open-axiom repository from github
\begin{patch}{ExpressionXmpPagePatch1}
\begin{paste}{ExpressionXmpPageFull1}{ExpressionXmpPageEmpty1}
\pastebutton{ExpressionXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{sin(x) + 3*cos(x)**2}
\indentrel{3}\begin{verbatim}
2
(1) sin(x) + 3cos(x)
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty1}
\begin{paste}{ExpressionXmpPageEmpty1}{ExpressionXmpPagePatch1}
\pastebutton{ExpressionXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{sin(x) + 3*cos(x)**2}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch2}
\begin{paste}{ExpressionXmpPageFull2}{ExpressionXmpPageEmpty2}
\pastebutton{ExpressionXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{tan(x) - 3.45*x}
\indentrel{3}\begin{verbatim}
(2) tan(x) - 3.45 x
Type: Expression Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty2}
\begin{paste}{ExpressionXmpPageEmpty2}{ExpressionXmpPagePatch2}
\pastebutton{ExpressionXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{tan(x) - 3.45*x}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch3}
\begin{paste}{ExpressionXmpPageFull3}{ExpressionXmpPageEmpty3}
\pastebutton{ExpressionXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))}
\indentrel{3}\begin{verbatim}
(3)
�Ŀ 2 ��Ŀ �Ŀ ��Ŀ 2
- tan(\�7 ) + 2sin(\�11 )tan(\�7 ) - sin(\�11 )
�������������������������������������������������
cos(y - x) - 4
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty3}
\begin{paste}{ExpressionXmpPageEmpty3}{ExpressionXmpPagePatch3}
\pastebutton{ExpressionXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{(tan sqrt 7 - sin sqrt 11)**2 / (4 - cos(x - y))}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch4}
\begin{paste}{ExpressionXmpPageFull4}{ExpressionXmpPageEmpty4}
\pastebutton{ExpressionXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{log(exp x)@Expression(Integer)}
\indentrel{3}\begin{verbatim}
(4) x
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty4}
\begin{paste}{ExpressionXmpPageEmpty4}{ExpressionXmpPagePatch4}
\pastebutton{ExpressionXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{log(exp x)@Expression(Integer)}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch5}
\begin{paste}{ExpressionXmpPageFull5}{ExpressionXmpPageEmpty5}
\pastebutton{ExpressionXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{log(exp x)@Expression(Complex Integer)}
\indentrel{3}\begin{verbatim}
x
(5) log(%e )
Type: Expression Complex Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty5}
\begin{paste}{ExpressionXmpPageEmpty5}{ExpressionXmpPagePatch5}
\pastebutton{ExpressionXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{log(exp x)@Expression(Complex Integer)}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch6}
\begin{paste}{ExpressionXmpPageFull6}{ExpressionXmpPageEmpty6}
\pastebutton{ExpressionXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{sqrt 3 + sqrt(2 + sqrt(-5))\bound{algnum1 }}
\indentrel{3}\begin{verbatim}
����������Ŀ
� ���Ŀ �Ŀ
(6) \�\�- 5 + 2 + \�3
Type: AlgebraicNumber
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty6}
\begin{paste}{ExpressionXmpPageEmpty6}{ExpressionXmpPagePatch6}
\pastebutton{ExpressionXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{sqrt 3 + sqrt(2 + sqrt(-5))\bound{algnum1 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch7}
\begin{paste}{ExpressionXmpPageFull7}{ExpressionXmpPageEmpty7}
\pastebutton{ExpressionXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{\% :: Expression Integer\free{algnum1 }}
\indentrel{3}\begin{verbatim}
����������Ŀ
� ���Ŀ �Ŀ
(7) \�\�- 5 + 2 + \�3
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty7}
\begin{paste}{ExpressionXmpPageEmpty7}{ExpressionXmpPagePatch7}
\pastebutton{ExpressionXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{\% :: Expression Integer\free{algnum1 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch8}
\begin{paste}{ExpressionXmpPageFull8}{ExpressionXmpPageEmpty8}
\pastebutton{ExpressionXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{height mainKernel sin(x + 4)}
\indentrel{3}\begin{verbatim}
(8) 2
Type: PositiveInteger
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty8}
\begin{paste}{ExpressionXmpPageEmpty8}{ExpressionXmpPagePatch8}
\pastebutton{ExpressionXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{height mainKernel sin(x + 4)}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch9}
\begin{paste}{ExpressionXmpPageFull9}{ExpressionXmpPageEmpty9}
\pastebutton{ExpressionXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )\bound{e }}
\indentrel{3}\begin{verbatim}
2
- sin(x) + 8sin(x) - 16
(9) ������������������������
���Ŀ
2y\�- y - 1
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty9}
\begin{paste}{ExpressionXmpPageEmpty9}{ExpressionXmpPagePatch9}
\pastebutton{ExpressionXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{e := (sin(x) - 4)**2 / ( 1 - 2*y*sqrt(- y) )\bound{e }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch10}
\begin{paste}{ExpressionXmpPageFull10}{ExpressionXmpPageEmpty10}
\pastebutton{ExpressionXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{numer e\free{e }}
\indentrel{3}\begin{verbatim}
2
(10) - sin(x) + 8sin(x) - 16
Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty10}
\begin{paste}{ExpressionXmpPageEmpty10}{ExpressionXmpPagePatch10}
\pastebutton{ExpressionXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{numer e\free{e }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch11}
\begin{paste}{ExpressionXmpPageFull11}{ExpressionXmpPageEmpty11}
\pastebutton{ExpressionXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{denom e\free{e }}
\indentrel{3}\begin{verbatim}
���Ŀ
(11) 2y\�- y - 1
Type: SparseMultivariatePolynomial(Integer,Kernel Expression Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty11}
\begin{paste}{ExpressionXmpPageEmpty11}{ExpressionXmpPagePatch11}
\pastebutton{ExpressionXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{denom e\free{e }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch12}
\begin{paste}{ExpressionXmpPageFull12}{ExpressionXmpPageEmpty12}
\pastebutton{ExpressionXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{D(e, x)\free{e }}
\indentrel{3}\begin{verbatim}
(12)
���Ŀ
(4y cos(x)sin(x) - 16y cos(x))\�- y
+
- 2cos(x)sin(x) + 8cos(x)
/
���Ŀ 3
4y\�- y + 4y - 1
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty12}
\begin{paste}{ExpressionXmpPageEmpty12}{ExpressionXmpPagePatch12}
\pastebutton{ExpressionXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{D(e, x)\free{e }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch13}
\begin{paste}{ExpressionXmpPageFull13}{ExpressionXmpPageEmpty13}
\pastebutton{ExpressionXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{D(e, [x, y], [1, 2])\free{e }}
\indentrel{3}\begin{verbatim}
(13)
7 4
(- 2304y + 960y )cos(x)sin(x)
+
7 4
(9216y - 3840y )cos(x)
*
���Ŀ
\�- y
+
9 6 3
(- 960y + 2160y - 180y - 3)cos(x)sin(x)
+
9 6 3
(3840y - 8640y + 720y + 12)cos(x)
/
12 9 6 3 ���Ŀ
(256y - 1792y + 1120y - 112y + 1)\�- y
+
11 8 5 2
- 1024y + 1792y - 448y + 16y
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty13}
\begin{paste}{ExpressionXmpPageEmpty13}{ExpressionXmpPagePatch13}
\pastebutton{ExpressionXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{D(e, [x, y], [1, 2])\free{e }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch14}
\begin{paste}{ExpressionXmpPageFull14}{ExpressionXmpPageEmpty14}
\pastebutton{ExpressionXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{complexNumeric(cos(2 - 3*\%i))}
\indentrel{3}\begin{verbatim}
(14)
- 4.1896256909 688072301 + 9.1092278937 55336598 %i
Type: Complex Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty14}
\begin{paste}{ExpressionXmpPageEmpty14}{ExpressionXmpPagePatch14}
\pastebutton{ExpressionXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{complexNumeric(cos(2 - 3*\%i))}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch15}
\begin{paste}{ExpressionXmpPageFull15}{ExpressionXmpPageEmpty15}
\pastebutton{ExpressionXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{numeric(tan 3.8)}
\indentrel{3}\begin{verbatim}
(15) 0.7735560905 0312607286
Type: Float
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty15}
\begin{paste}{ExpressionXmpPageEmpty15}{ExpressionXmpPagePatch15}
\pastebutton{ExpressionXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{numeric(tan 3.8)}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch16}
\begin{paste}{ExpressionXmpPageFull16}{ExpressionXmpPageEmpty16}
\pastebutton{ExpressionXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{e2 := cos(x**2 - y + 3)\bound{e2 }}
\indentrel{3}\begin{verbatim}
2
(16) cos(y - x - 3)
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty16}
\begin{paste}{ExpressionXmpPageEmpty16}{ExpressionXmpPagePatch16}
\pastebutton{ExpressionXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{e2 := cos(x**2 - y + 3)\bound{e2 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch17}
\begin{paste}{ExpressionXmpPageFull17}{ExpressionXmpPageEmpty17}
\pastebutton{ExpressionXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{e3 := asin(e2) - \%pi/2\free{e2 }\bound{e3 }}
\indentrel{3}\begin{verbatim}
2
(17) - y + x + 3
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty17}
\begin{paste}{ExpressionXmpPageEmpty17}{ExpressionXmpPagePatch17}
\pastebutton{ExpressionXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{e3 := asin(e2) - \%pi/2\free{e2 }\bound{e3 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch18}
\begin{paste}{ExpressionXmpPageFull18}{ExpressionXmpPageEmpty18}
\pastebutton{ExpressionXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{e3 :: Polynomial Integer\free{e3 }}
\indentrel{3}\begin{verbatim}
2
(18) - y + x + 3
Type: Polynomial Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty18}
\begin{paste}{ExpressionXmpPageEmpty18}{ExpressionXmpPagePatch18}
\pastebutton{ExpressionXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{e3 :: Polynomial Integer\free{e3 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch19}
\begin{paste}{ExpressionXmpPageFull19}{ExpressionXmpPageEmpty19}
\pastebutton{ExpressionXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{e3 :: DMP([x, y], Integer)\free{e3 }}
\indentrel{3}\begin{verbatim}
2
(19) x - y + 3
Type: DistributedMultivariatePolynomial([x,y],Integer)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty19}
\begin{paste}{ExpressionXmpPageEmpty19}{ExpressionXmpPagePatch19}
\pastebutton{ExpressionXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{e3 :: DMP([x, y], Integer)\free{e3 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch20}
\begin{paste}{ExpressionXmpPageFull20}{ExpressionXmpPageEmpty20}
\pastebutton{ExpressionXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{sin \%pi}
\indentrel{3}\begin{verbatim}
(20) 0
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty20}
\begin{paste}{ExpressionXmpPageEmpty20}{ExpressionXmpPagePatch20}
\pastebutton{ExpressionXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{sin \%pi}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch21}
\begin{paste}{ExpressionXmpPageFull21}{ExpressionXmpPageEmpty21}
\pastebutton{ExpressionXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{cos(\%pi / 4)}
\indentrel{3}\begin{verbatim}
�Ŀ
\�2
(21) ����
2
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty21}
\begin{paste}{ExpressionXmpPageEmpty21}{ExpressionXmpPagePatch21}
\pastebutton{ExpressionXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{cos(\%pi / 4)}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch22}
\begin{paste}{ExpressionXmpPageFull22}{ExpressionXmpPageEmpty22}
\pastebutton{ExpressionXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1\bound{tan6 }}
\indentrel{3}\begin{verbatim}
6 4 2
(22) tan(x) + 3tan(x) + 3tan(x) + 1
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty22}
\begin{paste}{ExpressionXmpPageEmpty22}{ExpressionXmpPagePatch22}
\pastebutton{ExpressionXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{tan(x)**6 + 3*tan(x)**4 + 3*tan(x)**2 + 1\bound{tan6 }}
\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPagePatch23}
\begin{paste}{ExpressionXmpPageFull23}{ExpressionXmpPageEmpty23}
\pastebutton{ExpressionXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{simplify \%\free{tan6 }}
\indentrel{3}\begin{verbatim}
1
(23) �������
6
cos(x)
Type: Expression Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{ExpressionXmpPageEmpty23}
\begin{paste}{ExpressionXmpPageEmpty23}{ExpressionXmpPagePatch23}
\pastebutton{ExpressionXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{simplify \%\free{tan6 }}
\end{paste}\end{patch}