In [1]:

    

)version


    

    






 
Value = "Wednesday August 5, 2009 at 19:05:50 "

In [2]:

    

(1+x)^5


    

    






 
         5     4      3      2
   (1)  x  + 5x  + 10x  + 10x  + 5x + 1
                                                     Type: Polynomial Integer

In [3]:

    

)set output tex on


    

In [4]:

    

(1+x)^5


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{x \sp 5}+{5 \  {x \sp 4}}+{{10} \  {x \sp 3}}+{{10} \  {x \sp 2}}+{5 \  x}+1 
\leqno(2)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\
$$

In [5]:

    

(1+x^2)^2
(1+x^2)^3
(1+x^2)^4
(1+x^2)^5
binomial(7,3)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{x \sp 4}+{2 \  {x \sp 2}}+1 
\leqno(3)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\

{\color{black} \normalsize 
{x \sp 6}+{3 \  {x \sp 4}}+{3 \  {x \sp 2}}+1 
\leqno(4)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\

{\color{black} \normalsize 
{x \sp 8}+{4 \  {x \sp 6}}+{6 \  {x \sp 4}}+{4 \  {x \sp 2}}+1 
\leqno(5)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\

{\color{black} \normalsize 
{x \sp {10}}+{5 \  {x \sp 8}}+{{10} \  {x \sp 6}}+{{10} \  {x \sp 4}}+{5 \  
{x \sp 2}}+1 
\leqno(6)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\

{\color{black} \normalsize 
35 
\leqno(7)
} \\[0.9ex] {\color{blue} \scriptsize \text{PositiveInteger}} \\
$$

In [6]:

    

%


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
35 
\leqno(8)
} \\[0.9ex] {\color{blue} \scriptsize \text{PositiveInteger}} \\
$$

In [7]:

    

a+b+c


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
c+b+a 
\leqno(9)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\
$$

In [8]:

    

%^4


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{c \sp 4}+{{\left( {4 \  b}+{4 \  a} 
\right)}
\  {c \sp 3}}+{{\left( {6 \  {b \sp 2}}+{{12} \  a \  b}+{6 \  {a \sp 2}} 
\right)}
\  {c \sp 2}}+{{\left( {4 \  {b \sp 3}}+{{12} \  a \  {b \sp 2}}+{{12} \  {a 
\sp 2} \  b}+{4 \  {a \sp 3}} 
\right)}
\  c}+{b \sp 4}+{4 \  a \  {b \sp 3}}+{6 \  {a \sp 2} \  {b \sp 2}}+{4 \  {a 
\sp 3} \  b}+{a \sp 4} 
\leqno(10)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\
$$

In [9]:

    

(1+x^2)^4/(1+x^2)^5


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
1 \over {{x \sp 2}+1} 
\leqno(11)
} \\[0.9ex] {\color{blue} \scriptsize \text{Fraction Polynomial Integer}} \\
$$

In [10]:

    

integrate(exp(-x^2),x)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{{\erf 
\left(
{x} 
\right)}
\  {\sqrt {\pi}}} \over 2 
\leqno(12)
} \\[0.9ex] {\color{blue} \scriptsize \text{Union(Expression Integer}} \\
$$

In [11]:

    

continuedFraction %pi


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
3+ \zag{1}{7}+ \zag{1}{{15}}+ \zag{1}{1}+ \zag{1}{{292}}+ \zag{1}{1}+ 
\zag{1}{1}+ \zag{1}{1}+ \zag{1}{2}+ \zag{1}{1}+ \zag{1}{3}+\ldots 
\leqno(13)
} \\[0.9ex] {\color{blue} \scriptsize \text{ContinuedFraction Integer}} \\
$$

In [12]:

    

(1+x)^5


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{x \sp 5}+{5 \  {x \sp 4}}+{{10} \  {x \sp 3}}+{{10} \  {x \sp 2}}+{5 \  x}+1 
\leqno(14)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Integer}} \\
$$

In [13]:

    

continuedFraction %pi


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
3+ \zag{1}{7}+ \zag{1}{{15}}+ \zag{1}{1}+ \zag{1}{{292}}+ \zag{1}{1}+ 
\zag{1}{1}+ \zag{1}{1}+ \zag{1}{2}+ \zag{1}{1}+ \zag{1}{3}+\ldots 
\leqno(15)
} \\[0.9ex] {\color{blue} \scriptsize \text{ContinuedFraction Integer}} \\
$$

In [14]:

    

(a*x+b)/(c*y-z)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{-{a \  x} -b} \over {z -{c \  y}} 
\leqno(16)
} \\[0.9ex] {\color{blue} \scriptsize \text{Fraction Polynomial Integer}} \\
$$

In [60]:

    

)summary


    

    






  )credits      : list the people who have contributed to OpenAxiom

 )help <command> gives more information
 )quit         : exit OpenAxiom 

 )abbreviation : query, set and remove abbreviations for constructors
 )cd           : set working directory
 )clear        : remove declarations, definitions or values
 )close        : throw away an interpreter client and workspace
 )compile      : invoke constructor compiler
 )display      : display Library operations and objects in your workspace
 )edit         : edit a file
 )frame        : manage interpreter workspaces
 )history      : manage aspects of interactive session
 )library      : introduce new constructors 
 )lisp         : evaluate a LISP expression
 )read         : execute AXIOM commands from a file
 )savesystem   : save LISP image to a file
 )set          : view and set system variables
 )show         : show constructor information
 )spool        : log input and output to a file
 )synonym      : define an abbreviation for system commands
 )system       : issue shell commands
 )trace        : trace execution of functions
 )undo         : restore workspace to earlier state
 )what         : search for various things by name

In [16]:

    

M := matrix [[1,2,3,4],[5,6,7,8],[0,3,2,5],[5,8,3,4]] ; M


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
\begin{array}{cccc}
1 & 2 & 3 & 4 \\ 
5 & 6 & 7 & 8 \\ 
0 & 3 & 2 & 5 \\ 
5 & 8 & 3 & 4 
\end{array}
\right]
\leqno(17)
} \\[0.9ex] {\color{blue} \scriptsize \text{Matrix Integer}} \\
$$

In [17]:

    

v := vector [1,3,5,7] ; v


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
1, \: 3, \: 5, \: 7 
\right]
\leqno(18)
} \\[0.9ex] {\color{blue} \scriptsize \text{Vector PositiveInteger}} \\
$$

In [18]:

    

M^4*v


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{236970}, \: {596498}, \: {269400}, \: {491702} 
\right]
\leqno(19)
} \\[0.9ex] {\color{blue} \scriptsize \text{Vector Integer}} \\
$$

In [19]:

    

z_0 := 12+17*%i


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{12}+{{17} \  i} 
\leqno(20)
} \\[0.9ex] {\color{blue} \scriptsize \text{Complex Integer}} \\
$$

In [20]:

    

z_0^4


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
-{145439} -{{118320} \  i} 
\leqno(21)
} \\[0.9ex] {\color{blue} \scriptsize \text{Complex Integer}} \\
$$

In [21]:

    

z_1:=z_0 * (3-%i*66)
z_2:=z_0*z_1
[z_0,z_1,z_2]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{1158} -{{741} \  i} 
\leqno(22)
} \\[0.9ex] {\color{blue} \scriptsize \text{Complex Integer}} \\

{\color{black} \normalsize 
{26493}+{{10794} \  i} 
\leqno(23)
} \\[0.9ex] {\color{blue} \scriptsize \text{Complex Integer}} \\

{\color{black} \normalsize 
\left[
{{12}+{{17} \  i}}, \: {{1158} -{{741} \  i}}, \: {{26493}+{{10794} \  i}} 
\right]
\leqno(24)
} \\[0.9ex] {\color{blue} \scriptsize \text{List Complex Integer}} \\
$$

In [22]:

    

print "Hello"


    

    






    "Hello"
                                                                   Type: Void

In [23]:

    

tex(x^2+2)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
\mbox{\tt "{x \sp 2}+2"} 
\right]
\leqno(26)
} \\[0.9ex] {\color{blue} \scriptsize \text{List String}} \\
$$

In [24]:

    

-- abc


    

In [25]:

    

hello


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
hello 
\leqno(27)
} \\[0.9ex] {\color{blue} \scriptsize \text{Variable hello}} \\
$$

In [26]:

    

)logo


    

In [27]:

    

Welcome!


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
Welcome! 
\leqno(28)
} \\[0.9ex] {\color{blue} \scriptsize \text{Variable Welcome}} \\
$$

In [28]:

    

)plot


    

In [29]:

    

)logo


    

In [30]:

    

[matrix [[1,j],[-j^2,j+1]] for j in 1..3]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ 
\begin{array}{cc}
1 & 1 \\ 
-1 & 2 
\end{array}
\right]},
\: {\left[ 
\begin{array}{cc}
1 & 2 \\ 
-4 & 3 
\end{array}
\right]},
\: {\left[ 
\begin{array}{cc}
1 & 3 \\ 
-9 & 4 
\end{array}
\right]}
\right]
\leqno(29)
} \\[0.9ex] {\color{blue} \scriptsize \text{List Matrix Integer}} \\
$$

In [31]:

    

)set output tex on


    

In [32]:

    

[matrix [[1,j],[-j^2,j+1]] for j in 1..3]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ 
\begin{array}{cc}
1 & 1 \\ 
-1 & 2 
\end{array}
\right]},
\: {\left[ 
\begin{array}{cc}
1 & 2 \\ 
-4 & 3 
\end{array}
\right]},
\: {\left[ 
\begin{array}{cc}
1 & 3 \\ 
-9 & 4 
\end{array}
\right]}
\right]
\leqno(30)
} \\[0.9ex] {\color{blue} \scriptsize \text{List Matrix Integer}} \\
$$

In [33]:

    

S:= [3* x^3 + y + 1 = 0,y^2 = 4]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{{y+{3 \  {x \sp 3}}+1}=0}, \: {{y \sp 2}=4} 
\right]
\leqno(31)
} \\[0.9ex] {\color{blue} \scriptsize \text{List Equation Polynomial Integer}} \\
$$

In [34]:

    

solve (S ,1/10^30)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ {y=-2}, \: {x={{17578796712111842452 83070414507} \over 
{25353012004564588029 93406410752}}} 
\right]},
\: {\left[ {y=2}, \: {x=-1} 
\right]}
\right]
\leqno(32)
} \\[0.9ex] {\color{blue} \scriptsize \text{List List Equation Polynomial Fraction Integer}} \\
$$

In [35]:

    

radicalSolve(S)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ {y=2}, \: {x=-1} 
\right]},
\: {\left[ {y=2}, \: {x={{-{\sqrt {-3}}+1} \over 2}} 
\right]},
\: {\left[ {y=2}, \: {x={{{\sqrt {-3}}+1} \over 2}} 
\right]},
\: {\left[ {y=-2}, \: {x={1 \over {\root {3} \of {3}}}} 
\right]},
\: {\left[ {y=-2}, \: {x={{{{\sqrt {-1}} \  {\sqrt {3}}} -1} \over {2 \  
{\root {3} \of {3}}}}} 
\right]},
\: {\left[ {y=-2}, \: {x={{-{{\sqrt {-1}} \  {\sqrt {3}}} -1} \over {2 \  
{\root {3} \of {3}}}}} 
\right]}
\right]
\leqno(33)
} \\[0.9ex] {\color{blue} \scriptsize \text{List List Equation Expression Integer}} \\
$$

In [36]:

    

%%(-2)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ {y=-2}, \: {x={{17578796712111842452 83070414507} \over 
{25353012004564588029 93406410752}}} 
\right]},
\: {\left[ {y=2}, \: {x=-1} 
\right]}
\right]
\leqno(34)
} \\[0.9ex] {\color{blue} \scriptsize \text{List List Equation Polynomial Fraction Integer}} \\
$$

In [37]:

    

factor 643238070748569023720594412551704344145570763243


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{{11} \sp {13}} \  {{13} \sp {11}} \  {{17} \sp 7} \  {{19} \sp 5} \  {{23} 
\sp 3} \  {{29} \sp 2} 
\leqno(35)
} \\[0.9ex] {\color{blue} \scriptsize \text{Factored Integer}} \\
$$

In [38]:

    

roman (1992)
roman (2015)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
MCMXCII 
\leqno(36)
} \\[0.9ex] {\color{blue} \scriptsize \text{RomanNumeral}} \\

{\color{black} \normalsize 
MMXV 
\leqno(37)
} \\[0.9ex] {\color{blue} \scriptsize \text{RomanNumeral}} \\
$$

In [39]:

    

p(0) == 1
p(n) == ((2*n -1) *x*p(n -1) - (n -1) * p(n -2) )/n


    

    






                                                                    Type: Void
                                                                   Type: Void

In [43]:

    

p


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\begin{array}{l}
{p \  0 \  == \  1} \\ 
{p \  n \  == \  {{{{\left( {2 \  n} -1 
\right)}
\  x \  {p 
\left(
{{n -1}} 
\right)}}
-{{\left( n -1 
\right)}
\  {p 
\left(
{{n -2}} 
\right)}}}
\over n}} 
\end{array}
\leqno(40)
} \\[0.9ex] {\color{blue} \scriptsize \text{FunctionCalled p}} \\
$$

In [45]:

    

p(0)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
1 
\leqno(41)
} \\[0.9ex] {\color{blue} \scriptsize \text{Polynomial Fraction Integer}} \\
$$

In [51]:

    

S := [3* x^3 + y + 1 = 0,y^2 = 4]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{{y+{3 \  {x \sp 3}}+1}=0}, \: {{y \sp 2}=4} 
\right]
\leqno(46)
} \\[0.9ex] {\color{blue} \scriptsize \text{List Equation Polynomial Integer}} \\
$$

In [52]:

    

solve (S ,1/10^30)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
{\left[ {y=-2}, \: {x={{17578796712111842452 83070414507} \over 
{25353012004564588029 93406410752}}} 
\right]},
\: {\left[ {y=2}, \: {x=-1} 
\right]}
\right]
\leqno(47)
} \\[0.9ex] {\color{blue} \scriptsize \text{List List Equation Polynomial Fraction Integer}} \\
$$

In [53]:

    

matrix ([[1/( i + j - x) for i in 1..4] for j in 1..4])


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
\begin{array}{cccc}
-{1 \over {x -2}} & -{1 \over {x -3}} & -{1 \over {x -4}} & -{1 \over {x -5}} \\ 
-{1 \over {x -3}} & -{1 \over {x -4}} & -{1 \over {x -5}} & -{1 \over {x -6}} \\ 
-{1 \over {x -4}} & -{1 \over {x -5}} & -{1 \over {x -6}} & -{1 \over {x -7}} \\ 
-{1 \over {x -5}} & -{1 \over {x -6}} & -{1 \over {x -7}} & -{1 \over {x -8}} 
\end{array}
\right]
\leqno(48)
} \\[0.9ex] {\color{blue} \scriptsize \text{Matrix Fraction Polynomial Integer}} \\
$$

In [54]:

    

vm := matrix [[1 ,1 ,1] , [x,y,z], [x*x,y*y,z*z]]


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
\left[
\begin{array}{ccc}
1 & 1 & 1 \\ 
x & y & z \\ 
{x \sp 2} & {y \sp 2} & {z \sp 2} 
\end{array}
\right]
\leqno(49)
} \\[0.9ex] {\color{blue} \scriptsize \text{Matrix Polynomial Integer}} \\
$$

In [55]:

    

g := csc (a*x) / csch(b*x)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{\csc 
\left(
{{a \  x}} 
\right)}
\over {\csch 
\left(
{{b \  x}} 
\right)}
\leqno(50)
} \\[0.9ex] {\color{blue} \scriptsize \text{Expression Integer}} \\
$$

In [56]:

    

limit (g,x=0)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
b \over a 
\leqno(51)
} \\[0.9ex] {\color{blue} \scriptsize \text{Union(OrderedCompletion Expression Integer}} \\
$$

In [57]:

    

h := (1 + k/x)^x


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
{{x+k} \over x} \sp x 
\leqno(52)
} \\[0.9ex] {\color{blue} \scriptsize \text{Expression Integer}} \\
$$

In [59]:

    

limit (h,x=%plusInfinity)


    

    






\(\def\sp{^}\def\sb{_}\def\leqno(#1){}\)\(\def\erf\{\mathrm{erf}}\def\sinh{\mathrm{sinh}}\)\(\def\zag#1#2{{{ \left.{#1}\right|}\over{\left|{#2}\right.}}}\)\(\require{color}\)$$
{\color{black} \normalsize 
e \sp k 
\leqno(53)
} \\[0.9ex] {\color{blue} \scriptsize \text{Union(OrderedCompletion Expression Integer}} \\
$$

In [61]:

    

)set output


    

    






                    Current Values of  output  Variables                    

Variable     Description                                Current Value
-----------------------------------------------------------------------------
abbreviate   abbreviate type names                      off 
algebra      display output in algebraic form           On:CONSOLE 
characters   choose special output character set        plain 
fortran      create output in FORTRAN format            Off:CONSOLE 
fraction     how fractions are formatted                vertical 
length       line length of output displays             77 
openmath     create output in OpenMath style            Off:CONSOLE 
script       display output in SCRIPT formula format    Off:CONSOLE 
scripts      show subscripts,... linearly               off 
showeditor   view output of )show in editor             off 
tex          create output in TeX style                 On:CONSOLE 
mathml       create output in MathML style              Off:CONSOLE 

In [65]:

    

)copyright


    

    






 OpenAxiom is distributed under terms of the Modified BSD license.
OpenAxiom is an evolution of Axiom which  was released under this license 
as of September 3, 2002.

Copyrights remain with the original copyright holders.
Use of this material is by permission and/or license.
Individual files contain reference to these applicable copyrights.
The copyright and license statements are collected here for reference.

Portions Copyright (C) 2007- Gabriel Dos Reis
All modifications applied to the build-improvements branch of Axiom,
and to the OpenAxiom project are covered by this copyright and
the BSD-type License reproduced below.

Portions Copyright (c) 2003-2007 The Axiom Team

The Axiom Team is the collective name for the people who have
contributed to the Axiom project. Where no other copyright statement
is noted in a file this copyright will apply. 

Portions Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

    - Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.

    - Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in
      the documentation and/or other materials provided with the
      distribution.

    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
      names of its contributors may be used to endorse or promote products
      derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

In [ ]: