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

)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
)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]:




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




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]:




OpenAxiom is an evolution of Axiom which  was released under this license
as of September 3, 2002.

Use of this material is by permission and/or license.
Individual files contain reference to these applicable copyrights.

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

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.

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 [ ]: