +\pastebutton{ugIntroVariablesPageFull5}{\hidepaste} +\tab{5}\spadcommand{m :: DMP([y,x],INT)\free{m }} +\indentrel{3}\begin{verbatim} + 6 2 4 3 3 2 2 4 + (5) y x - 6y x - 2y x + 9y + 6y x + x + Type: DistributedMultivariatePolynomial([y,x],Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty5} +\begin{paste}{ugIntroVariablesPageEmpty5}{ugIntroVariablesPagePatch5} +\pastebutton{ugIntroVariablesPageEmpty5}{\showpaste} +\tab{5}\spadcommand{m :: DMP([y,x],INT)\free{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPagePatch6} +\begin{paste}{ugIntroVariablesPageFull6}{ugIntroVariablesPageEmpty6} +\pastebutton{ugIntroVariablesPageFull6}{\hidepaste} +\tab{5}\spadcommand{m :: HDMP([y,x],INT)\free{m }} +\indentrel{3}\begin{verbatim} + 6 2 3 3 4 4 2 2 + (6) y x - 2y x - 6y x + x + 6y x + 9y +Type: HomogeneousDistributedMultivariatePolynomial([y,x],Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroVariablesPageEmpty6} +\begin{paste}{ugIntroVariablesPageEmpty6}{ugIntroVariablesPagePatch6} +\pastebutton{ugIntroVariablesPageEmpty6}{\showpaste} +\tab{5}\spadcommand{m :: HDMP([y,x],INT)\free{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch1} +\begin{paste}{ugIntroIntegratePageFull1}{ugIntroIntegratePageEmpty1} +\pastebutton{ugIntroIntegratePageFull1}{\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}{ugIntroIntegratePageEmpty1} +\begin{paste}{ugIntroIntegratePageEmpty1}{ugIntroIntegratePagePatch1} +\pastebutton{ugIntroIntegratePageEmpty1}{\showpaste} +\tab{5}\spadcommand{integrate((x**2+2*x+1)/((x+1)**6+1),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch2} +\begin{paste}{ugIntroIntegratePageFull2}{ugIntroIntegratePageEmpty2} +\pastebutton{ugIntroIntegratePageFull2}{\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 + (2) [컴컴컴컴컴컴컴컴컴컴컴컴컴,컴컴컴컴컴�] + 旼컴� 旼� + 2\�- a \쿪 + Type: Union(List Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty2} +\begin{paste}{ugIntroIntegratePageEmpty2}{ugIntroIntegratePagePatch2} +\pastebutton{ugIntroIntegratePageEmpty2}{\showpaste} +\tab{5}\spadcommand{integrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch3} +\begin{paste}{ugIntroIntegratePageFull3}{ugIntroIntegratePageEmpty3} +\pastebutton{ugIntroIntegratePageFull3}{\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 + (3) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 旼컴� + 2\�- a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty3} +\begin{paste}{ugIntroIntegratePageEmpty3}{ugIntroIntegratePagePatch3} +\pastebutton{ugIntroIntegratePageEmpty3}{\showpaste} +\tab{5}\spadcommand{complexIntegrate(1/(x**2 + a),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch4} +\begin{paste}{ugIntroIntegratePageFull4}{ugIntroIntegratePageEmpty4} +\pastebutton{ugIntroIntegratePageFull4}{\hidepaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\indentrel{3}\begin{verbatim} + (4) + 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}{ugIntroIntegratePageEmpty4} +\begin{paste}{ugIntroIntegratePageEmpty4}{ugIntroIntegratePagePatch4} +\pastebutton{ugIntroIntegratePageEmpty4}{\showpaste} +\tab{5}\spadcommand{integrate(x**3 / (a+b*x)**(1/3),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch5} +\begin{paste}{ugIntroIntegratePageFull5}{ugIntroIntegratePageEmpty5} +\pastebutton{ugIntroIntegratePageFull5}{\hidepaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\indentrel{3}\begin{verbatim} + (5) + - + 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}{ugIntroIntegratePageEmpty5} +\begin{paste}{ugIntroIntegratePageEmpty5}{ugIntroIntegratePagePatch5} +\pastebutton{ugIntroIntegratePageEmpty5}{\showpaste} +\tab{5}\spadcommand{integrate(1 / (x**3 * (a+b*x)**(1/3)),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch6} +\begin{paste}{ugIntroIntegratePageFull6}{ugIntroIntegratePageEmpty6} +\pastebutton{ugIntroIntegratePageFull6}{\hidepaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\indentrel{3}\begin{verbatim} + x 旼컴컴컴커 + 悶 log(\쿫 + %S a + 1) + (6) � 컴컴컴컴컴컴컴컴컴컴 d%S + 잎 %S + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty6} +\begin{paste}{ugIntroIntegratePageEmpty6}{ugIntroIntegratePagePatch6} +\pastebutton{ugIntroIntegratePageEmpty6}{\showpaste} +\tab{5}\spadcommand{integrate(log(1 + sqrt(a*x + b)) / x,x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch7} +\begin{paste}{ugIntroIntegratePageFull7}{ugIntroIntegratePageEmpty7} +\pastebutton{ugIntroIntegratePageFull7}{\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} + (7) + 旼컴컴� + - 2cosh(\퀈 + b + 1) - 2x + 2log(컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴�) + 旼컴컴� 旼컴컴� + sinh(\퀈 + b + 1) - cosh(\퀈 + b + 1) + + + 旼컴컴� + - 2\퀈 + b + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty7} +\begin{paste}{ugIntroIntegratePageEmpty7}{ugIntroIntegratePagePatch7} +\pastebutton{ugIntroIntegratePageEmpty7}{\showpaste} +\tab{5}\spadcommand{integrate((sinh(1+sqrt(x+b))+2*sqrt(x+b)) / (sqrt(x+b) * (x + cosh(1+sqrt(x + b)))), x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch8} +\begin{paste}{ugIntroIntegratePageFull8}{ugIntroIntegratePageEmpty8} +\pastebutton{ugIntroIntegratePageFull8}{\hidepaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\indentrel{3}\begin{verbatim} + (8) + atan(x) 2 atan(x) 2 + 8log(3tan(컴컴컴�) - 1) - 3tan(컴컴컴�) + 3 3 + + + atan(x) + 18x tan(컴컴컴�) + 3 + / + 18 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty8} +\begin{paste}{ugIntroIntegratePageEmpty8}{ugIntroIntegratePagePatch8} +\pastebutton{ugIntroIntegratePageEmpty8}{\showpaste} +\tab{5}\spadcommand{integrate(tan(atan(x)/3),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch9} +\begin{paste}{ugIntroIntegratePageFull9}{ugIntroIntegratePageEmpty9} +\pastebutton{ugIntroIntegratePageFull9}{\hidepaste} +\tab{5}\spadcommand{integrate((x + 1) / (x*(x + log x) ** (3/2)), x)} +\indentrel{3}\begin{verbatim} + 旼컴컴컴컴커 + 2\쿹og(x) + x + (9) - 컴컴컴컴컴컴컴 + log(x) + x + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty9} +\begin{paste}{ugIntroIntegratePageEmpty9}{ugIntroIntegratePagePatch9} +\pastebutton{ugIntroIntegratePageEmpty9}{\showpaste} +\tab{5}\spadcommand{integrate((x + 1) / (x*(x + log x) ** (3/2)), x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePagePatch10} +\begin{paste}{ugIntroIntegratePageFull10}{ugIntroIntegratePageEmpty10} +\pastebutton{ugIntroIntegratePageFull10}{\hidepaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\indentrel{3}\begin{verbatim} + 旼컴� erf(x) - 1 旼컴� + (erf(x) - 1)\�%pi log(컴컴컴컴컴) - 2\�%pi + erf(x) + 1 + (10) 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� + 8erf(x) - 8 + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroIntegratePageEmpty10} +\begin{paste}{ugIntroIntegratePageEmpty10}{ugIntroIntegratePagePatch10} +\pastebutton{ugIntroIntegratePageEmpty10}{\showpaste} +\tab{5}\spadcommand{integrate(exp(-x**2) * erf(x) / (erf(x)**3 - erf(x)**2 - erf(x) + 1),x)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch1} +\begin{paste}{ugIntroCalcLimitsPageFull1}{ugIntroCalcLimitsPageEmpty1} +\pastebutton{ugIntroCalcLimitsPageFull1}{\hidepaste} +\tab{5}\spadcommand{g := csc(a*x) / csch(b*x)\bound{g }} +\indentrel{3}\begin{verbatim} + csc(a x) + (1) 컴컴컴컴� + csch(b x) + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty1} +\begin{paste}{ugIntroCalcLimitsPageEmpty1}{ugIntroCalcLimitsPagePatch1} +\pastebutton{ugIntroCalcLimitsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{g := csc(a*x) / csch(b*x)\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch2} +\begin{paste}{ugIntroCalcLimitsPageFull2}{ugIntroCalcLimitsPageEmpty2} +\pastebutton{ugIntroCalcLimitsPageFull2}{\hidepaste} +\tab{5}\spadcommand{limit(g,x=0)\free{g }} +\indentrel{3}\begin{verbatim} + b + (2) � + a + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty2} +\begin{paste}{ugIntroCalcLimitsPageEmpty2}{ugIntroCalcLimitsPagePatch2} +\pastebutton{ugIntroCalcLimitsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{limit(g,x=0)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch3} +\begin{paste}{ugIntroCalcLimitsPageFull3}{ugIntroCalcLimitsPageEmpty3} +\pastebutton{ugIntroCalcLimitsPageFull3}{\hidepaste} +\tab{5}\spadcommand{h := (1 + k/x)**x\bound{h }} +\indentrel{3}\begin{verbatim} + x + k x + (3) (컴컴�) + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty3} +\begin{paste}{ugIntroCalcLimitsPageEmpty3}{ugIntroCalcLimitsPagePatch3} +\pastebutton{ugIntroCalcLimitsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{h := (1 + k/x)**x\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch4} +\begin{paste}{ugIntroCalcLimitsPageFull4}{ugIntroCalcLimitsPageEmpty4} +\pastebutton{ugIntroCalcLimitsPageFull4}{\hidepaste} +\tab{5}\spadcommand{limit(h,x=\%plusInfinity)\free{h }} +\indentrel{3}\begin{verbatim} + k + (4) %e + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty4} +\begin{paste}{ugIntroCalcLimitsPageEmpty4}{ugIntroCalcLimitsPagePatch4} +\pastebutton{ugIntroCalcLimitsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{limit(h,x=\%plusInfinity)\free{h }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch5} +\begin{paste}{ugIntroCalcLimitsPageFull5}{ugIntroCalcLimitsPageEmpty5} +\pastebutton{ugIntroCalcLimitsPageFull5}{\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}{ugIntroCalcLimitsPageEmpty5} +\begin{paste}{ugIntroCalcLimitsPageEmpty5}{ugIntroCalcLimitsPagePatch5} +\pastebutton{ugIntroCalcLimitsPageEmpty5}{\showpaste} +\tab{5}\spadcommand{limit(sqrt(y**2)/y,y = 0)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch6} +\begin{paste}{ugIntroCalcLimitsPageFull6}{ugIntroCalcLimitsPageEmpty6} +\pastebutton{ugIntroCalcLimitsPageFull6}{\hidepaste} +\tab{5}\spadcommand{limit(exp(-1/x**2),x = 0)} +\indentrel{3}\begin{verbatim} + (6) 0 + Type: Union(OrderedCompletion Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty6} +\begin{paste}{ugIntroCalcLimitsPageEmpty6}{ugIntroCalcLimitsPagePatch6} +\pastebutton{ugIntroCalcLimitsPageEmpty6}{\showpaste} +\tab{5}\spadcommand{limit(exp(-1/x**2),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPagePatch7} +\begin{paste}{ugIntroCalcLimitsPageFull7}{ugIntroCalcLimitsPageEmpty7} +\pastebutton{ugIntroCalcLimitsPageFull7}{\hidepaste} +\tab{5}\spadcommand{complexLimit(exp(-1/x**2),x = 0)} +\indentrel{3}\begin{verbatim} + (7) "failed" + Type: Union("failed",...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCalcLimitsPageEmpty7} +\begin{paste}{ugIntroCalcLimitsPageEmpty7}{ugIntroCalcLimitsPagePatch7} +\pastebutton{ugIntroCalcLimitsPageEmpty7}{\showpaste} +\tab{5}\spadcommand{complexLimit(exp(-1/x**2),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch1} +\begin{paste}{ugIntroSysCmmandsPageFull1}{ugIntroSysCmmandsPageEmpty1} +\pastebutton{ugIntroSysCmmandsPageFull1}{\hidepaste} +\tab{5}\spadcommand{)what operations integrate} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty1} +\begin{paste}{ugIntroSysCmmandsPageEmpty1}{ugIntroSysCmmandsPagePatch1} +\pastebutton{ugIntroSysCmmandsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{)what operations integrate} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch2} +\begin{paste}{ugIntroSysCmmandsPageFull2}{ugIntroSysCmmandsPageEmpty2} +\pastebutton{ugIntroSysCmmandsPageFull2}{\hidepaste} +\tab{5}\spadcommand{f(0) == 1; g(0) == 1\bound{u1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty2} +\begin{paste}{ugIntroSysCmmandsPageEmpty2}{ugIntroSysCmmandsPagePatch2} +\pastebutton{ugIntroSysCmmandsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{f(0) == 1; g(0) == 1\bound{u1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch3} +\begin{paste}{ugIntroSysCmmandsPageFull3}{ugIntroSysCmmandsPageEmpty3} +\pastebutton{ugIntroSysCmmandsPageFull3}{\hidepaste} +\tab{5}\spadcommand{f(n) == e/2*f(n-1) - x*g(n-1)\bound{u2 }\free{u1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty3} +\begin{paste}{ugIntroSysCmmandsPageEmpty3}{ugIntroSysCmmandsPagePatch3} +\pastebutton{ugIntroSysCmmandsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{f(n) == e/2*f(n-1) - x*g(n-1)\bound{u2 }\free{u1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch4} +\begin{paste}{ugIntroSysCmmandsPageFull4}{ugIntroSysCmmandsPageEmpty4} +\pastebutton{ugIntroSysCmmandsPageFull4}{\hidepaste} +\tab{5}\spadcommand{g(n) == -x*f(n-1) + d/3*g(n-1)\bound{u3 }\free{u2 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty4} +\begin{paste}{ugIntroSysCmmandsPageEmpty4}{ugIntroSysCmmandsPagePatch4} +\pastebutton{ugIntroSysCmmandsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{g(n) == -x*f(n-1) + d/3*g(n-1)\bound{u3 }\free{u2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch5} +\begin{paste}{ugIntroSysCmmandsPageFull5}{ugIntroSysCmmandsPageEmpty5} +\pastebutton{ugIntroSysCmmandsPageFull5}{\hidepaste} +\tab{5}\spadcommand{f(3)\bound{u4 }\free{u3 }} +\indentrel{3}\begin{verbatim} + (4) + 3 1 2 1 2 1 1 2 1 3 + - x + (e + � d)x + (- � e - � d e - � d )x + � e + 3 4 6 9 8 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty5} +\begin{paste}{ugIntroSysCmmandsPageEmpty5}{ugIntroSysCmmandsPagePatch5} +\pastebutton{ugIntroSysCmmandsPageEmpty5}{\showpaste} +\tab{5}\spadcommand{f(3)\bound{u4 }\free{u3 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch6} +\begin{paste}{ugIntroSysCmmandsPageFull6}{ugIntroSysCmmandsPageEmpty6} +\pastebutton{ugIntroSysCmmandsPageFull6}{\hidepaste} +\tab{5}\spadcommand{)undo 2\bound{u5 }\free{u4 }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty6} +\begin{paste}{ugIntroSysCmmandsPageEmpty6}{ugIntroSysCmmandsPagePatch6} +\pastebutton{ugIntroSysCmmandsPageEmpty6}{\showpaste} +\tab{5}\spadcommand{)undo 2\bound{u5 }\free{u4 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch7} +\begin{paste}{ugIntroSysCmmandsPageFull7}{ugIntroSysCmmandsPageEmpty7} +\pastebutton{ugIntroSysCmmandsPageFull7}{\hidepaste} +\tab{5}\spadcommand{f(n) == d/3*f(n-1) - x*g(n-1)\bound{u6 }\free{u5 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty7} +\begin{paste}{ugIntroSysCmmandsPageEmpty7}{ugIntroSysCmmandsPagePatch7} +\pastebutton{ugIntroSysCmmandsPageEmpty7}{\showpaste} +\tab{5}\spadcommand{f(n) == d/3*f(n-1) - x*g(n-1)\bound{u6 }\free{u5 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch8} +\begin{paste}{ugIntroSysCmmandsPageFull8}{ugIntroSysCmmandsPageEmpty8} +\pastebutton{ugIntroSysCmmandsPageFull8}{\hidepaste} +\tab{5}\spadcommand{)undo )redo\bound{u7 }\free{u6 }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty8} +\begin{paste}{ugIntroSysCmmandsPageEmpty8}{ugIntroSysCmmandsPagePatch8} +\pastebutton{ugIntroSysCmmandsPageEmpty8}{\showpaste} +\tab{5}\spadcommand{)undo )redo\bound{u7 }\free{u6 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch9} +\begin{paste}{ugIntroSysCmmandsPageFull9}{ugIntroSysCmmandsPageEmpty9} +\pastebutton{ugIntroSysCmmandsPageFull9}{\hidepaste} +\tab{5}\spadcommand{)undo 4\bound{u8 }\free{u7 }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty9} +\begin{paste}{ugIntroSysCmmandsPageEmpty9}{ugIntroSysCmmandsPagePatch9} +\pastebutton{ugIntroSysCmmandsPageEmpty9}{\showpaste} +\tab{5}\spadcommand{)undo 4\bound{u8 }\free{u7 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPagePatch10} +\begin{paste}{ugIntroSysCmmandsPageFull10}{ugIntroSysCmmandsPageEmpty10} +\pastebutton{ugIntroSysCmmandsPageFull10}{\hidepaste} +\tab{5}\spadcommand{f(3)\bound{u9 }\free{u8 }} +\indentrel{3}\begin{verbatim} + (6) + 3 1 2 1 2 1 1 2 1 3 + - x + (e + � d)x + (- � e - � d e - � d )x + � e + 3 4 6 9 8 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSysCmmandsPageEmpty10} +\begin{paste}{ugIntroSysCmmandsPageEmpty10}{ugIntroSysCmmandsPagePatch10} +\pastebutton{ugIntroSysCmmandsPageEmpty10}{\showpaste} +\tab{5}\spadcommand{f(3)\bound{u9 }\free{u8 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPagePatch1} +\begin{paste}{ugIntroArithmeticPageFull1}{ugIntroArithmeticPageEmpty1} +\pastebutton{ugIntroArithmeticPageFull1}{\hidepaste} +\tab{5}\spadcommand{1 + 2 - 3 / 4 * 3 ** 2 - 1} +\indentrel{3}\begin{verbatim} + 19 + (1) - 컴 + 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPageEmpty1} +\begin{paste}{ugIntroArithmeticPageEmpty1}{ugIntroArithmeticPagePatch1} +\pastebutton{ugIntroArithmeticPageEmpty1}{\showpaste} +\tab{5}\spadcommand{1 + 2 - 3 / 4 * 3 ** 2 - 1} +\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPagePatch2} +\begin{paste}{ugIntroArithmeticPageFull2}{ugIntroArithmeticPageEmpty2} +\pastebutton{ugIntroArithmeticPageFull2}{\hidepaste} +\tab{5}\spadcommand{((1 + 2) - ((3 / 4) * (3 ** 2))) - 1} +\indentrel{3}\begin{verbatim} + 19 + (2) - 컴 + 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPageEmpty2} +\begin{paste}{ugIntroArithmeticPageEmpty2}{ugIntroArithmeticPagePatch2} +\pastebutton{ugIntroArithmeticPageEmpty2}{\showpaste} +\tab{5}\spadcommand{((1 + 2) - ((3 / 4) * (3 ** 2))) - 1} +\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPagePatch3} +\begin{paste}{ugIntroArithmeticPageFull3}{ugIntroArithmeticPageEmpty3} +\pastebutton{ugIntroArithmeticPageFull3}{\hidepaste} +\tab{5}\spadcommand{1 + 2 - 3/ (4 * 3 ** (2 - 1))} +\indentrel{3}\begin{verbatim} + 11 + (3) 컴 + 4 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroArithmeticPageEmpty3} +\begin{paste}{ugIntroArithmeticPageEmpty3}{ugIntroArithmeticPagePatch3} +\pastebutton{ugIntroArithmeticPageEmpty3}{\showpaste} +\tab{5}\spadcommand{1 + 2 - 3/ (4 * 3 ** (2 - 1))} +\end{paste}\end{patch} + +\begin{patch}{ugIntroConversionPagePatch1} +\begin{paste}{ugIntroConversionPageFull1}{ugIntroConversionPageEmpty1} +\pastebutton{ugIntroConversionPageFull1}{\hidepaste} +\tab{5}\spadcommand{p := r**2 + 2/3\bound{p }} +\indentrel{3}\begin{verbatim} + 2 2 + (1) r + � + 3 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroConversionPageEmpty1} +\begin{paste}{ugIntroConversionPageEmpty1}{ugIntroConversionPagePatch1} +\pastebutton{ugIntroConversionPageEmpty1}{\showpaste} +\tab{5}\spadcommand{p := r**2 + 2/3\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroConversionPagePatch2} +\begin{paste}{ugIntroConversionPageFull2}{ugIntroConversionPageEmpty2} +\pastebutton{ugIntroConversionPageFull2}{\hidepaste} +\tab{5}\spadcommand{p :: Fraction Polynomial Integer\free{p }} +\indentrel{3}\begin{verbatim} + 2 + 3r + 2 + (2) 컴컴컴� + 3 + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroConversionPageEmpty2} +\begin{paste}{ugIntroConversionPageEmpty2}{ugIntroConversionPagePatch2} +\pastebutton{ugIntroConversionPageEmpty2}{\showpaste} +\tab{5}\spadcommand{p :: Fraction Polynomial Integer\free{p }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch1} +\begin{paste}{ugIntroYouPageFull1}{ugIntroYouPageEmpty1} +\pastebutton{ugIntroYouPageFull1}{\hidepaste} +\tab{5}\spadcommand{fact(0) == 1\bound{fact }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty1} +\begin{paste}{ugIntroYouPageEmpty1}{ugIntroYouPagePatch1} +\pastebutton{ugIntroYouPageEmpty1}{\showpaste} +\tab{5}\spadcommand{fact(0) == 1\bound{fact }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch2} +\begin{paste}{ugIntroYouPageFull2}{ugIntroYouPageEmpty2} +\pastebutton{ugIntroYouPageFull2}{\hidepaste} +\tab{5}\spadcommand{fact(n) == n*fact(n-1)\bound{facta }\free{fact }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty2} +\begin{paste}{ugIntroYouPageEmpty2}{ugIntroYouPagePatch2} +\pastebutton{ugIntroYouPageEmpty2}{\showpaste} +\tab{5}\spadcommand{fact(n) == n*fact(n-1)\bound{facta }\free{fact }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch3} +\begin{paste}{ugIntroYouPageFull3}{ugIntroYouPageEmpty3} +\pastebutton{ugIntroYouPageFull3}{\hidepaste} +\tab{5}\spadcommand{fact(50)\free{facta }} +\indentrel{3}\begin{verbatim} + (3) + 304140932017133780436126081660647688443776415689605120_ + 00000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty3} +\begin{paste}{ugIntroYouPageEmpty3}{ugIntroYouPagePatch3} +\pastebutton{ugIntroYouPageEmpty3}{\showpaste} +\tab{5}\spadcommand{fact(50)\free{facta }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch4} +\begin{paste}{ugIntroYouPageFull4}{ugIntroYouPageEmpty4} +\pastebutton{ugIntroYouPageFull4}{\hidepaste} +\tab{5}\spadcommand{fac(n) == if n < 3 then n else n * fac(n - 1)\bound{fac }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty4} +\begin{paste}{ugIntroYouPageEmpty4}{ugIntroYouPagePatch4} +\pastebutton{ugIntroYouPageEmpty4}{\showpaste} +\tab{5}\spadcommand{fac(n) == if n < 3 then n else n * fac(n - 1)\bound{fac }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch5} +\begin{paste}{ugIntroYouPageFull5}{ugIntroYouPageEmpty5} +\pastebutton{ugIntroYouPageFull5}{\hidepaste} +\tab{5}\spadcommand{fac(50)\free{fac }} +\indentrel{3}\begin{verbatim} + (5) + 304140932017133780436126081660647688443776415689605120_ + 00000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty5} +\begin{paste}{ugIntroYouPageEmpty5}{ugIntroYouPagePatch5} +\pastebutton{ugIntroYouPageEmpty5}{\showpaste} +\tab{5}\spadcommand{fac(50)\free{fac }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch6} +\begin{paste}{ugIntroYouPageFull6}{ugIntroYouPageEmpty6} +\pastebutton{ugIntroYouPageFull6}{\hidepaste} +\tab{5}\spadcommand{fa(n) == (a := 1; for i in 2..n repeat a := a*i; a)\bound{fa }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty6} +\begin{paste}{ugIntroYouPageEmpty6}{ugIntroYouPagePatch6} +\pastebutton{ugIntroYouPageEmpty6}{\showpaste} +\tab{5}\spadcommand{fa(n) == (a := 1; for i in 2..n repeat a := a*i; a)\bound{fa }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch7} +\begin{paste}{ugIntroYouPageFull7}{ugIntroYouPageEmpty7} +\pastebutton{ugIntroYouPageFull7}{\hidepaste} +\tab{5}\spadcommand{fa(50)\free{fa }} +\indentrel{3}\begin{verbatim} + (7) + 304140932017133780436126081660647688443776415689605120_ + 00000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty7} +\begin{paste}{ugIntroYouPageEmpty7}{ugIntroYouPagePatch7} +\pastebutton{ugIntroYouPageEmpty7}{\showpaste} +\tab{5}\spadcommand{fa(50)\free{fa }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch8} +\begin{paste}{ugIntroYouPageFull8}{ugIntroYouPageEmpty8} +\pastebutton{ugIntroYouPageFull8}{\hidepaste} +\tab{5}\spadcommand{f(n) == reduce(*,[i for i in 2..n])\bound{f }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty8} +\begin{paste}{ugIntroYouPageEmpty8}{ugIntroYouPagePatch8} +\pastebutton{ugIntroYouPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f(n) == reduce(*,[i for i in 2..n])\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch9} +\begin{paste}{ugIntroYouPageFull9}{ugIntroYouPageEmpty9} +\pastebutton{ugIntroYouPageFull9}{\hidepaste} +\tab{5}\spadcommand{f(50)\free{f }} +\indentrel{3}\begin{verbatim} + (9) + 304140932017133780436126081660647688443776415689605120_ + 00000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty9} +\begin{paste}{ugIntroYouPageEmpty9}{ugIntroYouPagePatch9} +\pastebutton{ugIntroYouPageEmpty9}{\showpaste} +\tab{5}\spadcommand{f(50)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch10} +\begin{paste}{ugIntroYouPageFull10}{ugIntroYouPageEmpty10} +\pastebutton{ugIntroYouPageFull10}{\hidepaste} +\tab{5}\spadcommand{factorial(50)} +\indentrel{3}\begin{verbatim} + (10) + 304140932017133780436126081660647688443776415689605120_ + 00000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty10} +\begin{paste}{ugIntroYouPageEmpty10}{ugIntroYouPagePatch10} +\pastebutton{ugIntroYouPageEmpty10}{\showpaste} +\tab{5}\spadcommand{factorial(50)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch11} +\begin{paste}{ugIntroYouPageFull11}{ugIntroYouPageEmpty11} +\pastebutton{ugIntroYouPageFull11}{\hidepaste} +\tab{5}\spadcommand{permMat(n, i, j) == + m := diagonalMatrix + [(if i = k or j = k then 0 else 1) + for k in 1..n] + m(i,j) := 1 + m(j,i) := 1 + m +\bound{permMat }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty11} +\begin{paste}{ugIntroYouPageEmpty11}{ugIntroYouPagePatch11} +\pastebutton{ugIntroYouPageEmpty11}{\showpaste} +\tab{5}\spadcommand{permMat(n, i, j) == + m := diagonalMatrix + [(if i = k or j = k then 0 else 1) + for k in 1..n] + m(i,j) := 1 + m(j,i) := 1 + m +\bound{permMat }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch12} +\begin{paste}{ugIntroYouPageFull12}{ugIntroYouPageEmpty12} +\pastebutton{ugIntroYouPageFull12}{\hidepaste} +\tab{5}\spadcommand{p := permMat(4,2,3)\free{permMat }\bound{p }} +\indentrel{3}\begin{verbatim} + �1 0 0 0� + � � + �0 0 1 0� + (12) � � + �0 1 0 0� + � � + �0 0 0 1� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty12} +\begin{paste}{ugIntroYouPageEmpty12}{ugIntroYouPagePatch12} +\pastebutton{ugIntroYouPageEmpty12}{\showpaste} +\tab{5}\spadcommand{p := permMat(4,2,3)\free{permMat }\bound{p }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch13} +\begin{paste}{ugIntroYouPageFull13}{ugIntroYouPageEmpty13} +\pastebutton{ugIntroYouPageFull13}{\hidepaste} +\tab{5}\spadcommand{m := matrix [[4*i + j for j in 1..4] for i in 0..3]\bound{m }} +\indentrel{3}\begin{verbatim} + �1 2 3 4 � + � � + �5 6 7 8 � + (13) � � + �9 10 11 12� + � � + �13 14 15 16� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty13} +\begin{paste}{ugIntroYouPageEmpty13}{ugIntroYouPagePatch13} +\pastebutton{ugIntroYouPageEmpty13}{\showpaste} +\tab{5}\spadcommand{m := matrix [[4*i + j for j in 1..4] for i in 0..3]\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch14} +\begin{paste}{ugIntroYouPageFull14}{ugIntroYouPageEmpty14} +\pastebutton{ugIntroYouPageFull14}{\hidepaste} +\tab{5}\spadcommand{permMat(4,2,3) * m\free{p m }} +\indentrel{3}\begin{verbatim} + �1 2 3 4 � + � � + �9 10 11 12� + (14) � � + �5 6 7 8 � + � � + �13 14 15 16� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty14} +\begin{paste}{ugIntroYouPageEmpty14}{ugIntroYouPagePatch14} +\pastebutton{ugIntroYouPageEmpty14}{\showpaste} +\tab{5}\spadcommand{permMat(4,2,3) * m\free{p m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch15} +\begin{paste}{ugIntroYouPageFull15}{ugIntroYouPageEmpty15} +\pastebutton{ugIntroYouPageFull15}{\hidepaste} +\tab{5}\spadcommand{t : (Float -> Float, Float) -> Float\bound{tdecl }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty15} +\begin{paste}{ugIntroYouPageEmpty15}{ugIntroYouPagePatch15} +\pastebutton{ugIntroYouPageEmpty15}{\showpaste} +\tab{5}\spadcommand{t : (Float -> Float, Float) -> Float\bound{tdecl }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch16} +\begin{paste}{ugIntroYouPageFull16}{ugIntroYouPageEmpty16} +\pastebutton{ugIntroYouPageFull16}{\hidepaste} +\tab{5}\spadcommand{t(fun, x) == fun(x)**2 + sin(x)**2\free{tdecl }\bound{t }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty16} +\begin{paste}{ugIntroYouPageEmpty16}{ugIntroYouPagePatch16} +\pastebutton{ugIntroYouPageEmpty16}{\showpaste} +\tab{5}\spadcommand{t(fun, x) == fun(x)**2 + sin(x)**2\free{tdecl }\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch17} +\begin{paste}{ugIntroYouPageFull17}{ugIntroYouPageEmpty17} +\pastebutton{ugIntroYouPageFull17}{\hidepaste} +\tab{5}\spadcommand{t(cos, 5.2058)\free{t }} +\indentrel{3}\begin{verbatim} + (17) 1.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty17} +\begin{paste}{ugIntroYouPageEmpty17}{ugIntroYouPagePatch17} +\pastebutton{ugIntroYouPageEmpty17}{\showpaste} +\tab{5}\spadcommand{t(cos, 5.2058)\free{t }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch18} +\begin{paste}{ugIntroYouPageFull18}{ugIntroYouPageEmpty18} +\pastebutton{ugIntroYouPageFull18}{\hidepaste} +\tab{5}\spadcommand{cosinv(y) == cos(1/y)\bound{cosinv }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty18} +\begin{paste}{ugIntroYouPageEmpty18}{ugIntroYouPagePatch18} +\pastebutton{ugIntroYouPageEmpty18}{\showpaste} +\tab{5}\spadcommand{cosinv(y) == cos(1/y)\bound{cosinv }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch19} +\begin{paste}{ugIntroYouPageFull19}{ugIntroYouPageEmpty19} +\pastebutton{ugIntroYouPageFull19}{\hidepaste} +\tab{5}\spadcommand{t(cosinv, 5.2058)\free{t }\free{cosinv }} +\indentrel{3}\begin{verbatim} + (19) 1.7392237241 800516493 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty19} +\begin{paste}{ugIntroYouPageEmpty19}{ugIntroYouPagePatch19} +\pastebutton{ugIntroYouPageEmpty19}{\showpaste} +\tab{5}\spadcommand{t(cosinv, 5.2058)\free{t }\free{cosinv }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch20} +\begin{paste}{ugIntroYouPageFull20}{ugIntroYouPageEmpty20} +\pastebutton{ugIntroYouPageFull20}{\hidepaste} +\tab{5}\spadcommand{groupSqrt := rule(sqrt(a) * sqrt(b) == sqrt(a*b))\bound{g }} +\indentrel{3}\begin{verbatim} + 旼� 旼� 旼컴� + (20) %BD\쿪 \쿫 == %BD\쿪 b + Type: RewriteRule(Integer,Integer,Expression Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty20} +\begin{paste}{ugIntroYouPageEmpty20}{ugIntroYouPagePatch20} +\pastebutton{ugIntroYouPageEmpty20}{\showpaste} +\tab{5}\spadcommand{groupSqrt := rule(sqrt(a) * sqrt(b) == sqrt(a*b))\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch21} +\begin{paste}{ugIntroYouPageFull21}{ugIntroYouPageEmpty21} +\pastebutton{ugIntroYouPageFull21}{\hidepaste} +\tab{5}\spadcommand{a := (sqrt(x) + sqrt(y) + sqrt(z))**4\bound{sxy }} +\indentrel{3}\begin{verbatim} + (21) + 旼� 旼� 旼� + ((4z + 4y + 12x)\퀉 + (4z + 12y + 4x)\퀈 )\퀊 + + + 旼� 旼� 2 2 + (12z + 4y + 4x)\퀈 \퀉 + z + (6y + 6x)z + y + 6x y + + + 2 + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty21} +\begin{paste}{ugIntroYouPageEmpty21}{ugIntroYouPagePatch21} +\pastebutton{ugIntroYouPageEmpty21}{\showpaste} +\tab{5}\spadcommand{a := (sqrt(x) + sqrt(y) + sqrt(z))**4\bound{sxy }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPagePatch22} +\begin{paste}{ugIntroYouPageFull22}{ugIntroYouPageEmpty22} +\pastebutton{ugIntroYouPageFull22}{\hidepaste} +\tab{5}\spadcommand{groupSqrt a\free{sxy }\free{g }} +\indentrel{3}\begin{verbatim} + (22) + 旼컴� 旼컴� + (4z + 4y + 12x)\퀉 z + (4z + 12y + 4x)\퀈 z + + + 旼컴� 2 2 + (12z + 4y + 4x)\퀈 y + z + (6y + 6x)z + y + 6x y + + + 2 + x + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroYouPageEmpty22} +\begin{paste}{ugIntroYouPageEmpty22}{ugIntroYouPagePatch22} +\pastebutton{ugIntroYouPageEmpty22}{\showpaste} +\tab{5}\spadcommand{groupSqrt a\free{sxy }\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPagePatch1} +\begin{paste}{ugIntroTypesPageFull1}{ugIntroTypesPageEmpty1} +\pastebutton{ugIntroTypesPageFull1}{\hidepaste} +\tab{5}\spadcommand{8} +\indentrel{3}\begin{verbatim} + (1) 8 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPageEmpty1} +\begin{paste}{ugIntroTypesPageEmpty1}{ugIntroTypesPagePatch1} +\pastebutton{ugIntroTypesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{8} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPagePatch2} +\begin{paste}{ugIntroTypesPageFull2}{ugIntroTypesPageEmpty2} +\pastebutton{ugIntroTypesPageFull2}{\hidepaste} +\tab{5}\spadcommand{-8} +\indentrel{3}\begin{verbatim} + (2) - 8 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPageEmpty2} +\begin{paste}{ugIntroTypesPageEmpty2}{ugIntroTypesPagePatch2} +\pastebutton{ugIntroTypesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{-8} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPagePatch3} +\begin{paste}{ugIntroTypesPageFull3}{ugIntroTypesPageEmpty3} +\pastebutton{ugIntroTypesPageFull3}{\hidepaste} +\tab{5}\spadcommand{x**8} +\indentrel{3}\begin{verbatim} + 8 + (3) x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPageEmpty3} +\begin{paste}{ugIntroTypesPageEmpty3}{ugIntroTypesPagePatch3} +\pastebutton{ugIntroTypesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{x**8} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPagePatch4} +\begin{paste}{ugIntroTypesPageFull4}{ugIntroTypesPageEmpty4} +\pastebutton{ugIntroTypesPageFull4}{\hidepaste} +\tab{5}\spadcommand{x**(-8)} +\indentrel{3}\begin{verbatim} + 1 + (4) 컴 + 8 + x + Type: Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTypesPageEmpty4} +\begin{paste}{ugIntroTypesPageEmpty4}{ugIntroTypesPagePatch4} +\pastebutton{ugIntroTypesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{x**(-8)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch1} +\begin{paste}{ugIntroTwoDimPageFull1}{ugIntroTwoDimPageEmpty1} +\pastebutton{ugIntroTwoDimPageFull1}{\hidepaste} +\tab{5}\spadcommand{m := matrix([[1,2], [3,4]])\bound{m }} +\indentrel{3}\begin{verbatim} + �1 2� + (1) � � + �3 4� + Type: Matrix Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty1} +\begin{paste}{ugIntroTwoDimPageEmpty1}{ugIntroTwoDimPagePatch1} +\pastebutton{ugIntroTwoDimPageEmpty1}{\showpaste} +\tab{5}\spadcommand{m := matrix([[1,2], [3,4]])\bound{m }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch2} +\begin{paste}{ugIntroTwoDimPageFull2}{ugIntroTwoDimPageEmpty2} +\pastebutton{ugIntroTwoDimPageFull2}{\hidepaste} +\tab{5}\spadcommand{matrix([[1/(i + j - x) for i in 1..4] for j in 1..4])\bound{hilb }} +\indentrel{3}\begin{verbatim} + � 1 1 1 1 � + �- 컴컴� - 컴컴� - 컴컴� - 컴컴캐 + � x - 2 x - 3 x - 4 x - 5� + � � + � 1 1 1 1 � + �- 컴컴� - 컴컴� - 컴컴� - 컴컴캐 + � x - 3 x - 4 x - 5 x - 6� + (2) � � + � 1 1 1 1 � + �- 컴컴� - 컴컴� - 컴컴� - 컴컴캐 + � x - 4 x - 5 x - 6 x - 7� + � � + � 1 1 1 1 � + �- 컴컴� - 컴컴� - 컴컴� - 컴컴캐 + � x - 5 x - 6 x - 7 x - 8� + Type: Matrix Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty2} +\begin{paste}{ugIntroTwoDimPageEmpty2}{ugIntroTwoDimPagePatch2} +\pastebutton{ugIntroTwoDimPageEmpty2}{\showpaste} +\tab{5}\spadcommand{matrix([[1/(i + j - x) for i in 1..4] for j in 1..4])\bound{hilb }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch3} +\begin{paste}{ugIntroTwoDimPageFull3}{ugIntroTwoDimPageEmpty3} +\pastebutton{ugIntroTwoDimPageFull3}{\hidepaste} +\tab{5}\spadcommand{vm := matrix [[1,1,1], [x,y,z], [x*x,y*y,z*z]]\bound{vm }} +\indentrel{3}\begin{verbatim} + �1 1 1 � + � � + (3) 퀈 y z � + � � + � 2 2 2� + 픵 y z � + Type: Matrix Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty3} +\begin{paste}{ugIntroTwoDimPageEmpty3}{ugIntroTwoDimPagePatch3} +\pastebutton{ugIntroTwoDimPageEmpty3}{\showpaste} +\tab{5}\spadcommand{vm := matrix [[1,1,1], [x,y,z], [x*x,y*y,z*z]]\bound{vm }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch4} +\begin{paste}{ugIntroTwoDimPageFull4}{ugIntroTwoDimPageEmpty4} +\pastebutton{ugIntroTwoDimPageFull4}{\hidepaste} +\tab{5}\spadcommand{vm(3,3)\free{vm }} +\indentrel{3}\begin{verbatim} + 2 + (4) z + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty4} +\begin{paste}{ugIntroTwoDimPageEmpty4}{ugIntroTwoDimPagePatch4} +\pastebutton{ugIntroTwoDimPageEmpty4}{\showpaste} +\tab{5}\spadcommand{vm(3,3)\free{vm }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch5} +\begin{paste}{ugIntroTwoDimPageFull5}{ugIntroTwoDimPageEmpty5} +\pastebutton{ugIntroTwoDimPageFull5}{\hidepaste} +\tab{5}\spadcommand{column(vm,2)\free{vm }} +\indentrel{3}\begin{verbatim} + 2 + (5) [1,y,y ] + Type: Vector Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty5} +\begin{paste}{ugIntroTwoDimPageEmpty5}{ugIntroTwoDimPagePatch5} +\pastebutton{ugIntroTwoDimPageEmpty5}{\showpaste} +\tab{5}\spadcommand{column(vm,2)\free{vm }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch6} +\begin{paste}{ugIntroTwoDimPageFull6}{ugIntroTwoDimPageEmpty6} +\pastebutton{ugIntroTwoDimPageFull6}{\hidepaste} +\tab{5}\spadcommand{vm * vm\free{vm }} +\indentrel{3}\begin{verbatim} + (6) + � 2 2 2 � + � x + x + 1 y + y + 1 z + z + 1 � + � � + � 2 2 2 3 � + � x z + x y + x y z + y + x z + y z + x � + � � + � 2 2 2 2 2 2 3 2 4 2 2� + 픵 z + x y + x y z + y + x z + y z + x � + Type: Matrix Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty6} +\begin{paste}{ugIntroTwoDimPageEmpty6}{ugIntroTwoDimPagePatch6} +\pastebutton{ugIntroTwoDimPageEmpty6}{\showpaste} +\tab{5}\spadcommand{vm * vm\free{vm }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPagePatch7} +\begin{paste}{ugIntroTwoDimPageFull7}{ugIntroTwoDimPageEmpty7} +\pastebutton{ugIntroTwoDimPageFull7}{\hidepaste} +\tab{5}\spadcommand{factor determinant vm\free{vm }\bound{d }} +\indentrel{3}\begin{verbatim} + (7) (y - x)(z - y)(z - x) + Type: Factored Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroTwoDimPageEmpty7} +\begin{paste}{ugIntroTwoDimPageEmpty7}{ugIntroTwoDimPagePatch7} +\pastebutton{ugIntroTwoDimPageEmpty7}{\showpaste} +\tab{5}\spadcommand{factor determinant vm\free{vm }\bound{d }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch1} +\begin{paste}{ugIntroAssignPageFull1}{ugIntroAssignPageEmpty1} +\pastebutton{ugIntroAssignPageFull1}{\hidepaste} +\tab{5}\spadcommand{(x - y*z)**2} +\indentrel{3}\begin{verbatim} + 2 2 2 + (1) y z - 2x y z + x + Type: Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty1} +\begin{paste}{ugIntroAssignPageEmpty1}{ugIntroAssignPagePatch1} +\pastebutton{ugIntroAssignPageEmpty1}{\showpaste} +\tab{5}\spadcommand{(x - y*z)**2} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch2} +\begin{paste}{ugIntroAssignPageFull2}{ugIntroAssignPageEmpty2} +\pastebutton{ugIntroAssignPageFull2}{\hidepaste} +\tab{5}\spadcommand{x := 4} +\indentrel{3}\begin{verbatim} + (2) 4 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty2} +\begin{paste}{ugIntroAssignPageEmpty2}{ugIntroAssignPagePatch2} +\pastebutton{ugIntroAssignPageEmpty2}{\showpaste} +\tab{5}\spadcommand{x := 4} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch3} +\begin{paste}{ugIntroAssignPageFull3}{ugIntroAssignPageEmpty3} +\pastebutton{ugIntroAssignPageFull3}{\hidepaste} +\tab{5}\spadcommand{x := z + 3/5} +\indentrel{3}\begin{verbatim} + 3 + (3) z + � + 5 + Type: Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty3} +\begin{paste}{ugIntroAssignPageEmpty3}{ugIntroAssignPagePatch3} +\pastebutton{ugIntroAssignPageEmpty3}{\showpaste} +\tab{5}\spadcommand{x := z + 3/5} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch4} +\begin{paste}{ugIntroAssignPageFull4}{ugIntroAssignPageEmpty4} +\pastebutton{ugIntroAssignPageFull4}{\hidepaste} +\tab{5}\spadcommand{y : Integer\bound{y }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty4} +\begin{paste}{ugIntroAssignPageEmpty4}{ugIntroAssignPagePatch4} +\pastebutton{ugIntroAssignPageEmpty4}{\showpaste} +\tab{5}\spadcommand{y : Integer\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch5} +\begin{paste}{ugIntroAssignPageFull5}{ugIntroAssignPageEmpty5} +\pastebutton{ugIntroAssignPageFull5}{\hidepaste} +\tab{5}\spadcommand{y := 89\bound{y1 }\free{y }} +\indentrel{3}\begin{verbatim} + (5) 89 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty5} +\begin{paste}{ugIntroAssignPageEmpty5}{ugIntroAssignPagePatch5} +\pastebutton{ugIntroAssignPageEmpty5}{\showpaste} +\tab{5}\spadcommand{y := 89\bound{y1 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch6} +\begin{paste}{ugIntroAssignPageFull6}{ugIntroAssignPageEmpty6} +\pastebutton{ugIntroAssignPageFull6}{\hidepaste} +\tab{5}\spadcommand{y := sin \%pi} +\indentrel{3}\begin{verbatim} + (6) 0 + Type: Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty6} +\begin{paste}{ugIntroAssignPageEmpty6}{ugIntroAssignPagePatch6} +\pastebutton{ugIntroAssignPageEmpty6}{\showpaste} +\tab{5}\spadcommand{y := sin \%pi} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch7} +\begin{paste}{ugIntroAssignPageFull7}{ugIntroAssignPageEmpty7} +\pastebutton{ugIntroAssignPageFull7}{\hidepaste} +\tab{5}\spadcommand{y := 2/3} +\indentrel{3}\begin{verbatim} + 2 + � + 3 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty7} +\begin{paste}{ugIntroAssignPageEmpty7}{ugIntroAssignPagePatch7} +\pastebutton{ugIntroAssignPageEmpty7}{\showpaste} +\tab{5}\spadcommand{y := 2/3} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch8} +\begin{paste}{ugIntroAssignPageFull8}{ugIntroAssignPageEmpty8} +\pastebutton{ugIntroAssignPageFull8}{\hidepaste} +\tab{5}\spadcommand{f : Float := 2/3} +\indentrel{3}\begin{verbatim} + (7) 0.6666666666 6666666667 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty8} +\begin{paste}{ugIntroAssignPageEmpty8}{ugIntroAssignPagePatch8} +\pastebutton{ugIntroAssignPageEmpty8}{\showpaste} +\tab{5}\spadcommand{f : Float := 2/3} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch9} +\begin{paste}{ugIntroAssignPageFull9}{ugIntroAssignPageEmpty9} +\pastebutton{ugIntroAssignPageFull9}{\hidepaste} +\tab{5}\spadcommand{f : Float; f := 2/3\bound{fff }} +\indentrel{3}\begin{verbatim} + (8) 0.6666666666 6666666667 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty9} +\begin{paste}{ugIntroAssignPageEmpty9}{ugIntroAssignPagePatch9} +\pastebutton{ugIntroAssignPageEmpty9}{\showpaste} +\tab{5}\spadcommand{f : Float; f := 2/3\bound{fff }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch10} +\begin{paste}{ugIntroAssignPageFull10}{ugIntroAssignPageEmpty10} +\pastebutton{ugIntroAssignPageFull10}{\hidepaste} +\tab{5}\spadcommand{q} +\indentrel{3}\begin{verbatim} + (9) q + Type: Variable q +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty10} +\begin{paste}{ugIntroAssignPageEmpty10}{ugIntroAssignPagePatch10} +\pastebutton{ugIntroAssignPageEmpty10}{\showpaste} +\tab{5}\spadcommand{q} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch11} +\begin{paste}{ugIntroAssignPageFull11}{ugIntroAssignPageEmpty11} +\pastebutton{ugIntroAssignPageFull11}{\hidepaste} +\tab{5}\spadcommand{[q, r]} +\indentrel{3}\begin{verbatim} + (10) [q,r] + Type: List OrderedVariableList [q,r] +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty11} +\begin{paste}{ugIntroAssignPageEmpty11}{ugIntroAssignPagePatch11} +\pastebutton{ugIntroAssignPageEmpty11}{\showpaste} +\tab{5}\spadcommand{[q, r]} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch12} +\begin{paste}{ugIntroAssignPageFull12}{ugIntroAssignPageEmpty12} +\pastebutton{ugIntroAssignPageFull12}{\hidepaste} +\tab{5}\spadcommand{f\free{fff }} +\indentrel{3}\begin{verbatim} + (11) 0.6666666666 6666666667 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty12} +\begin{paste}{ugIntroAssignPageEmpty12}{ugIntroAssignPagePatch12} +\pastebutton{ugIntroAssignPageEmpty12}{\showpaste} +\tab{5}\spadcommand{f\free{fff }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPagePatch13} +\begin{paste}{ugIntroAssignPageFull13}{ugIntroAssignPageEmpty13} +\pastebutton{ugIntroAssignPageFull13}{\hidepaste} +\tab{5}\spadcommand{'f} +\indentrel{3}\begin{verbatim} + (12) f + Type: Variable f +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroAssignPageEmpty13} +\begin{paste}{ugIntroAssignPageEmpty13}{ugIntroAssignPagePatch13} +\pastebutton{ugIntroAssignPageEmpty13}{\showpaste} +\tab{5}\spadcommand{'f} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch1} +\begin{paste}{ugIntroSeriesPageFull1}{ugIntroSeriesPageEmpty1} +\pastebutton{ugIntroSeriesPageFull1}{\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}{ugIntroSeriesPageEmpty1} +\begin{paste}{ugIntroSeriesPageEmpty1}{ugIntroSeriesPagePatch1} +\pastebutton{ugIntroSeriesPageEmpty1}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),x = 0)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch2} +\begin{paste}{ugIntroSeriesPageFull2}{ugIntroSeriesPageEmpty2} +\pastebutton{ugIntroSeriesPageFull2}{\hidepaste} +\tab{5}\spadcommand{series(sin(a*x),x = \%pi/4)} +\indentrel{3}\begin{verbatim} + (2) + a %pi a %pi %pi + sin(컴컴�) + a cos(컴컴�)(x - 컴�) + 4 4 4 + + + 2 a %pi 3 a %pi + a sin(컴컴�) a cos(컴컴�) + 4 %pi 2 4 %pi 3 + - 컴컴컴컴컴컴 (x - 컴�) - 컴컴컴컴컴컴 (x - 컴�) + 2 4 6 4 + + + 4 a %pi 5 a %pi + a sin(컴컴�) a cos(컴컴�) + 4 %pi 4 4 %pi 5 + 컴컴컴컴컴컴 (x - 컴�) + 컴컴컴컴컴컴 (x - 컴�) + 24 4 120 4 + + + 6 a %pi 7 a %pi + a sin(컴컴�) a cos(컴컴�) + 4 %pi 6 4 %pi 7 + - 컴컴컴컴컴컴 (x - 컴�) - 컴컴컴컴컴컴 (x - 컴�) + 720 4 5040 4 + + + 8 a %pi 9 a %pi + a sin(컴컴�) a cos(컴컴�) + 4 %pi 8 4 %pi 9 + 컴컴컴컴컴컴 (x - 컴�) + 컴컴컴컴컴컴 (x - 컴�) + 40320 4 362880 4 + + + 10 a %pi + a sin(컴컴�) + 4 %pi 10 %pi 11 + - 컴컴컴컴컴컴� (x - 컴�) + O((x - 컴�) ) + 3628800 4 4 +Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/4) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPageEmpty2} +\begin{paste}{ugIntroSeriesPageEmpty2}{ugIntroSeriesPagePatch2} +\pastebutton{ugIntroSeriesPageEmpty2}{\showpaste} +\tab{5}\spadcommand{series(sin(a*x),x = \%pi/4)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch3} +\begin{paste}{ugIntroSeriesPageFull3}{ugIntroSeriesPageEmpty3} +\pastebutton{ugIntroSeriesPageFull3}{\hidepaste} +\tab{5}\spadcommand{series(n +-> (-1)**((3*n - 4)/6)/factorial(n - 1/3),x = 0,4/3..,2)} +\indentrel{3}\begin{verbatim} + 4 10 + � 컴 + 3 1 3 5 + (3) x - � x + O(x ) + 6 + Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPageEmpty3} +\begin{paste}{ugIntroSeriesPageEmpty3}{ugIntroSeriesPagePatch3} +\pastebutton{ugIntroSeriesPageEmpty3}{\showpaste} +\tab{5}\spadcommand{series(n +-> (-1)**((3*n - 4)/6)/factorial(n - 1/3),x = 0,4/3..,2)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch4} +\begin{paste}{ugIntroSeriesPageFull4}{ugIntroSeriesPageEmpty4} +\pastebutton{ugIntroSeriesPageFull4}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\indentrel{3}\begin{verbatim} + (4) + 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}{ugIntroSeriesPageEmpty4} +\begin{paste}{ugIntroSeriesPageEmpty4}{ugIntroSeriesPagePatch4} +\pastebutton{ugIntroSeriesPageEmpty4}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch5} +\begin{paste}{ugIntroSeriesPageFull5}{ugIntroSeriesPageEmpty5} +\pastebutton{ugIntroSeriesPageFull5}{\hidepaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\indentrel{3}\begin{verbatim} + (5) + 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}{ugIntroSeriesPageEmpty5} +\begin{paste}{ugIntroSeriesPageEmpty5}{ugIntroSeriesPagePatch5} +\pastebutton{ugIntroSeriesPageEmpty5}{\showpaste} +\tab{5}\spadcommand{f ** 2\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch6} +\begin{paste}{ugIntroSeriesPageFull6}{ugIntroSeriesPageEmpty6} +\pastebutton{ugIntroSeriesPageFull6}{\hidepaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\indentrel{3}\begin{verbatim} + (6) + 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}{ugIntroSeriesPageEmpty6} +\begin{paste}{ugIntroSeriesPageEmpty6}{ugIntroSeriesPagePatch6} +\pastebutton{ugIntroSeriesPageEmpty6}{\showpaste} +\tab{5}\spadcommand{f := series(1/(1-x),x = 0)\bound{f1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch7} +\begin{paste}{ugIntroSeriesPageFull7}{ugIntroSeriesPageEmpty7} +\pastebutton{ugIntroSeriesPageFull7}{\hidepaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\indentrel{3}\begin{verbatim} + (7) + 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}{ugIntroSeriesPageEmpty7} +\begin{paste}{ugIntroSeriesPageEmpty7}{ugIntroSeriesPagePatch7} +\pastebutton{ugIntroSeriesPageEmpty7}{\showpaste} +\tab{5}\spadcommand{g := log(f)\free{f1 }\bound{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch8} +\begin{paste}{ugIntroSeriesPageFull8}{ugIntroSeriesPageEmpty8} +\pastebutton{ugIntroSeriesPageFull8}{\hidepaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\indentrel{3}\begin{verbatim} + (8) + 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}{ugIntroSeriesPageEmpty8} +\begin{paste}{ugIntroSeriesPageEmpty8}{ugIntroSeriesPagePatch8} +\pastebutton{ugIntroSeriesPageEmpty8}{\showpaste} +\tab{5}\spadcommand{exp(g)\free{g }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch9} +\begin{paste}{ugIntroSeriesPageFull9}{ugIntroSeriesPageEmpty9} +\pastebutton{ugIntroSeriesPageFull9}{\hidepaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\indentrel{3}\begin{verbatim} + (9) + 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}{ugIntroSeriesPageEmpty9} +\begin{paste}{ugIntroSeriesPageEmpty9}{ugIntroSeriesPagePatch9} +\pastebutton{ugIntroSeriesPageEmpty9}{\showpaste} +\tab{5}\spadcommand{f := taylor(exp(x))\bound{f2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSeriesPagePatch10} +\begin{paste}{ugIntroSeriesPageFull10}{ugIntroSeriesPageEmpty10} +\pastebutton{ugIntroSeriesPageFull10}{\hidepaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\indentrel{3}\begin{verbatim} + (10) + [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}{ugIntroSeriesPageEmpty10} +\begin{paste}{ugIntroSeriesPageEmpty10}{ugIntroSeriesPagePatch10} +\pastebutton{ugIntroSeriesPageEmpty10}{\showpaste} +\tab{5}\spadcommand{eval(f,1.0)\free{f2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPagePatch1} +\begin{paste}{ugIntroCallFunPageFull1}{ugIntroCallFunPageEmpty1} +\pastebutton{ugIntroCallFunPageFull1}{\hidepaste} +\tab{5}\spadcommand{factor(120)} +\indentrel{3}\begin{verbatim} + 3 + (1) 2 3 5 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPageEmpty1} +\begin{paste}{ugIntroCallFunPageEmpty1}{ugIntroCallFunPagePatch1} +\pastebutton{ugIntroCallFunPageEmpty1}{\showpaste} +\tab{5}\spadcommand{factor(120)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPagePatch2} +\begin{paste}{ugIntroCallFunPageFull2}{ugIntroCallFunPageEmpty2} +\pastebutton{ugIntroCallFunPageFull2}{\hidepaste} +\tab{5}\spadcommand{divide(125,7)} +\indentrel{3}\begin{verbatim} + (2) [quotient= 17,remainder= 6] + Type: Record(quotient: Integer,remainder: Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPageEmpty2} +\begin{paste}{ugIntroCallFunPageEmpty2}{ugIntroCallFunPagePatch2} +\pastebutton{ugIntroCallFunPageEmpty2}{\showpaste} +\tab{5}\spadcommand{divide(125,7)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPagePatch3} +\begin{paste}{ugIntroCallFunPageFull3}{ugIntroCallFunPageEmpty3} +\pastebutton{ugIntroCallFunPageFull3}{\hidepaste} +\tab{5}\spadcommand{quatern(3.4,5.6,2.9,0.1)} +\indentrel{3}\begin{verbatim} + (3) 3.4 + 5.6 i + 2.9 j + 0.1 k + Type: Quaternion Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPageEmpty3} +\begin{paste}{ugIntroCallFunPageEmpty3}{ugIntroCallFunPagePatch3} +\pastebutton{ugIntroCallFunPageEmpty3}{\showpaste} +\tab{5}\spadcommand{quatern(3.4,5.6,2.9,0.1)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPagePatch4} +\begin{paste}{ugIntroCallFunPageFull4}{ugIntroCallFunPageEmpty4} +\pastebutton{ugIntroCallFunPageFull4}{\hidepaste} +\tab{5}\spadcommand{factorial 10} +\indentrel{3}\begin{verbatim} + (4) 3628800 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCallFunPageEmpty4} +\begin{paste}{ugIntroCallFunPageEmpty4}{ugIntroCallFunPagePatch4} +\pastebutton{ugIntroCallFunPageEmpty4}{\showpaste} +\tab{5}\spadcommand{factorial 10} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch1} +\begin{paste}{ugIntroCollectPageFull1}{ugIntroCollectPageEmpty1} +\pastebutton{ugIntroCollectPageFull1}{\hidepaste} +\tab{5}\spadcommand{u := [1,-7,11]\bound{u }} +\indentrel{3}\begin{verbatim} + (1) [1,- 7,11] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty1} +\begin{paste}{ugIntroCollectPageEmpty1}{ugIntroCollectPagePatch1} +\pastebutton{ugIntroCollectPageEmpty1}{\showpaste} +\tab{5}\spadcommand{u := [1,-7,11]\bound{u }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch2} +\begin{paste}{ugIntroCollectPageFull2}{ugIntroCollectPageEmpty2} +\pastebutton{ugIntroCollectPageFull2}{\hidepaste} +\tab{5}\spadcommand{first rest rest u\free{u }} +\indentrel{3}\begin{verbatim} + (2) 11 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty2} +\begin{paste}{ugIntroCollectPageEmpty2}{ugIntroCollectPagePatch2} +\pastebutton{ugIntroCollectPageEmpty2}{\showpaste} +\tab{5}\spadcommand{first rest rest u\free{u }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch3} +\begin{paste}{ugIntroCollectPageFull3}{ugIntroCollectPageEmpty3} +\pastebutton{ugIntroCollectPageFull3}{\hidepaste} +\tab{5}\spadcommand{concat!(u,[9,1,3,-4]); u\free{u }\bound{u1 }} +\indentrel{3}\begin{verbatim} + (3) [1,- 7,11,9,1,3,- 4] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty3} +\begin{paste}{ugIntroCollectPageEmpty3}{ugIntroCollectPagePatch3} +\pastebutton{ugIntroCollectPageEmpty3}{\showpaste} +\tab{5}\spadcommand{concat!(u,[9,1,3,-4]); u\free{u }\bound{u1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch4} +\begin{paste}{ugIntroCollectPageFull4}{ugIntroCollectPageEmpty4} +\pastebutton{ugIntroCollectPageFull4}{\hidepaste} +\tab{5}\spadcommand{lastnode := rest(u,3)\free{u1 }\bound{u2 }} +\indentrel{3}\begin{verbatim} + (4) [9,1,3,- 4] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty4} +\begin{paste}{ugIntroCollectPageEmpty4}{ugIntroCollectPagePatch4} +\pastebutton{ugIntroCollectPageEmpty4}{\showpaste} +\tab{5}\spadcommand{lastnode := rest(u,3)\free{u1 }\bound{u2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch5} +\begin{paste}{ugIntroCollectPageFull5}{ugIntroCollectPageEmpty5} +\pastebutton{ugIntroCollectPageFull5}{\hidepaste} +\tab{5}\spadcommand{setrest!(lastnode,rest(u,2)); u\free{u2 }} +\indentrel{3}\begin{verbatim} + ____ + (5) [1,- 7,11,9] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty5} +\begin{paste}{ugIntroCollectPageEmpty5}{ugIntroCollectPagePatch5} +\pastebutton{ugIntroCollectPageEmpty5}{\showpaste} +\tab{5}\spadcommand{setrest!(lastnode,rest(u,2)); u\free{u2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch6} +\begin{paste}{ugIntroCollectPageFull6}{ugIntroCollectPageEmpty6} +\pastebutton{ugIntroCollectPageFull6}{\hidepaste} +\tab{5}\spadcommand{[factor(i) for i in 2.. by 2]\bound{stream1 }} +\indentrel{3}\begin{verbatim} + 2 3 2 4 2 2 + (6) [2,2 ,2 3,2 ,2 5,2 3,2 7,2 ,2 3 ,2 5,...] + Type: Stream Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty6} +\begin{paste}{ugIntroCollectPageEmpty6}{ugIntroCollectPagePatch6} +\pastebutton{ugIntroCollectPageEmpty6}{\showpaste} +\tab{5}\spadcommand{[factor(i) for i in 2.. by 2]\bound{stream1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch7} +\begin{paste}{ugIntroCollectPageFull7}{ugIntroCollectPageEmpty7} +\pastebutton{ugIntroCollectPageFull7}{\hidepaste} +\tab{5}\spadcommand{\%.36\free{stream1 }} +\indentrel{3}\begin{verbatim} + 3 2 + (7) 2 3 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty7} +\begin{paste}{ugIntroCollectPageEmpty7}{ugIntroCollectPagePatch7} +\pastebutton{ugIntroCollectPageEmpty7}{\showpaste} +\tab{5}\spadcommand{\%.36\free{stream1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch8} +\begin{paste}{ugIntroCollectPageFull8}{ugIntroCollectPageEmpty8} +\pastebutton{ugIntroCollectPageFull8}{\hidepaste} +\tab{5}\spadcommand{a := oneDimensionalArray [1, -7, 3, 3/2]\bound{a }} +\indentrel{3}\begin{verbatim} + 3 + (8) [1,- 7,3,�] + 2 + Type: OneDimensionalArray Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty8} +\begin{paste}{ugIntroCollectPageEmpty8}{ugIntroCollectPagePatch8} +\pastebutton{ugIntroCollectPageEmpty8}{\showpaste} +\tab{5}\spadcommand{a := oneDimensionalArray [1, -7, 3, 3/2]\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch9} +\begin{paste}{ugIntroCollectPageFull9}{ugIntroCollectPageEmpty9} +\pastebutton{ugIntroCollectPageFull9}{\hidepaste} +\tab{5}\spadcommand{a.3 := 11; a\bound{a1 }\free{a }} +\indentrel{3}\begin{verbatim} + 3 + (9) [1,- 7,11,�] + 2 + Type: OneDimensionalArray Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty9} +\begin{paste}{ugIntroCollectPageEmpty9}{ugIntroCollectPagePatch9} +\pastebutton{ugIntroCollectPageEmpty9}{\showpaste} +\tab{5}\spadcommand{a.3 := 11; a\bound{a1 }\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch10} +\begin{paste}{ugIntroCollectPageFull10}{ugIntroCollectPageEmpty10} +\pastebutton{ugIntroCollectPageFull10}{\hidepaste} +\tab{5}\spadcommand{concat!(a,oneDimensionalArray [1,-2])\free{a1 }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty10} +\begin{paste}{ugIntroCollectPageEmpty10}{ugIntroCollectPagePatch10} +\pastebutton{ugIntroCollectPageEmpty10}{\showpaste} +\tab{5}\spadcommand{concat!(a,oneDimensionalArray [1,-2])\free{a1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch11} +\begin{paste}{ugIntroCollectPageFull11}{ugIntroCollectPageEmpty11} +\pastebutton{ugIntroCollectPageFull11}{\hidepaste} +\tab{5}\spadcommand{bits(32,true)} +\indentrel{3}\begin{verbatim} + (10) "11111111111111111111111111111111" + Type: Bits +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty11} +\begin{paste}{ugIntroCollectPageEmpty11}{ugIntroCollectPagePatch11} +\pastebutton{ugIntroCollectPageEmpty11}{\showpaste} +\tab{5}\spadcommand{bits(32,true)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch12} +\begin{paste}{ugIntroCollectPageFull12}{ugIntroCollectPageEmpty12} +\pastebutton{ugIntroCollectPageFull12}{\hidepaste} +\tab{5}\spadcommand{f := flexibleArray [2, 7, -5]\bound{f }} +\indentrel{3}\begin{verbatim} + (11) [2,7,- 5] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty12} +\begin{paste}{ugIntroCollectPageEmpty12}{ugIntroCollectPagePatch12} +\pastebutton{ugIntroCollectPageEmpty12}{\showpaste} +\tab{5}\spadcommand{f := flexibleArray [2, 7, -5]\bound{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch13} +\begin{paste}{ugIntroCollectPageFull13}{ugIntroCollectPageEmpty13} +\pastebutton{ugIntroCollectPageFull13}{\hidepaste} +\tab{5}\spadcommand{insert!(flexibleArray [11, -3],f,2)\free{f }} +\indentrel{3}\begin{verbatim} + (12) [2,11,- 3,7,- 5] + Type: FlexibleArray Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty13} +\begin{paste}{ugIntroCollectPageEmpty13}{ugIntroCollectPagePatch13} +\pastebutton{ugIntroCollectPageEmpty13}{\showpaste} +\tab{5}\spadcommand{insert!(flexibleArray [11, -3],f,2)\free{f }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch14} +\begin{paste}{ugIntroCollectPageFull14}{ugIntroCollectPageEmpty14} +\pastebutton{ugIntroCollectPageFull14}{\hidepaste} +\tab{5}\spadcommand{h := heap [-4,7,11,3,4,-7]\bound{h }} +\indentrel{3}\begin{verbatim} + (13) [11,4,7,- 4,3,- 7] + Type: Heap Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty14} +\begin{paste}{ugIntroCollectPageEmpty14}{ugIntroCollectPagePatch14} +\pastebutton{ugIntroCollectPageEmpty14}{\showpaste} +\tab{5}\spadcommand{h := heap [-4,7,11,3,4,-7]\bound{h }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch15} +\begin{paste}{ugIntroCollectPageFull15}{ugIntroCollectPageEmpty15} +\pastebutton{ugIntroCollectPageFull15}{\hidepaste} +\tab{5}\spadcommand{[extract!(h) while not empty?(h)]\free{h }} +\indentrel{3}\begin{verbatim} + (14) [11,7,4,3,- 4,- 7] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty15} +\begin{paste}{ugIntroCollectPageEmpty15}{ugIntroCollectPagePatch15} +\pastebutton{ugIntroCollectPageEmpty15}{\showpaste} +\tab{5}\spadcommand{[extract!(h) while not empty?(h)]\free{h }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch16} +\begin{paste}{ugIntroCollectPageFull16}{ugIntroCollectPageEmpty16} +\pastebutton{ugIntroCollectPageFull16}{\hidepaste} +\tab{5}\spadcommand{binarySearchTree [5,3,2,9,4,7,11]} +\indentrel{3}\begin{verbatim} + (15) [[2,3,4],5,[7,9,11]] + Type: BinarySearchTree PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty16} +\begin{paste}{ugIntroCollectPageEmpty16}{ugIntroCollectPagePatch16} +\pastebutton{ugIntroCollectPageEmpty16}{\showpaste} +\tab{5}\spadcommand{binarySearchTree [5,3,2,9,4,7,11]} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch17} +\begin{paste}{ugIntroCollectPageFull17}{ugIntroCollectPageEmpty17} +\pastebutton{ugIntroCollectPageFull17}{\hidepaste} +\tab{5}\spadcommand{modTree(8,[2,3,5,7])} +\indentrel{3}\begin{verbatim} + (16) [0,2,3,1] + Type: List Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty17} +\begin{paste}{ugIntroCollectPageEmpty17}{ugIntroCollectPagePatch17} +\pastebutton{ugIntroCollectPageEmpty17}{\showpaste} +\tab{5}\spadcommand{modTree(8,[2,3,5,7])} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch18} +\begin{paste}{ugIntroCollectPageFull18}{ugIntroCollectPageEmpty18} +\pastebutton{ugIntroCollectPageFull18}{\hidepaste} +\tab{5}\spadcommand{fs := set[1/3,4/5,-1/3,4/5]\bound{fs }} +\indentrel{3}\begin{verbatim} + 1 1 4 + (17) {- �,�,�} + 3 3 5 + Type: Set Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty18} +\begin{paste}{ugIntroCollectPageEmpty18}{ugIntroCollectPagePatch18} +\pastebutton{ugIntroCollectPageEmpty18}{\showpaste} +\tab{5}\spadcommand{fs := set[1/3,4/5,-1/3,4/5]\bound{fs }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch19} +\begin{paste}{ugIntroCollectPageFull19}{ugIntroCollectPageEmpty19} +\pastebutton{ugIntroCollectPageFull19}{\hidepaste} +\tab{5}\spadcommand{multiset [x rem 5 for x in primes(2,1000)]} +\indentrel{3}\begin{verbatim} + (18) {0,42: 3,40: 1,38: 4,47: 2} + Type: Multiset Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty19} +\begin{paste}{ugIntroCollectPageEmpty19}{ugIntroCollectPagePatch19} +\pastebutton{ugIntroCollectPageEmpty19}{\showpaste} +\tab{5}\spadcommand{multiset [x rem 5 for x in primes(2,1000)]} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch20} +\begin{paste}{ugIntroCollectPageFull20}{ugIntroCollectPageEmpty20} +\pastebutton{ugIntroCollectPageFull20}{\hidepaste} +\tab{5}\spadcommand{t : Table(Integer,Integer) := empty()\bound{t }} +\indentrel{3}\begin{verbatim} + (19) table() + Type: Table(Integer,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty20} +\begin{paste}{ugIntroCollectPageEmpty20}{ugIntroCollectPagePatch20} +\pastebutton{ugIntroCollectPageEmpty20}{\showpaste} +\tab{5}\spadcommand{t : Table(Integer,Integer) := empty()\bound{t }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch21} +\begin{paste}{ugIntroCollectPageFull21}{ugIntroCollectPageEmpty21} +\pastebutton{ugIntroCollectPageFull21}{\hidepaste} +\tab{5}\spadcommand{howMany(k) == (n:=search(k,t); n case "failed" => 1; n+1)\bound{how }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty21} +\begin{paste}{ugIntroCollectPageEmpty21}{ugIntroCollectPagePatch21} +\pastebutton{ugIntroCollectPageEmpty21}{\showpaste} +\tab{5}\spadcommand{howMany(k) == (n:=search(k,t); n case "failed" => 1; n+1)\bound{how }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch22} +\begin{paste}{ugIntroCollectPageFull22}{ugIntroCollectPageEmpty22} +\pastebutton{ugIntroCollectPageFull22}{\hidepaste} +\tab{5}\spadcommand{for p in primes(2,1000) repeat (m:= p rem 5; t.m:= howMany(m)); t\free{how t }} +\indentrel{3}\begin{verbatim} + (21) table(2= 47,4= 38,1= 40,3= 42,0= 1) + Type: Table(Integer,Integer) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty22} +\begin{paste}{ugIntroCollectPageEmpty22}{ugIntroCollectPagePatch22} +\pastebutton{ugIntroCollectPageEmpty22}{\showpaste} +\tab{5}\spadcommand{for p in primes(2,1000) repeat (m:= p rem 5; t.m:= howMany(m)); t\free{how t }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch23} +\begin{paste}{ugIntroCollectPageFull23}{ugIntroCollectPageEmpty23} +\pastebutton{ugIntroCollectPageFull23}{\hidepaste} +\tab{5}\spadcommand{daniel : Record(age : Integer, salary : Float)\bound{danieldec }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty23} +\begin{paste}{ugIntroCollectPageEmpty23}{ugIntroCollectPagePatch23} +\pastebutton{ugIntroCollectPageEmpty23}{\showpaste} +\tab{5}\spadcommand{daniel : Record(age : Integer, salary : Float)\bound{danieldec }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch24} +\begin{paste}{ugIntroCollectPageFull24}{ugIntroCollectPageEmpty24} +\pastebutton{ugIntroCollectPageFull24}{\hidepaste} +\tab{5}\spadcommand{daniel := [28, 32005.12]\free{danieldec }\bound{daniel }} +\indentrel{3}\begin{verbatim} + (23) [age= 28,salary= 32005.12] + Type: Record(age: Integer,salary: Float) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty24} +\begin{paste}{ugIntroCollectPageEmpty24}{ugIntroCollectPagePatch24} +\pastebutton{ugIntroCollectPageEmpty24}{\showpaste} +\tab{5}\spadcommand{daniel := [28, 32005.12]\free{danieldec }\bound{daniel }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch25} +\begin{paste}{ugIntroCollectPageFull25}{ugIntroCollectPageEmpty25} +\pastebutton{ugIntroCollectPageFull25}{\hidepaste} +\tab{5}\spadcommand{daniel.salary := 35000; daniel\free{daniel }} +\indentrel{3}\begin{verbatim} + (24) [age= 28,salary= 35000.0] + Type: Record(age: Integer,salary: Float) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty25} +\begin{paste}{ugIntroCollectPageEmpty25}{ugIntroCollectPagePatch25} +\pastebutton{ugIntroCollectPageEmpty25}{\showpaste} +\tab{5}\spadcommand{daniel.salary := 35000; daniel\free{daniel }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch26} +\begin{paste}{ugIntroCollectPageFull26}{ugIntroCollectPageEmpty26} +\pastebutton{ugIntroCollectPageFull26}{\hidepaste} +\tab{5}\spadcommand{dog: Union(licenseNumber: Integer, name: String)\bound{xint }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty26} +\begin{paste}{ugIntroCollectPageEmpty26}{ugIntroCollectPagePatch26} +\pastebutton{ugIntroCollectPageEmpty26}{\showpaste} +\tab{5}\spadcommand{dog: Union(licenseNumber: Integer, name: String)\bound{xint }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPagePatch27} +\begin{paste}{ugIntroCollectPageFull27}{ugIntroCollectPageEmpty27} +\pastebutton{ugIntroCollectPageFull27}{\hidepaste} +\tab{5}\spadcommand{dog := "Whisper"\free{xint }} +\indentrel{3}\begin{verbatim} + (26) "Whisper" + Type: Union(name: String,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCollectPageEmpty27} +\begin{paste}{ugIntroCollectPageEmpty27}{ugIntroCollectPagePatch27} +\pastebutton{ugIntroCollectPageEmpty27}{\showpaste} +\tab{5}\spadcommand{dog := "Whisper"\free{xint }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch1} +\begin{paste}{ugIntroNumbersPageFull1}{ugIntroNumbersPageEmpty1} +\pastebutton{ugIntroNumbersPageFull1}{\hidepaste} +\tab{5}\spadcommand{11**13 * 13**11 * 17**7 - 19**5 * 23**3} +\indentrel{3}\begin{verbatim} + (1) 25387751112538918594666224484237298 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty1} +\begin{paste}{ugIntroNumbersPageEmpty1}{ugIntroNumbersPagePatch1} +\pastebutton{ugIntroNumbersPageEmpty1}{\showpaste} +\tab{5}\spadcommand{11**13 * 13**11 * 17**7 - 19**5 * 23**3} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch2} +\begin{paste}{ugIntroNumbersPageFull2}{ugIntroNumbersPageEmpty2} +\pastebutton{ugIntroNumbersPageFull2}{\hidepaste} +\tab{5}\spadcommand{factor 643238070748569023720594412551704344145570763243\bound{ex1 }} +\indentrel{3}\begin{verbatim} + 13 11 7 5 3 2 + (2) 11 13 17 19 23 29 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty2} +\begin{paste}{ugIntroNumbersPageEmpty2}{ugIntroNumbersPagePatch2} +\pastebutton{ugIntroNumbersPageEmpty2}{\showpaste} +\tab{5}\spadcommand{factor 643238070748569023720594412551704344145570763243\bound{ex1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch3} +\begin{paste}{ugIntroNumbersPageFull3}{ugIntroNumbersPageEmpty3} +\pastebutton{ugIntroNumbersPageFull3}{\hidepaste} +\tab{5}\spadcommand{\% * 12\free{ex1 }} +\indentrel{3}\begin{verbatim} + 2 13 11 7 5 3 2 + (3) 2 3 11 13 17 19 23 29 + Type: Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty3} +\begin{paste}{ugIntroNumbersPageEmpty3}{ugIntroNumbersPagePatch3} +\pastebutton{ugIntroNumbersPageEmpty3}{\showpaste} +\tab{5}\spadcommand{\% * 12\free{ex1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch4} +\begin{paste}{ugIntroNumbersPageFull4}{ugIntroNumbersPageEmpty4} +\pastebutton{ugIntroNumbersPageFull4}{\hidepaste} +\tab{5}\spadcommand{radix(25937424601,11)} +\indentrel{3}\begin{verbatim} + (4) 10000000000 + Type: RadixExpansion 11 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty4} +\begin{paste}{ugIntroNumbersPageEmpty4}{ugIntroNumbersPagePatch4} +\pastebutton{ugIntroNumbersPageEmpty4}{\showpaste} +\tab{5}\spadcommand{radix(25937424601,11)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch5} +\begin{paste}{ugIntroNumbersPageFull5}{ugIntroNumbersPageEmpty5} +\pastebutton{ugIntroNumbersPageFull5}{\hidepaste} +\tab{5}\spadcommand{roman(1992)} +\indentrel{3}\begin{verbatim} + (5) MCMXCII + Type: RomanNumeral +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty5} +\begin{paste}{ugIntroNumbersPageEmpty5}{ugIntroNumbersPagePatch5} +\pastebutton{ugIntroNumbersPageEmpty5}{\showpaste} +\tab{5}\spadcommand{roman(1992)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch6} +\begin{paste}{ugIntroNumbersPageFull6}{ugIntroNumbersPageEmpty6} +\pastebutton{ugIntroNumbersPageFull6}{\hidepaste} +\tab{5}\spadcommand{r := 10 + 9/2 + 8/3 + 7/4 + 6/5 + 5/6 + 4/7 + 3/8 + 2/9\bound{r }} +\indentrel{3}\begin{verbatim} + 55739 + (6) 컴컴� + 2520 + Type: Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty6} +\begin{paste}{ugIntroNumbersPageEmpty6}{ugIntroNumbersPagePatch6} +\pastebutton{ugIntroNumbersPageEmpty6}{\showpaste} +\tab{5}\spadcommand{r := 10 + 9/2 + 8/3 + 7/4 + 6/5 + 5/6 + 4/7 + 3/8 + 2/9\bound{r }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch7} +\begin{paste}{ugIntroNumbersPageFull7}{ugIntroNumbersPageEmpty7} +\pastebutton{ugIntroNumbersPageFull7}{\hidepaste} +\tab{5}\spadcommand{map(factor,r)\free{r }} +\indentrel{3}\begin{verbatim} + 139 401 + (7) 컴컴컴� + 3 2 + 2 3 5 7 + Type: Fraction Factored Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty7} +\begin{paste}{ugIntroNumbersPageEmpty7}{ugIntroNumbersPagePatch7} +\pastebutton{ugIntroNumbersPageEmpty7}{\showpaste} +\tab{5}\spadcommand{map(factor,r)\free{r }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch8} +\begin{paste}{ugIntroNumbersPageFull8}{ugIntroNumbersPageEmpty8} +\pastebutton{ugIntroNumbersPageFull8}{\hidepaste} +\tab{5}\spadcommand{11@SingleInteger} +\indentrel{3}\begin{verbatim} + (8) 11 + Type: SingleInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty8} +\begin{paste}{ugIntroNumbersPageEmpty8}{ugIntroNumbersPagePatch8} +\pastebutton{ugIntroNumbersPageEmpty8}{\showpaste} +\tab{5}\spadcommand{11@SingleInteger} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch9} +\begin{paste}{ugIntroNumbersPageFull9}{ugIntroNumbersPageEmpty9} +\pastebutton{ugIntroNumbersPageFull9}{\hidepaste} +\tab{5}\spadcommand{123.21@DoubleFloat} +\indentrel{3}\begin{verbatim} + (9) 123.21000000000001 + Type: DoubleFloat +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty9} +\begin{paste}{ugIntroNumbersPageEmpty9}{ugIntroNumbersPagePatch9} +\pastebutton{ugIntroNumbersPageEmpty9}{\showpaste} +\tab{5}\spadcommand{123.21@DoubleFloat} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch10} +\begin{paste}{ugIntroNumbersPageFull10}{ugIntroNumbersPageEmpty10} +\pastebutton{ugIntroNumbersPageFull10}{\hidepaste} +\tab{5}\spadcommand{r :: Float\free{r }} +\indentrel{3}\begin{verbatim} + (10) 22.1186507936 50793651 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty10} +\begin{paste}{ugIntroNumbersPageEmpty10}{ugIntroNumbersPagePatch10} +\pastebutton{ugIntroNumbersPageEmpty10}{\showpaste} +\tab{5}\spadcommand{r :: Float\free{r }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch11} +\begin{paste}{ugIntroNumbersPageFull11}{ugIntroNumbersPageEmpty11} +\pastebutton{ugIntroNumbersPageFull11}{\hidepaste} +\tab{5}\spadcommand{digits(22)\bound{fewerdigits }} +\indentrel{3}\begin{verbatim} + (11) 20 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty11} +\begin{paste}{ugIntroNumbersPageEmpty11}{ugIntroNumbersPagePatch11} +\pastebutton{ugIntroNumbersPageEmpty11}{\showpaste} +\tab{5}\spadcommand{digits(22)\bound{fewerdigits }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch12} +\begin{paste}{ugIntroNumbersPageFull12}{ugIntroNumbersPageEmpty12} +\pastebutton{ugIntroNumbersPageFull12}{\hidepaste} +\tab{5}\spadcommand{exp(\%pi * sqrt 163.0)\free{fewerdigits }} +\indentrel{3}\begin{verbatim} + (12) 26253741 2640768744.0 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty12} +\begin{paste}{ugIntroNumbersPageEmpty12}{ugIntroNumbersPagePatch12} +\pastebutton{ugIntroNumbersPageEmpty12}{\showpaste} +\tab{5}\spadcommand{exp(\%pi * sqrt 163.0)\free{fewerdigits }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch13} +\begin{paste}{ugIntroNumbersPageFull13}{ugIntroNumbersPageEmpty13} +\pastebutton{ugIntroNumbersPageFull13}{\hidepaste} +\tab{5}\spadcommand{digits(40); exp(\%pi * sqrt 163.0)\free{moredigits }} +\indentrel{3}\begin{verbatim} + (13) 26253741 2640768743.9999999999 9925007259 76 + Type: Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty13} +\begin{paste}{ugIntroNumbersPageEmpty13}{ugIntroNumbersPagePatch13} +\pastebutton{ugIntroNumbersPageEmpty13}{\showpaste} +\tab{5}\spadcommand{digits(40); exp(\%pi * sqrt 163.0)\free{moredigits }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch14} +\begin{paste}{ugIntroNumbersPageFull14}{ugIntroNumbersPageEmpty14} +\pastebutton{ugIntroNumbersPageFull14}{\hidepaste} +\tab{5}\spadcommand{(2/3 + \%i)**3\bound{gaussint }} +\indentrel{3}\begin{verbatim} + 46 1 + (14) - 컴 + � %i + 27 3 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty14} +\begin{paste}{ugIntroNumbersPageEmpty14}{ugIntroNumbersPagePatch14} +\pastebutton{ugIntroNumbersPageEmpty14}{\showpaste} +\tab{5}\spadcommand{(2/3 + \%i)**3\bound{gaussint }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch15} +\begin{paste}{ugIntroNumbersPageFull15}{ugIntroNumbersPageEmpty15} +\pastebutton{ugIntroNumbersPageFull15}{\hidepaste} +\tab{5}\spadcommand{conjugate \%\free{gaussint }} +\indentrel{3}\begin{verbatim} + 46 1 + (15) - 컴 - � %i + 27 3 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty15} +\begin{paste}{ugIntroNumbersPageEmpty15}{ugIntroNumbersPagePatch15} +\pastebutton{ugIntroNumbersPageEmpty15}{\showpaste} +\tab{5}\spadcommand{conjugate \%\free{gaussint }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch16} +\begin{paste}{ugIntroNumbersPageFull16}{ugIntroNumbersPageEmpty16} +\pastebutton{ugIntroNumbersPageFull16}{\hidepaste} +\tab{5}\spadcommand{factor(89 - 23 * \%i)} +\indentrel{3}\begin{verbatim} + 2 2 + (16) - (1 + %i)(2 + %i) (3 + 2%i) + Type: Factored Complex Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty16} +\begin{paste}{ugIntroNumbersPageEmpty16}{ugIntroNumbersPagePatch16} +\pastebutton{ugIntroNumbersPageEmpty16}{\showpaste} +\tab{5}\spadcommand{factor(89 - 23 * \%i)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch17} +\begin{paste}{ugIntroNumbersPageFull17}{ugIntroNumbersPageEmpty17} +\pastebutton{ugIntroNumbersPageFull17}{\hidepaste} +\tab{5}\spadcommand{exp(\%pi/4.0 * \%i)} +\indentrel{3}\begin{verbatim} + (17) + 0.7071067811 8654752440 0844362104 8490392849 + + + 0.7071067811 8654752440 0844362104 8490392848 %i + Type: Complex Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty17} +\begin{paste}{ugIntroNumbersPageEmpty17}{ugIntroNumbersPagePatch17} +\pastebutton{ugIntroNumbersPageEmpty17}{\showpaste} +\tab{5}\spadcommand{exp(\%pi/4.0 * \%i)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch18} +\begin{paste}{ugIntroNumbersPageFull18}{ugIntroNumbersPageEmpty18} +\pastebutton{ugIntroNumbersPageFull18}{\hidepaste} +\tab{5}\spadcommand{decimal(1/352)} +\indentrel{3}\begin{verbatim} + __ + (18) 0.0028409 + Type: DecimalExpansion +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty18} +\begin{paste}{ugIntroNumbersPageEmpty18}{ugIntroNumbersPagePatch18} +\pastebutton{ugIntroNumbersPageEmpty18}{\showpaste} +\tab{5}\spadcommand{decimal(1/352)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch19} +\begin{paste}{ugIntroNumbersPageFull19}{ugIntroNumbersPageEmpty19} +\pastebutton{ugIntroNumbersPageFull19}{\hidepaste} +\tab{5}\spadcommand{continuedFraction(6543/210)} +\indentrel{3}\begin{verbatim} + 1 � 1 � 1 � 1 � + (19) 31 + 旼컴� + 旼컴� + 旼컴� + 旼컴� + � 6 � 2 � 1 � 3 + Type: ContinuedFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty19} +\begin{paste}{ugIntroNumbersPageEmpty19}{ugIntroNumbersPagePatch19} +\pastebutton{ugIntroNumbersPageEmpty19}{\showpaste} +\tab{5}\spadcommand{continuedFraction(6543/210)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch20} +\begin{paste}{ugIntroNumbersPageFull20}{ugIntroNumbersPageEmpty20} +\pastebutton{ugIntroNumbersPageFull20}{\hidepaste} +\tab{5}\spadcommand{partialFraction(1,factorial(10))\bound{partfrac }} +\indentrel{3}\begin{verbatim} + 159 23 12 1 + (20) 컴� - 컴 - 컴 + � + 8 4 2 7 + 2 3 5 + Type: PartialFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty20} +\begin{paste}{ugIntroNumbersPageEmpty20}{ugIntroNumbersPagePatch20} +\pastebutton{ugIntroNumbersPageEmpty20}{\showpaste} +\tab{5}\spadcommand{partialFraction(1,factorial(10))\bound{partfrac }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch21} +\begin{paste}{ugIntroNumbersPageFull21}{ugIntroNumbersPageEmpty21} +\pastebutton{ugIntroNumbersPageFull21}{\hidepaste} +\tab{5}\spadcommand{padicFraction(\%)\free{partfrac }} +\indentrel{3}\begin{verbatim} + (21) + 1 1 1 1 1 1 2 1 2 2 2 1 + � + 컴 + 컴 + 컴 + 컴 + 컴 - 컴 - 컴 - 컴 - � - 컴 + � + 2 4 5 6 7 8 2 3 4 5 2 7 + 2 2 2 2 2 3 3 3 5 + Type: PartialFraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty21} +\begin{paste}{ugIntroNumbersPageEmpty21}{ugIntroNumbersPagePatch21} +\pastebutton{ugIntroNumbersPageEmpty21}{\showpaste} +\tab{5}\spadcommand{padicFraction(\%)\free{partfrac }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch22} +\begin{paste}{ugIntroNumbersPageFull22}{ugIntroNumbersPageEmpty22} +\pastebutton{ugIntroNumbersPageFull22}{\hidepaste} +\tab{5}\spadcommand{radix(4/7, 8)\bound{rad }} +\indentrel{3}\begin{verbatim} + _ + (22) 0.4 + Type: RadixExpansion 8 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty22} +\begin{paste}{ugIntroNumbersPageEmpty22}{ugIntroNumbersPagePatch22} +\pastebutton{ugIntroNumbersPageEmpty22}{\showpaste} +\tab{5}\spadcommand{radix(4/7, 8)\bound{rad }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch23} +\begin{paste}{ugIntroNumbersPageFull23}{ugIntroNumbersPageEmpty23} +\pastebutton{ugIntroNumbersPageFull23}{\hidepaste} +\tab{5}\spadcommand{\% + 2/3*\%i\free{rad }} +\indentrel{3}\begin{verbatim} + 4 2 + (23) � + � %i + 7 3 + Type: Complex Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty23} +\begin{paste}{ugIntroNumbersPageEmpty23}{ugIntroNumbersPagePatch23} +\pastebutton{ugIntroNumbersPageEmpty23}{\showpaste} +\tab{5}\spadcommand{\% + 2/3*\%i\free{rad }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch24} +\begin{paste}{ugIntroNumbersPageFull24}{ugIntroNumbersPageEmpty24} +\pastebutton{ugIntroNumbersPageFull24}{\hidepaste} +\tab{5}\spadcommand{(5 + sqrt 63 + sqrt 847)**(1/3)} +\indentrel{3}\begin{verbatim} + 旼컴컴컴컴커 + 3� 旼� + (24) \�14\�7 + 5 + Type: AlgebraicNumber +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty24} +\begin{paste}{ugIntroNumbersPageEmpty24}{ugIntroNumbersPagePatch24} +\pastebutton{ugIntroNumbersPageEmpty24}{\showpaste} +\tab{5}\spadcommand{(5 + sqrt 63 + sqrt 847)**(1/3)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch25} +\begin{paste}{ugIntroNumbersPageFull25}{ugIntroNumbersPageEmpty25} +\pastebutton{ugIntroNumbersPageFull25}{\hidepaste} +\tab{5}\spadcommand{x : PrimeField 7 := 5\bound{x }} +\indentrel{3}\begin{verbatim} + (25) 5 + Type: PrimeField 7 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty25} +\begin{paste}{ugIntroNumbersPageEmpty25}{ugIntroNumbersPagePatch25} +\pastebutton{ugIntroNumbersPageEmpty25}{\showpaste} +\tab{5}\spadcommand{x : PrimeField 7 := 5\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch26} +\begin{paste}{ugIntroNumbersPageFull26}{ugIntroNumbersPageEmpty26} +\pastebutton{ugIntroNumbersPageFull26}{\hidepaste} +\tab{5}\spadcommand{x**3\free{x }} +\indentrel{3}\begin{verbatim} + (26) 6 + Type: PrimeField 7 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty26} +\begin{paste}{ugIntroNumbersPageEmpty26}{ugIntroNumbersPagePatch26} +\pastebutton{ugIntroNumbersPageEmpty26}{\showpaste} +\tab{5}\spadcommand{x**3\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch27} +\begin{paste}{ugIntroNumbersPageFull27}{ugIntroNumbersPageEmpty27} +\pastebutton{ugIntroNumbersPageFull27}{\hidepaste} +\tab{5}\spadcommand{1/x\free{x }} +\indentrel{3}\begin{verbatim} + (27) 3 + Type: PrimeField 7 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty27} +\begin{paste}{ugIntroNumbersPageEmpty27}{ugIntroNumbersPagePatch27} +\pastebutton{ugIntroNumbersPageEmpty27}{\showpaste} +\tab{5}\spadcommand{1/x\free{x }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch28} +\begin{paste}{ugIntroNumbersPageFull28}{ugIntroNumbersPageEmpty28} +\pastebutton{ugIntroNumbersPageFull28}{\hidepaste} +\tab{5}\spadcommand{y : IntegerMod 6 := 5\bound{y }} +\indentrel{3}\begin{verbatim} + (28) 5 + Type: IntegerMod 6 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty28} +\begin{paste}{ugIntroNumbersPageEmpty28}{ugIntroNumbersPagePatch28} +\pastebutton{ugIntroNumbersPageEmpty28}{\showpaste} +\tab{5}\spadcommand{y : IntegerMod 6 := 5\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch29} +\begin{paste}{ugIntroNumbersPageFull29}{ugIntroNumbersPageEmpty29} +\pastebutton{ugIntroNumbersPageFull29}{\hidepaste} +\tab{5}\spadcommand{y**3\free{y }} +\indentrel{3}\begin{verbatim} + (29) 5 + Type: IntegerMod 6 +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty29} +\begin{paste}{ugIntroNumbersPageEmpty29}{ugIntroNumbersPagePatch29} +\pastebutton{ugIntroNumbersPageEmpty29}{\showpaste} +\tab{5}\spadcommand{y**3\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch30} +\begin{paste}{ugIntroNumbersPageFull30}{ugIntroNumbersPageEmpty30} +\pastebutton{ugIntroNumbersPageFull30}{\hidepaste} +\tab{5}\spadcommand{1/y\free{y }} +\indentrel{3}\begin{verbatim} +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty30} +\begin{paste}{ugIntroNumbersPageEmpty30}{ugIntroNumbersPagePatch30} +\pastebutton{ugIntroNumbersPageEmpty30}{\showpaste} +\tab{5}\spadcommand{1/y\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch31} +\begin{paste}{ugIntroNumbersPageFull31}{ugIntroNumbersPageEmpty31} +\pastebutton{ugIntroNumbersPageFull31}{\hidepaste} +\tab{5}\spadcommand{a := rootOf(a**5 + a**3 + a**2 + 3,a)\bound{a }} +\indentrel{3}\begin{verbatim} + (30) a + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty31} +\begin{paste}{ugIntroNumbersPageEmpty31}{ugIntroNumbersPagePatch31} +\pastebutton{ugIntroNumbersPageEmpty31}{\showpaste} +\tab{5}\spadcommand{a := rootOf(a**5 + a**3 + a**2 + 3,a)\bound{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch32} +\begin{paste}{ugIntroNumbersPageFull32}{ugIntroNumbersPageEmpty32} +\pastebutton{ugIntroNumbersPageFull32}{\hidepaste} +\tab{5}\spadcommand{(a + 1)**10\free{a }} +\indentrel{3}\begin{verbatim} + 4 3 2 + (31) - 85a - 264a - 378a - 458a - 287 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty32} +\begin{paste}{ugIntroNumbersPageEmpty32}{ugIntroNumbersPagePatch32} +\pastebutton{ugIntroNumbersPageEmpty32}{\showpaste} +\tab{5}\spadcommand{(a + 1)**10\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch33} +\begin{paste}{ugIntroNumbersPageFull33}{ugIntroNumbersPageEmpty33} +\pastebutton{ugIntroNumbersPageFull33}{\hidepaste} +\tab{5}\spadcommand{b := rootOf(b**4 + a,b)\bound{b }\free{a }} +\indentrel{3}\begin{verbatim} + (32) b + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty33} +\begin{paste}{ugIntroNumbersPageEmpty33}{ugIntroNumbersPagePatch33} +\pastebutton{ugIntroNumbersPageEmpty33}{\showpaste} +\tab{5}\spadcommand{b := rootOf(b**4 + a,b)\bound{b }\free{a }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch34} +\begin{paste}{ugIntroNumbersPageFull34}{ugIntroNumbersPageEmpty34} +\pastebutton{ugIntroNumbersPageFull34}{\hidepaste} +\tab{5}\spadcommand{2/(b - 1)\free{b }\bound{check }} +\indentrel{3}\begin{verbatim} + 2 + (33) 컴컴� + b - 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty34} +\begin{paste}{ugIntroNumbersPageEmpty34}{ugIntroNumbersPagePatch34} +\pastebutton{ugIntroNumbersPageEmpty34}{\showpaste} +\tab{5}\spadcommand{2/(b - 1)\free{b }\bound{check }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch35} +\begin{paste}{ugIntroNumbersPageFull35}{ugIntroNumbersPageEmpty35} +\pastebutton{ugIntroNumbersPageFull35}{\hidepaste} +\tab{5}\spadcommand{ratDenom(\%)\free{check }\bound{check1 }} +\indentrel{3}\begin{verbatim} + (34) + 4 3 2 3 4 3 2 2 + (a - a + 2a - a + 1)b + (a - a + 2a - a + 1)b + + + 4 3 2 4 3 2 + (a - a + 2a - a + 1)b + a - a + 2a - a + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty35} +\begin{paste}{ugIntroNumbersPageEmpty35}{ugIntroNumbersPagePatch35} +\pastebutton{ugIntroNumbersPageEmpty35}{\showpaste} +\tab{5}\spadcommand{ratDenom(\%)\free{check }\bound{check1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch36} +\begin{paste}{ugIntroNumbersPageFull36}{ugIntroNumbersPageEmpty36} +\pastebutton{ugIntroNumbersPageFull36}{\hidepaste} +\tab{5}\spadcommand{2/\%+1\free{check1 }\bound{check2 }} +\indentrel{3}\begin{verbatim} + (35) + 4 3 2 3 + (a - a + 2a - a + 1)b + + + 4 3 2 2 + (a - a + 2a - a + 1)b + + + 4 3 2 4 3 2 + (a - a + 2a - a + 1)b + a - a + 2a - a + 3 + / + 4 3 2 3 + (a - a + 2a - a + 1)b + + + 4 3 2 2 + (a - a + 2a - a + 1)b + + + 4 3 2 4 3 2 + (a - a + 2a - a + 1)b + a - a + 2a - a + 1 + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty36} +\begin{paste}{ugIntroNumbersPageEmpty36}{ugIntroNumbersPagePatch36} +\pastebutton{ugIntroNumbersPageEmpty36}{\showpaste} +\tab{5}\spadcommand{2/\%+1\free{check1 }\bound{check2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch37} +\begin{paste}{ugIntroNumbersPageFull37}{ugIntroNumbersPageEmpty37} +\pastebutton{ugIntroNumbersPageFull37}{\hidepaste} +\tab{5}\spadcommand{ratDenom(\%)\free{check2 }} +\indentrel{3}\begin{verbatim} + (36) b + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty37} +\begin{paste}{ugIntroNumbersPageEmpty37}{ugIntroNumbersPagePatch37} +\pastebutton{ugIntroNumbersPageEmpty37}{\showpaste} +\tab{5}\spadcommand{ratDenom(\%)\free{check2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPagePatch38} +\begin{paste}{ugIntroNumbersPageFull38}{ugIntroNumbersPageEmpty38} +\pastebutton{ugIntroNumbersPageFull38}{\hidepaste} +\tab{5}\spadcommand{q:=quatern(1,2,3,4)*quatern(5,6,7,8) - quatern(5,6,7,8)*quatern(1,2,3,4)} +\indentrel{3}\begin{verbatim} + (37) - 8i + 16j - 8k + Type: Quaternion Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroNumbersPageEmpty38} +\begin{paste}{ugIntroNumbersPageEmpty38}{ugIntroNumbersPagePatch38} +\pastebutton{ugIntroNumbersPageEmpty38}{\showpaste} +\tab{5}\spadcommand{q:=quatern(1,2,3,4)*quatern(5,6,7,8) - quatern(5,6,7,8)*quatern(1,2,3,4)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch1} +\begin{paste}{ugIntroDiffEqnsPageFull1}{ugIntroDiffEqnsPageEmpty1} +\pastebutton{ugIntroDiffEqnsPageFull1}{\hidepaste} +\tab{5}\spadcommand{y := operator 'y\bound{y }} +\indentrel{3}\begin{verbatim} + (1) y + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty1} +\begin{paste}{ugIntroDiffEqnsPageEmpty1}{ugIntroDiffEqnsPagePatch1} +\pastebutton{ugIntroDiffEqnsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{y := operator 'y\bound{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch2} +\begin{paste}{ugIntroDiffEqnsPageFull2}{ugIntroDiffEqnsPageEmpty2} +\pastebutton{ugIntroDiffEqnsPageFull2}{\hidepaste} +\tab{5}\spadcommand{deq := x**3 * D(y x, x, 3) + x**2 * D(y x, x, 2) - 2 * x * D(y x, x) + 2 * y x = 2 * x**4\bound{e3 }\free{y }} +\indentrel{3}\begin{verbatim} + 3 ,,, 2 ,, , 4 + (2) x y (x) + x y (x) - 2xy (x) + 2y(x)= 2x + + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty2} +\begin{paste}{ugIntroDiffEqnsPageEmpty2}{ugIntroDiffEqnsPagePatch2} +\pastebutton{ugIntroDiffEqnsPageEmpty2}{\showpaste} +\tab{5}\spadcommand{deq := x**3 * D(y x, x, 3) + x**2 * D(y x, x, 2) - 2 * x * D(y x, x) + 2 * y x = 2 * x**4\bound{e3 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch3} +\begin{paste}{ugIntroDiffEqnsPageFull3}{ugIntroDiffEqnsPageEmpty3} +\pastebutton{ugIntroDiffEqnsPageFull3}{\hidepaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e3 }\free{y }} +\indentrel{3}\begin{verbatim} + (3) + 5 3 2 + x - 10x + 20x + 4 + [particular= 컴컴컴컴컴컴컴컴컴컴, + 15x + 3 2 3 3 2 + 2x - 3x + 1 x - 1 x - 3x - 1 + basis= [컴컴컴컴컴컴�,컴컴컴,컴컴컴컴컴컴]] + x x x +Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty3} +\begin{paste}{ugIntroDiffEqnsPageEmpty3}{ugIntroDiffEqnsPagePatch3} +\pastebutton{ugIntroDiffEqnsPageEmpty3}{\showpaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e3 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch4} +\begin{paste}{ugIntroDiffEqnsPageFull4}{ugIntroDiffEqnsPageEmpty4} +\pastebutton{ugIntroDiffEqnsPageFull4}{\hidepaste} +\tab{5}\spadcommand{deq := (x**2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0\bound{e5 }\free{y }} +\indentrel{3}\begin{verbatim} + 2 ,, , + (4) (x + 1)y (x) + 3xy (x) + y(x)= 0 + + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty4} +\begin{paste}{ugIntroDiffEqnsPageEmpty4}{ugIntroDiffEqnsPagePatch4} +\pastebutton{ugIntroDiffEqnsPageEmpty4}{\showpaste} +\tab{5}\spadcommand{deq := (x**2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0\bound{e5 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch5} +\begin{paste}{ugIntroDiffEqnsPageFull5}{ugIntroDiffEqnsPageEmpty5} +\pastebutton{ugIntroDiffEqnsPageFull5}{\hidepaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e5 }\free{y }} +\indentrel{3}\begin{verbatim} + (5) + 旼컴컴커 + � 2 + 1 log(\퀈 + 1 - x) + [particular= 0,basis= [컴컴컴컴�,컴컴컴컴컴컴컴컴컴]] + 旼컴컴커 旼컴컴커 + � 2 � 2 + \퀈 + 1 \퀈 + 1 +Type: Union(Record(particular: Expression Integer,basis: List Expression Integer),...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty5} +\begin{paste}{ugIntroDiffEqnsPageEmpty5}{ugIntroDiffEqnsPagePatch5} +\pastebutton{ugIntroDiffEqnsPageEmpty5}{\showpaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{e5 }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch6} +\begin{paste}{ugIntroDiffEqnsPageFull6}{ugIntroDiffEqnsPageEmpty6} +\pastebutton{ugIntroDiffEqnsPageFull6}{\hidepaste} +\tab{5}\spadcommand{eq := 2*x**3 * D(y x,x,2) + 3*x**2 * D(y x,x) - 2 * y x\bound{eq }\free{y }} +\indentrel{3}\begin{verbatim} + 3 ,, 2 , + (6) 2x y (x) + 3x y (x) - 2y(x) + + Type: Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty6} +\begin{paste}{ugIntroDiffEqnsPageEmpty6}{ugIntroDiffEqnsPagePatch6} +\pastebutton{ugIntroDiffEqnsPageEmpty6}{\showpaste} +\tab{5}\spadcommand{eq := 2*x**3 * D(y x,x,2) + 3*x**2 * D(y x,x) - 2 * y x\bound{eq }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch7} +\begin{paste}{ugIntroDiffEqnsPageFull7}{ugIntroDiffEqnsPageEmpty7} +\pastebutton{ugIntroDiffEqnsPageFull7}{\hidepaste} +\tab{5}\spadcommand{solve(eq,y,x).basis\free{eq }} +\indentrel{3}\begin{verbatim} + 2 2 + - 컴컴 컴컴 + 旼� 旼� + \퀈 \퀈 + (7) [%e ,%e ] + Type: List Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty7} +\begin{paste}{ugIntroDiffEqnsPageEmpty7}{ugIntroDiffEqnsPagePatch7} +\pastebutton{ugIntroDiffEqnsPageEmpty7}{\showpaste} +\tab{5}\spadcommand{solve(eq,y,x).basis\free{eq }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch8} +\begin{paste}{ugIntroDiffEqnsPageFull8}{ugIntroDiffEqnsPageEmpty8} +\pastebutton{ugIntroDiffEqnsPageFull8}{\hidepaste} +\tab{5}\spadcommand{deq := D(y x, x) = y(x) / (x + y(x) * log y x)\bound{deqi }\free{y }} +\indentrel{3}\begin{verbatim} + , y(x) + (8) y (x)= 컴컴컴컴컴컴컴컴� + y(x)log(y(x)) + x + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty8} +\begin{paste}{ugIntroDiffEqnsPageEmpty8}{ugIntroDiffEqnsPagePatch8} +\pastebutton{ugIntroDiffEqnsPageEmpty8}{\showpaste} +\tab{5}\spadcommand{deq := D(y x, x) = y(x) / (x + y(x) * log y x)\bound{deqi }\free{y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch9} +\begin{paste}{ugIntroDiffEqnsPageFull9}{ugIntroDiffEqnsPageEmpty9} +\pastebutton{ugIntroDiffEqnsPageFull9}{\hidepaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{deqi y }} +\indentrel{3}\begin{verbatim} + 2 + y(x)log(y(x)) - 2x + (9) 컴컴컴컴컴컴컴컴컴� + 2y(x) + Type: Union(Expression Integer,...) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty9} +\begin{paste}{ugIntroDiffEqnsPageEmpty9}{ugIntroDiffEqnsPagePatch9} +\pastebutton{ugIntroDiffEqnsPageEmpty9}{\showpaste} +\tab{5}\spadcommand{solve(deq, y, x)\free{deqi y }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch10} +\begin{paste}{ugIntroDiffEqnsPageFull10}{ugIntroDiffEqnsPageEmpty10} +\pastebutton{ugIntroDiffEqnsPageFull10}{\hidepaste} +\tab{5}\spadcommand{x := operator 'x\bound{x }} +\indentrel{3}\begin{verbatim} + (10) x + Type: BasicOperator +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty10} +\begin{paste}{ugIntroDiffEqnsPageEmpty10}{ugIntroDiffEqnsPagePatch10} +\pastebutton{ugIntroDiffEqnsPageEmpty10}{\showpaste} +\tab{5}\spadcommand{x := operator 'x\bound{x }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch11} +\begin{paste}{ugIntroDiffEqnsPageFull11}{ugIntroDiffEqnsPageEmpty11} +\pastebutton{ugIntroDiffEqnsPageFull11}{\hidepaste} +\tab{5}\spadcommand{eq1 := D(x(t), t) = 1 + x(t)**2\free{x }\free{y }\bound{eq1 }} +\indentrel{3}\begin{verbatim} + , 2 + (11) x (t)= x(t) + 1 + + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty11} +\begin{paste}{ugIntroDiffEqnsPageEmpty11}{ugIntroDiffEqnsPagePatch11} +\pastebutton{ugIntroDiffEqnsPageEmpty11}{\showpaste} +\tab{5}\spadcommand{eq1 := D(x(t), t) = 1 + x(t)**2\free{x }\free{y }\bound{eq1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch12} +\begin{paste}{ugIntroDiffEqnsPageFull12}{ugIntroDiffEqnsPageEmpty12} +\pastebutton{ugIntroDiffEqnsPageFull12}{\hidepaste} +\tab{5}\spadcommand{eq2 := D(y(t), t) = x(t) * y(t)\free{x }\free{y }\bound{eq2 }} +\indentrel{3}\begin{verbatim} + , + (12) y (t)= x(t)y(t) + + Type: Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty12} +\begin{paste}{ugIntroDiffEqnsPageEmpty12}{ugIntroDiffEqnsPagePatch12} +\pastebutton{ugIntroDiffEqnsPageEmpty12}{\showpaste} +\tab{5}\spadcommand{eq2 := D(y(t), t) = x(t) * y(t)\free{x }\free{y }\bound{eq2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPagePatch13} +\begin{paste}{ugIntroDiffEqnsPageFull13}{ugIntroDiffEqnsPageEmpty13} +\pastebutton{ugIntroDiffEqnsPageFull13}{\hidepaste} +\tab{5}\spadcommand{seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])\free{x }\free{y }\free{eq1 }\free{eq2 }} +\indentrel{3}\begin{verbatim} + (13) + 1 3 2 5 17 7 62 9 11 + [t + � t + 컴 t + 컴� t + 컴컴 t + O(t ), + 3 15 315 2835 + + 1 2 5 4 61 6 277 8 50521 10 + 1 + � t + 컴 t + 컴� t + 컴컴 t + 컴컴컴� t + 2 24 720 8064 3628800 + + + 11 + O(t ) + ] +Type: List UnivariateTaylorSeries(Expression Integer,t,0) +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroDiffEqnsPageEmpty13} +\begin{paste}{ugIntroDiffEqnsPageEmpty13}{ugIntroDiffEqnsPagePatch13} +\pastebutton{ugIntroDiffEqnsPageEmpty13}{\showpaste} +\tab{5}\spadcommand{seriesSolve([eq2, eq1], [x, y], t = 0, [y(0) = 1, x(0) = 0])\free{x }\free{y }\free{eq1 }\free{eq2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroGraphicsPagePatch1} +\begin{paste}{ugIntroGraphicsPageFull1}{ugIntroGraphicsPageEmpty1} +\pastebutton{ugIntroGraphicsPageFull1}{\hidepaste} +\tab{5}\spadgraph{draw(cos(5*t/8), t=0..16*\%pi, coordinates==polar)} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/ugIntroGraphicsPage1.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/ugIntroGraphicsPage1}} +\end{paste}\end{patch} + +\begin{patch}{ugIntroGraphicsPageEmpty1} +\begin{paste}{ugIntroGraphicsPageEmpty1}{ugIntroGraphicsPagePatch1} +\pastebutton{ugIntroGraphicsPageEmpty1}{\showpaste} +\tab{5}\spadgraph{draw(cos(5*t/8), t=0..16*\%pi, coordinates==polar)} +\end{paste}\end{patch} + +\begin{patch}{ugIntroGraphicsPagePatch2} +\begin{paste}{ugIntroGraphicsPageFull2}{ugIntroGraphicsPageEmpty2} +\pastebutton{ugIntroGraphicsPageFull2}{\hidepaste} +\tab{5}\spadgraph{draw((x,y) +-> real atan complex(x,y), -\%pi..\%pi, -\%pi..\%pi, colorFunction == (x,y) +-> argument atan complex(x,y))} +\center{\unixcommand{\inputimage{\env{AXIOM}/doc/viewports/ugIntroGraphicsPage2.VIEW/image}}{viewAlone\space{1} \env{AXIOM}/doc/viewports/ugIntroGraphicsPage2}} +\end{paste}\end{patch} + +\begin{patch}{ugIntroGraphicsPageEmpty2} +\begin{paste}{ugIntroGraphicsPageEmpty2}{ugIntroGraphicsPagePatch2} +\pastebutton{ugIntroGraphicsPageEmpty2}{\showpaste} +\tab{5}\spadgraph{draw((x,y) +-> real atan complex(x,y), -\%pi..\%pi, -\%pi..\%pi, colorFunction == (x,y) +-> argument atan complex(x,y))} +\end{paste}\end{patch} + +\begin{patch}{ugIntroCommentsPagePatch1} +\begin{paste}{ugIntroCommentsPageFull1}{ugIntroCommentsPageEmpty1} +\pastebutton{ugIntroCommentsPageFull1}{\hidepaste} +\tab{5}\spadcommand{2 + 3 -- this is rather simple, no?} +\indentrel{3}\begin{verbatim} + (1) 5 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroCommentsPageEmpty1} +\begin{paste}{ugIntroCommentsPageEmpty1}{ugIntroCommentsPagePatch1} +\pastebutton{ugIntroCommentsPageEmpty1}{\showpaste} +\tab{5}\spadcommand{2 + 3 -- this is rather simple, no?} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch1} +\begin{paste}{ugIntroSolutionPageFull1}{ugIntroSolutionPageEmpty1} +\pastebutton{ugIntroSolutionPageFull1}{\hidepaste} +\tab{5}\spadcommand{S(t) == [x**2-2*y**2 - t,x*y-y-5*x + 5]\bound{S1 }} +\indentrel{3}\begin{verbatim} + Type: Void +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty1} +\begin{paste}{ugIntroSolutionPageEmpty1}{ugIntroSolutionPagePatch1} +\pastebutton{ugIntroSolutionPageEmpty1}{\showpaste} +\tab{5}\spadcommand{S(t) == [x**2-2*y**2 - t,x*y-y-5*x + 5]\bound{S1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch2} +\begin{paste}{ugIntroSolutionPageFull2}{ugIntroSolutionPageEmpty2} +\pastebutton{ugIntroSolutionPageFull2}{\hidepaste} +\tab{5}\spadcommand{solve(S(19),1/10**20)\free{S1 }} +\indentrel{3}\begin{verbatim} + (2) + 2451682632253093442511 + [[y= 5,x= - 컴컴컴컴컴컴컴컴컴컴컴], + 295147905179352825856 + 2451682632253093442511 + [y= 5,x= 컴컴컴컴컴컴컴컴컴컴컴]] + 295147905179352825856 + Type: List List Equation Polynomial Fraction Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty2} +\begin{paste}{ugIntroSolutionPageEmpty2}{ugIntroSolutionPagePatch2} +\pastebutton{ugIntroSolutionPageEmpty2}{\showpaste} +\tab{5}\spadcommand{solve(S(19),1/10**20)\free{S1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch3} +\begin{paste}{ugIntroSolutionPageFull3}{ugIntroSolutionPageEmpty3} +\pastebutton{ugIntroSolutionPageFull3}{\hidepaste} +\tab{5}\spadcommand{complexSolve(S(19),10.e-20)\free{S1 }} +\indentrel{3}\begin{verbatim} + (3) + [ + [y= 5.0, + x= 8.3066238629 1807485256 1669055295 290320373] + , + + [y= 5.0, + x= - 8.3066238629 1807485256 1669055295 290320373] + , + [y= - 3.0 %i,x= 1.0], [y= 3.0 %i,x= 1.0]] + Type: List List Equation Polynomial Complex Float +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty3} +\begin{paste}{ugIntroSolutionPageEmpty3}{ugIntroSolutionPagePatch3} +\pastebutton{ugIntroSolutionPageEmpty3}{\showpaste} +\tab{5}\spadcommand{complexSolve(S(19),10.e-20)\free{S1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch4} +\begin{paste}{ugIntroSolutionPageFull4}{ugIntroSolutionPageEmpty4} +\pastebutton{ugIntroSolutionPageFull4}{\hidepaste} +\tab{5}\spadcommand{radicalSolve(S(a),[x,y])\free{S1 }} +\indentrel{3}\begin{verbatim} + (4) + 旼컴컴커 旼컴컴커 + [[x= - \쿪 + 50 ,y= 5], [x= \쿪 + 50 ,y= 5], + 旼컴컴컴� 旼컴컴컴� + �- a + 1 �- a + 1 + [x= 1,y= 냐컴컴컴 ], [x= 1,y= - 냐컴컴컴 ]] + \� 2 \� 2 + Type: List List Equation Expression Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty4} +\begin{paste}{ugIntroSolutionPageEmpty4}{ugIntroSolutionPagePatch4} +\pastebutton{ugIntroSolutionPageEmpty4}{\showpaste} +\tab{5}\spadcommand{radicalSolve(S(a),[x,y])\free{S1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch5} +\begin{paste}{ugIntroSolutionPageFull5}{ugIntroSolutionPageEmpty5} +\pastebutton{ugIntroSolutionPageFull5}{\hidepaste} +\tab{5}\spadcommand{eqns := [x**2 - y + z,x**2*z + x**4 - b*y, y**2 *z - a - b*x]\bound{e }} +\indentrel{3}\begin{verbatim} + 2 2 4 2 + (5) [z - y + x ,x z - b y + x ,y z - b x - a] + Type: List Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty5} +\begin{paste}{ugIntroSolutionPageEmpty5}{ugIntroSolutionPagePatch5} +\pastebutton{ugIntroSolutionPageEmpty5}{\showpaste} +\tab{5}\spadcommand{eqns := [x**2 - y + z,x**2*z + x**4 - b*y, y**2 *z - a - b*x]\bound{e }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPagePatch6} +\begin{paste}{ugIntroSolutionPageFull6}{ugIntroSolutionPageEmpty6} +\pastebutton{ugIntroSolutionPageFull6}{\hidepaste} +\tab{5}\spadcommand{solve(eqns,[x,y,z])\free{e }} +\indentrel{3}\begin{verbatim} + (6) + 2 + a a + [[x= - �,y= 0,z= - 컴], + b 2 + b + + 3 2 2 + z + 2b z + b z - a + [x= 컴컴컴컴컴컴컴컴컴컴, y= z + b, + b + + 6 5 2 4 3 3 4 2 + z + 4b z + 6b z + (4b - 2a)z + (b - 4a b)z + + + 2 3 2 + - 2a b z - b + a + = + 0 + ] + ] + Type: List List Equation Fraction Polynomial Integer +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroSolutionPageEmpty6} +\begin{paste}{ugIntroSolutionPageEmpty6}{ugIntroSolutionPagePatch6} +\pastebutton{ugIntroSolutionPageEmpty6}{\showpaste} +\tab{5}\spadcommand{solve(eqns,[x,y,z])\free{e }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPagePatch1} +\begin{paste}{ugIntroPreviousPageFull1}{ugIntroPreviousPageEmpty1} +\pastebutton{ugIntroPreviousPageFull1}{\hidepaste} +\tab{5}\spadcommand{10 ** 10\bound{prev }} +\indentrel{3}\begin{verbatim} + (1) 10000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPageEmpty1} +\begin{paste}{ugIntroPreviousPageEmpty1}{ugIntroPreviousPagePatch1} +\pastebutton{ugIntroPreviousPageEmpty1}{\showpaste} +\tab{5}\spadcommand{10 ** 10\bound{prev }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPagePatch2} +\begin{paste}{ugIntroPreviousPageFull2}{ugIntroPreviousPageEmpty2} +\pastebutton{ugIntroPreviousPageFull2}{\hidepaste} +\tab{5}\spadcommand{\% - 1\free{prev }\bound{prev1 }} +\indentrel{3}\begin{verbatim} + (2) 9999999999 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPageEmpty2} +\begin{paste}{ugIntroPreviousPageEmpty2}{ugIntroPreviousPagePatch2} +\pastebutton{ugIntroPreviousPageEmpty2}{\showpaste} +\tab{5}\spadcommand{\% - 1\free{prev }\bound{prev1 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPagePatch3} +\begin{paste}{ugIntroPreviousPageFull3}{ugIntroPreviousPageEmpty3} +\pastebutton{ugIntroPreviousPageFull3}{\hidepaste} +\tab{5}\spadcommand{\%\%(-1)\free{prev1 }\bound{prev2 }} +\indentrel{3}\begin{verbatim} + (3) 9999999999 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPageEmpty3} +\begin{paste}{ugIntroPreviousPageEmpty3}{ugIntroPreviousPagePatch3} +\pastebutton{ugIntroPreviousPageEmpty3}{\showpaste} +\tab{5}\spadcommand{\%\%(-1)\free{prev1 }\bound{prev2 }} +\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPagePatch4} +\begin{paste}{ugIntroPreviousPageFull4}{ugIntroPreviousPageEmpty4} +\pastebutton{ugIntroPreviousPageFull4}{\hidepaste} +\tab{5}\spadcommand{\%\%(1)\free{prev2 }} +\indentrel{3}\begin{verbatim} + (4) 10000000000 + Type: PositiveInteger +\end{verbatim} +\indentrel{-3}\end{paste}\end{patch} + +\begin{patch}{ugIntroPreviousPageEmpty4} +\begin{paste}{ugIntroPreviousPageEmpty4}{ugIntroPreviousPagePatch4} +\pastebutton{ugIntroPreviousPageEmpty4}{\showpaste} +\tab{5}\spadcommand{\%\%(1)\free{prev2 }} +\end{paste}\end{patch} + -- cgit v1.2.3