"Fossies" - the Fresh Open Source Software Archive  

Source code changes of the file "plugins/giac/doc/giac-demo.en.tm" between
TeXmacs-2.1.1-src.tar.gz and TeXmacs-2.1.2-src.tar.gz

About: GNU TeXmacs is a scientific editing platform designed to create beautiful technical documents using a wysiwyg interface.

giac-demo.en.tm  (TeXmacs-2.1.1-src):giac-demo.en.tm  (TeXmacs-2.1.2-src)
<TeXmacs|1.99.20> <TeXmacs|2.1.1>
<style|<tuple|tmdoc|giac>> <style|<tuple|tmdoc|giac|old-lengths>>
<\body> <\body>
<tmdoc-title|Example Giac session> <tmdoc-title|Example <name|Giac> session>
Here follows a sample session, which was started using Here follows a sample session, which was started using
<menu|Insert|Session|Giac>. <menu|Insert|Session|Giac>. Note that you may also use <name|Giac> as a
scripting language in ordinary documents.
<\session|giac|default> <\session|giac|default>
<\output> <\output>
<hrule> <hrule>
Giac 1.7.0 for TeXmacs, released under the GPL license (3.0) Giac 1.7.0 for TeXmacs, released under the GPL license (3.0)
See www.gnu.org for license details See www.gnu.org for license details
May contain BSD licensed software parts (lapack, atlas, tinymt) May contain BSD licensed software parts (lapack, atlas, tinymt)
skipping to change at line 31 skipping to change at line 32
\<copyright\> 2003\U2021 B. Parisse & al (giac), J. van der Hoeven \<copyright\> 2003\U2021 B. Parisse & al (giac), J. van der Hoeven
(TeXmacs), L. Marohnió (interface) (TeXmacs), L. Marohnió (interface)
<hrule> <hrule>
Xcas (C-like) syntax mode Xcas (C-like) syntax mode
Type ? for documentation or ?commandname for help on commandname Type ? for documentation or ?commandname for help on commandname
Type tabulation key to complete a partial command Type tabulation key to complete a partial command
<\errput>
// Using locale /usr/local/share/locale/
// en_US.UTF-8
// /usr/local/share/locale/
// giac
// UTF-8
// Maximum number of parallel threads 6
Added 0 synonyms
</errput>
</output> </output>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
f(x):=sin(x)+x f(x):=x*sin(x)
<|unfolded-io> <|unfolded-io>
<equation*|<math|x\<mapsto\>sin <around*|\<nobracket\>|x|\<nobracket\>>+x> <\equation*>
> x\<mapsto\>x*sin <around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
<\errput> <\errput>
// Parsing f // Parsing f
// Success // Success
// compiling f // compiling f
</errput> </errput>
</unfolded-io> </unfolded-io>
<\textput>
Some basic calculus examples:
</textput>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
diff(f(x),x) diff(f(x),x,2)
<|unfolded-io> <|unfolded-io>
<equation*|<math|cos <around*|\<nobracket\>|x|\<nobracket\>>+1>> <\equation*>
-x*sin <around*|\<nobracket\>|x|\<nobracket\>>+2*cos
<around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
integrate(f(x),x=0..pi) integrate(f(x),x)
<|unfolded-io> <|unfolded-io>
<equation*|<math|<frac|\<mathpi\><rsup|2>+2|2>+1>> <\equation*>
-x*cos <around*|\<nobracket\>|x|\<nobracket\>>+sin
<around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
plot(f(x),x=0..2*pi) integrate(f(x),x=0..pi)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-1.pdf|0.7par|||> <\equation*>
\<mathpi\>
</equation*>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
plot([x^2*sin(x),f(x)],x=-pi..pi,color=[blue,magenta]) integrate(sqrt(tan(x)),x)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-2.pdf|0.7par|||> <\equation*>
2*<around*|(|<frac|1|8>*<sqrt|2>*ln <around*|(|tan
<around*|\<nobracket\>|x|\<nobracket\>>-<sqrt|2>*<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>+1|)>+<frac|1|4>*<sqrt|2>*arctan
<around*|(|<frac|2*<around*|(|<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>-<frac|<sqrt|2>|2>|)>|<sqrt|2>>|
)>-<frac|1|8>*<sqrt|2>*ln
<around*|(|tan <around*|\<nobracket\>|x|\<nobracket\>>+<sqrt|2>*<sqrt|ta
n
<around*|\<nobracket\>|x|\<nobracket\>>>+1|)>+<frac|1|4>*<sqrt|2>*arctan
<around*|(|<frac|2*<around*|(|<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>+<frac|<sqrt|2>|2>|)>|<sqrt|2>>|
)>|)>
</equation*>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
implicitplot(x^2=y^3-3y+1,x=-4..4,y=-4..4) g(x,y):=(1+x*y)/(1+sqrt(x))
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-3.pdf|0.7par|||> <\equation*>
</unfolded-io> <around*|(|x,y|)>\<mapsto\><frac|1+x*y|1+<sqrt|x>>
</equation*>
<\textput> <\errput>
Mathematical and physical constants, as well as physical units, are // Parsing g
typeset using the conventional notation whenever possible, as in the
example below. // Success
</textput>
// compiling g
</errput>
</unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
e,i,pi,euler_gamma,inf,5_Angstrom,_NA_,_REarth_,_hbar_ simplify(diff(g(x,y),x,x,y))
<|unfolded-io> <|unfolded-io>
<equation*|<math|\<mathe\>,\<mathi\>,\<mathpi\>,\<matheuler\>,+\<infty\>,5 <\equation*>
\<space\>\<space\>\<nosymbol\>\<AA\>,1\<space\>\<space\>\<nosymbol\>N<rsub|A>\<n <frac|-<sqrt|x>-3|4*x<rsup|2>+12*x*<sqrt|x>+12*x+4*<sqrt|x>>
osymbol\>,1\<space\>\<space\>\<nosymbol\>R<rsub|\<oplus\>>\<nosymbol\>,1\<space\ </equation*>
>\<space\>\<nosymbol\>\<hbar\>\<nosymbol\>>>
</unfolded-io> </unfolded-io>
<\textput>
Graphs can be constructed, manipulated with and drawn.
</textput>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
G:=graph("grotzsch") simplify(hessian(g(x,y),[x,y]))
<|unfolded-io> <|unfolded-io>
<equation*|<math|<text|an undirected unweighted graph with 11 vertices <\equation*>
and 20 edges>>> <matrix|<tformat|<table|<row|<cell|<frac|-x*y*<sqrt|x>-3*x*y+3*<sqrt|x>+
1|4*x<rsup|3>+12*x<rsup|2>*<sqrt|x>+12*x<rsup|2>+4*x*<sqrt|x>>>|<cell|<frac|<sqr
t|x>+2|2*x+4*<sqrt|x>+2>>>|<row|<cell|<frac|<sqrt|x>+2|2*x+4*<sqrt|x>+2>>|<cell|
0>>>>>
</equation*>
</unfolded-io> </unfolded-io>
<\textput>
Plots and charts:
</textput>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
draw_graph(highlight_vertex(G,vertices(G),greedy_color(G))) plot(sin(x)/x,x=0..10)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-4.pdf|0.7par|||> <htab|><image|giac-demo.en-image-1.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
draw_graph(random_tree(30),labels=false) plot3d(sin(sqrt(x^2+y^2))/sqrt(x^2+y^2),x=-10..10,y=-10..10)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-5.pdf|0.7par|||> <htab|><image|giac-demo.en-image-2.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\textput>
In the following examples it is demonstrated how to create bar plots,
histograms and pie charts.
</textput>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
bar_plot([[2,"Yesterday","Today"],["A",2,5],["B",5,6],["C",7,7]]) bar_plot([[2,"Yesterday","Today"],["A",2,5],["B",5,6],["C",7,7]])
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-6.pdf|0.7par|||> <htab|><image|giac-demo.en-image-3.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
histogram(seq(rand(1000),k,0,100),0,100) camembert([["France",6],["Allemagne",12],["Suisse",5]])
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-7.pdf|0.7par|||> <htab|><image|giac-demo.en-image-4.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
camembert([["France",6],["Allemagne",12],["Suisse",5]]) histogram(seq(rand(1000),k,0,100),0,100)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-8.pdf|0.7par|||> <htab|><image|giac-demo.en-image-5.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\textput> <\textput>
A <abbr|2D> geometry example: <abbr|2D> geometry example:
</textput> </textput>
<\unfolded-io> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io> <|unfolded-io>
P1:=point(3,4); P2:=point(6,2); P3:=point(4,3); P1:=point(3,4); P2:=point(6,2); P3:=point(4,3);
Sq:=square(P1,P2,color=blue); Sq:=square(P1,P2,color=blue);
Cr:=circle(P3,2); Cr:=circle(P3,2);
Q:=inter(Sq,Cr); Q:=inter(Sq,Cr);
T1:=tangent(Cr,Q[0],color=magenta); T1:=tangent(Cr,Q[0],color=magenta);
T2:=tangent(Cr,Q[1],color=green) T2:=tangent(Cr,Q[1],color=green)
<|unfolded-io> <|unfolded-io>
<image|giac-demo.en-image-9.pdf|0.7par|||> <htab|><image|giac-demo.en-image-6.pdf|0.618par|||><htab|>
</unfolded-io> </unfolded-io>
<\textput> <\textput>
The <name|Giac> plugin has a good support for mathematical input mode. Graph drawing example:
Besides the usual algebraic expressions, the following standard
notations are supported:
<\itemize-dot>
<item>(partial) derivatives
<item>integrals, sums and products
<item>limits
<item>piecewise defined functions
<item>simplified notation for powers of trigonometric and other
elementary functions (e.g. <math|sin<rsup|2>
<around*|\<nobracket\>|x|\<nobracket\>>>)
<item>absolute values, floor, ceiling
<item>sets, lists, and matrices
<item>special functions
<item>complex conjugates, real and imaginary parts
<item>etc.
</itemize-dot>
</textput> </textput>
Parentheses around function arguments are mandatory in <name|Giac>. <\unfolded-io>
However, in <TeXmacs> mathematical input mode one can enter hidden
parentheses by pressing <key|(> <key|Tab>, which work the same as the
ordinary ones. Therefore it is possible to enter e.g.<nbsp><math|sin
<around*|\<nobracket\>|x|\<nobracket\>>> (note the hidden parentheses
around <math|x>!) instead of <math|sin <around*|(|x|)>>.
When entering derivatives, the function application symbol (entered by
pressing <key|Space>) between the derivative operator and the argument is
mandatory, as well as the (hidden) parentheses around the argument.
<\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io>
<frac|\<mathd\>|\<mathd\> x> <around*|(|x*ln G:=graph("groetzsch")
<around*|\<nobracket\>|x|\<nobracket\>>-<frac|1|1-x>|)> <|unfolded-io>
<|unfolded-io-math> <\equation*>
<equation*|<math|ln <around*|\<nobracket\>|x|\<nobracket\>>+1-<frac|1|<aro <text|an undirected unweighted graph with 11 vertices and 20 edges>
und*|(|1-x|)><rsup|2>>>> </equation*>
</unfolded-io-math> </unfolded-io>
<\unfolded-io-math> <\unfolded-io>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io>
<frac|\<mathd\><rsup|2>|\<mathd\> x<rsup|2>> <around*|(|x*ln draw_graph(highlight_vertex(G,vertices(G),greedy_color(G)))
<around*|\<nobracket\>|x|\<nobracket\>>-<frac|1|1-x>|)> <|unfolded-io>
<|unfolded-io-math> <htab|><image|giac-demo.en-image-7.pdf|0.618par|||><htab|>
<equation*|<math|<frac|x<rsup|3>-3*x<rsup|2>+5*x-1|x<rsup|4>-3*x<rsup|3>+3 </unfolded-io>
*x<rsup|2>-x>>> </session>
</unfolded-io-math>
<\textput> <name|Giac> plugin has a good support for mathematical input mode. Besides
In the following example, the stationary points of the function the usual algebraic expressions, the following standard notations are
<math|f> are computed. supported:
</textput>
<\unfolded-io-math> <\itemize-dot>
\<gtr\>\ <item>(partial) derivatives
<|unfolded-io-math>
assume <around*|(|r\<gtr\>0|)>
<|unfolded-io-math>
<equation*|<math|r>>
</unfolded-io-math>
<\unfolded-io-math> <item>integrals, sums and products
\<gtr\>\
<|unfolded-io-math>
f\<assign\>unapply <around*|(|<frac|ln
<around*|\<nobracket\>|x|\<nobracket\>>|r>-<frac|r*x|x+1>,x|)>
<|unfolded-io-math>
<equation*|<math|x\<mapsto\><frac|ln
<around*|\<nobracket\>|x|\<nobracket\>>|r>-<frac|r*x|x+1>>>
</unfolded-io-math>
<\unfolded-io-math> <item>limits
\<gtr\>\
<|unfolded-io-math>
solve <around*|(|<frac|\<mathd\>|\<mathd\> x>
<around*|\<nobracket\>|f<around*|(|x|)>|\<nobracket\>>=0,x|)>
<|unfolded-io-math>
<equation*|<math|<around*|[|<frac|r<rsup|2>+r*<sqrt|r<rsup|2>-4>-2|2>,<fra
c|r<rsup|2>-r*<sqrt|r<rsup|2>-4>-2|2>|]>>>
</unfolded-io-math>
<\textput> <item>piecewise defined functions
Various notations for deriatives in differential equations are
supported.
</textput>
<\unfolded-io-math> <item>simplified notation for powers of trigonometric and other
\<gtr\>\ elementary functions (e.g. <math|sin<rsup|2>
<|unfolded-io-math> <around*|\<nobracket\>|x|\<nobracket\>>>)
dsolve <around*|(|<frac|\<mathd\><rsup|2> y|\<mathd\>
x<rsup|2>>-y=2*sin <around*|\<nobracket\>|x|\<nobracket\>>,x,y|)>
<|unfolded-io-math>
<equation*|<math|c\<nosymbol\><rsub|0>*\<mathe\><rsup|x>+c\<nosymbol\><rsu
b|1>*\<mathe\><rsup|-x>-sin
<around*|\<nobracket\>|x|\<nobracket\>>>>
</unfolded-io-math>
<\unfolded-io-math> <item>absolute values, floor, ceiling
\<gtr\>\
<|unfolded-io-math>
dsolve <around*|(|y<rprime|''>-y=2*sin
<around*|\<nobracket\>|x|\<nobracket\>>\<wedge\>y<around*|(|0|)>=0\<wedge\
>y<rprime|'><around*|(|0|)>=1,x,y|)>
<|unfolded-io-math>
<equation*|<math|\<mathe\><rsup|x>-\<mathe\><rsup|-x>-sin
<around*|\<nobracket\>|x|\<nobracket\>>>>
</unfolded-io-math>
<\unfolded-io-math> <item>sets, lists, and matrices
\<gtr\>\
<|unfolded-io-math>
dsolve <around*|(|<wide|x|\<ddot\>>=x,t,x|)>
<|unfolded-io-math>
<equation*|<math|c\<nosymbol\><rsub|0>*\<mathe\><rsup|t>+c\<nosymbol\><rsu
b|1>*\<mathe\><rsup|-t>>>
</unfolded-io-math>
<\unfolded-io-math> <item>special functions
\<gtr\>\
<|unfolded-io-math>
simplify <around*|(|dsolve <around*|(|y<rsup|<around*|(|3|)>>=y,t,y|)>|)>
<|unfolded-io-math>
<equation*|<math|<frac|c\<nosymbol\><rsub|0>*<around*|(|\<mathe\><rsup|<fr
ac|1|2>*t>|)><rsup|3>*tan<rsup|2>
<around*|(|<frac|1|4>*t*<sqrt|3>|)>+c\<nosymbol\><rsub|0>*<around*|(|\<mat
he\><rsup|<frac|1|2>*t>|)><rsup|3>-c\<nosymbol\><rsub|1>*tan<rsup|2>
<around*|(|<frac|1|4>*t*<sqrt|3>|)>+c\<nosymbol\><rsub|1>+2*c\<nosymbol\><
rsub|2>*tan
<around*|(|<frac|1|4>*t*<sqrt|3>|)>|\<mathe\><rsup|<frac|1|2>*t>*tan<rsup|
2>
<around*|(|<frac|1|4>*t*<sqrt|3>|)>+\<mathe\><rsup|<frac|1|2>*t>>>>
</unfolded-io-math>
<\textput> <item>complex conjugates, real and imaginary parts
Partial derivatives are supported as well. </itemize-dot>
</textput>
<\unfolded-io-math> Note that <name|Giac> output (or a part of it) can be selected and copied
\<gtr\>\ to an input field.
<|unfolded-io-math>
collect <around*|(|<frac|\<partial\><rsup|3>|\<partial\> x*\<partial\>
y<rsup|2>> <around*|(|<frac|y*\<mathe\><rsup|-x>|x<rsup|2>+y<rsup|2>>|)>|)
>
<|unfolded-io-math>
<equation*|<math|<frac|2*y*<around*|(|3*x<rsup|4>+12*x<rsup|3>+2*x<rsup|2>
*y<rsup|2>-12*x*y<rsup|2>-y<rsup|4>|)>*\<mathe\><rsup|-x>|<around*|(|y<rsup|2>+x
<rsup|2>|)><rsup|4>>>>
</unfolded-io-math>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<frac|\<partial\><rsup|2>|\<partial\> x*\<partial\> y>
<around*|\<nobracket\>|g <around*|(|x,x*y|)>|\<nobracket\>>
<|unfolded-io-math>
<equation*|<math|x*y*g<rsup|<around*|(|2,2|)>>
<around*|(|x,x*y|)>+x*g<rsup|<around*|(|1,2|)>>
<around*|(|x,x*y|)>+g<rsup|<around*|(|2|)>> <around*|(|x,x*y|)>>>
</unfolded-io-math>
<\textput> Parentheses around function arguments are mandatory in <name|Giac>.
Laplace and Fourier transform functions are available. However, in <TeXmacs> mathematical input mode one can enter hidden
</textput> parentheses by pressing <key|(> <key|Tab>, which work the same as the
ordinary ones. Therefore it is possible to enter e.g.<nbsp><math|sin
<around*|\<nobracket\>|x|\<nobracket\>>> (note the hidden parentheses
around <math|x>!) instead of <math|sin <around*|(|x|)>>.
<\unfolded-io-math> When entering derivatives, the function application symbol (entered by
\<gtr\>\ pressing <key|Space>) between the derivative operator and the argument is
<|unfolded-io-math> mandatory, as well as the (hidden) parentheses around the argument.
F\<assign\>laplace <around*|(|t*sin <around*|(|3*t|)>,t,s|)>
<|unfolded-io-math>
<equation*|<math|<frac|6*s|s<rsup|4>+18*s<rsup|2>+81>>>
</unfolded-io-math>
<\unfolded-io-math> In the following examples we switch to the mathematical input mode.
\<gtr\>\
<|unfolded-io-math>
fourier <around*|(|rect <around*|(|x|)>,x,s|)>
<|unfolded-io-math>
<equation*|<math|<frac|2*sin <around*|(|<frac|s|2>|)>|s>>>
</unfolded-io-math>
<\unfolded-io-math> <\session|giac|default>
\<gtr\>\ <\textput>
<|unfolded-io-math> Hidden parentheses example:
addtable <around*|(|fourier,y <around*|(|x|)>,Y <around*|(|s|)>,x,s|)> </textput>
<|unfolded-io-math>
<equation*|<math|1>>
</unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
T\<assign\>fourier <around*|(|y <around*|(|x+1|)>-<frac|\<mathd\><rsup|3>| sin <around*|\<nobracket\>|\<pi\>|\<nobracket\>>
\<mathd\>
x<rsup|3>> <around*|\<nobracket\>|y
<around*|(|x|)>|\<nobracket\>>,x,s|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|(|\<mathe\><rsup|\<mathi\>*s>+\<mathi\>*s<rsup|3 <\equation*>
>|)>*Y 0
<around*|(|s|)>>> </equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Heaviside function and Dirac <math|\<delta\>>-distribution are Derivatives:
associated with upright Greek symbols <math|<math-up|\<theta\>>> and
<math|<math-up|\<delta\>>>, respectively.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
F\<assign\>exp2pow <around*|(|lin <around*|(|fourier <frac|\<mathd\><rsup|2>|\<mathd\> x<rsup|2>> <around*|(|x*ln
<around*|(|<frac|x|x<rsup|2>-x+1>,x,\<omega\>|)>|)>|)> <around*|\<nobracket\>|x|\<nobracket\>>-<frac|1|1-x>|)>
<|unfolded-io-math>
<equation*|<math|\<mathpi\>*\<mathi\>*\<up-theta\>
<around*|(|-\<omega\>|)>*\<mathe\><rsup|<frac|\<omega\>*<sqrt|3>-\<mathi\>
*\<omega\>|2>>-\<mathpi\>*\<mathi\>*\<up-theta\>
<around*|(|\<omega\>|)>*\<mathe\><rsup|-<frac|\<omega\>*<sqrt|3>+\<mathi\>
*\<omega\>|2>>+\<mathpi\>*\<mathe\><rsup|<frac|-\<mathi\>*\<omega\>*<sqrt|3>-3*<
around*|\||\<omega\>|\|>|2*<sqrt|3>>>*<sqrt|3><rsup|-1>>>
</unfolded-io-math>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
ifourier <around*|(|F,\<omega\>,x|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|x|x<rsup|2>-x+1>>> <\equation*>
<frac|x<rsup|3>-3*x<rsup|2>+5*x-1|x<rsup|4>-3*x<rsup|3>+3*x<rsup|2>-x>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
h\<assign\>fourier <around*|(|1|)> collect <around*|(|<frac|\<partial\><rsup|3>|\<partial\> x*\<partial\>
y<rsup|2>> <around*|(|<frac|y*\<mathe\><rsup|-x>|x<rsup|2>+y<rsup|2>>|)>|)
>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|2*\<mathpi\>*\<up-delta\> <around*|(|x|)>>> <\equation*>
<frac|2*y*<around*|(|3*x<rsup|4>+12*x<rsup|3>+2*x<rsup|2>*y<rsup|2>-12*x
*y<rsup|2>-y<rsup|4>|)>*\<mathe\><rsup|-x>|<around*|(|y<rsup|2>+x<rsup|2>|)><rsu
p|4>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
<name|Giac> has basic support for variational calculus. Limits:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
eq\<assign\>euler_lagrange <around*|(|x<rsup|2>\<cdot\><around*|(|y<rprime lim<rsub|x\<rightarrow\>0> <around*|\<nobracket\>|<frac|1-<frac|1|2>*x<rsu
|'>|)><rsup|2>+2*y<rsup|2>|)> p|2>-cos
<around*|(|<frac|x|1-x<rsup|2>>|)>|x<rsup|4>>|\<nobracket\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|\<mathd\><rsup|2>|\<mathd\> x<rsup|2>> <\equation*>
<around*|\<nobracket\>|y <around*|(|x|)>|\<nobracket\>>=<frac|-2*<frac|\<m <frac|23|24>
athd\>|\<mathd\> </equation*>
x> <around*|\<nobracket\>|y <around*|(|x|)>|\<nobracket\>>*x+2*y
<around*|(|x|)>|x<rsup|2>>>>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
dsolve <around*|(|eq,x,y|)> lim<rsub|x\<rightarrow\>0<rsup|+>> <around*|\<nobracket\>|\<mathe\><rsup|- 1/x>|\<nobracket\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|<around*|(|-<frac|c\<nosymbol\><rsub|0>|3*x<rsup|3> <\equation*>
>+c\<nosymbol\><rsub|1>|)>*x<rsup|3>|x<rsup|2>>>> 0
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Integrals, sums and products are entered in the usual way. Integrals, sums, and products:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<big|int><frac|1|<around*|(|x<rsup|2>+9|)><rsup|3>>*\<mathd\> x <big|int><frac|1|<around*|(|x<rsup|2>+9|)><rsup|3>>*\<mathd\> x
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|x<rsup|3>+15*x|216*<around*|(|x<rsup|2>+9|)><rsup|2 <\equation*>
>>+<frac|arctan <frac|x<rsup|3>+15*x|216*<around*|(|x<rsup|2>+9|)><rsup|2>>+<frac|arctan
<around*|(|<frac|x|3>|)>|648>>> <around*|(|<frac|x|3>|)>|648>
</unfolded-io-math> </equation*>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<big|int><sqrt|tan <around*|\<nobracket\>|x|\<nobracket\>>>*\<mathd\> x
<|unfolded-io-math>
<equation*|<math|2*<around*|(|<frac|1|8>*<sqrt|2>*ln <around*|(|tan
<around*|\<nobracket\>|x|\<nobracket\>>-<sqrt|2>*<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>+1|)>+<frac|1|4>*<sqrt|2>*arctan
<around*|(|<frac|2*<around*|(|<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>-<frac|<sqrt|2>|2>|)>|<sqrt|2>>|)>
-<frac|1|8>*<sqrt|2>*ln
<around*|(|tan <around*|\<nobracket\>|x|\<nobracket\>>+<sqrt|2>*<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>+1|)>+<frac|1|4>*<sqrt|2>*arctan
<around*|(|<frac|2*<around*|(|<sqrt|tan
<around*|\<nobracket\>|x|\<nobracket\>>>+<frac|<sqrt|2>|2>|)>|<sqrt|2>>|)>
|)>>>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<big|int><rsub|-\<infty\>><rsup|+\<infty\>>\<mathe\><rsup|-x<rsup|2>>*\<ma thd\> <big|int><rsub|-\<infty\>><rsup|+\<infty\>>\<mathe\><rsup|-x<rsup|2>>*\<ma thd\>
x x
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<sqrt|\<mathpi\>>>> <\equation*>
</unfolded-io-math> <sqrt|\<mathpi\>>
</equation*>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
assume <around*|(|\<alpha\>\<gtr\>0|)>
<|unfolded-io-math>
<equation*|<math|\<alpha\>>>
</unfolded-io-math>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<big|int><rsub|0><rsup|+\<infty\>>ln
<around*|(|1+<frac|\<alpha\><rsup|2>|x<rsup|2>>|)>*\<mathd\> x
<|unfolded-io-math>
<equation*|<math|\<mathpi\>*\<alpha\>>>
<\errput>
No checks were made for singular points of antiderivative
x*ln(1+alpha^2/x^2)+2*alpha^2*2*1/2/alpha*atan(x/alpha) for definite
integration in [0,+infinity]
</errput>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<big|sum><rsub|k=1><rsup|+\<infty\>><frac|1|1+\<mathpi\><rsup|2>*k<rsup|2> > <big|sum><rsub|k=1><rsup|+\<infty\>><frac|1|1+\<mathpi\><rsup|2>*k<rsup|2> >
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|1|\<mathe\><rsup|2>-1>>> <\equation*>
<frac|1|\<mathe\><rsup|2>-1>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<big|prod><rsub|k=1><rsup|10><around*|(|1-<frac|1|2*k<rsup|2>>|)> trigsimplify <around*|(|2<rsup|10>*sin
<around*|\<nobracket\>|<frac|x|2<rsup|10>>|\<nobracket\>>*<big|prod><rsub|
k=1><rsup|10><around*|\<nobracket\>|cos
|\<nobracket\>><frac|x|2<rsup|k>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|103376401778279|275188285440000>>> <\equation*>
sin <around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
<name|Giac> can determine domain of an univariate real function and Simplification:
solve inequalities.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
domain <around*|(|<sqrt|3-<sqrt|2-<sqrt|1-x>>>,x|)> simplify <around*|(|<sqrt|5+2*<sqrt|6>>+<sqrt|9-2*<sqrt|6>-4*<sqrt|5-2*<sq rt|6>>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|x\<geqslant\>-3\<wedge\>x\<leqslant\>1>> <\equation*>
2*<sqrt|2>+2
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
solve <around*|(|<around*|\||2*x<rsup|2>-3|\|>\<leqslant\>5,x|)> simplify <around*|(|cot <around*|(|atan <around*|(|<frac|12|13>|)>+acos
<around*|(|<frac|4|5>|)>|)>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|[|x\<geqslant\>-2\<wedge\>x\<leqslant\>2|]>>> <\equation*>
<frac|16|87>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
solve <around*|(|x-<around*|\||x-<around*|\||x<rsup|2>-3*x-2|\|>|\|>-1\<gt r\>0,x|)> normal <around*|(|1+x-<frac|1-x|1-x<rsup|2>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|[|x\<gtr\><frac|<sqrt|13>+1|2>\<wedge\>x\<less\> <\equation*>
<frac|<sqrt|13>+3|2>,x\<gtr\><frac|<sqrt|21>+3|2>\<wedge\>x\<less\><frac|<sqrt|2 <frac|x<rsup|2>+2*x|x+1>
9>+5|2>|]>>> </equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
A partial fractions decomposition example:
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
partfrac <around*|(|<frac|x<rsup|4>-44*x<rsup|3>+22*x<rsup|2>-11*x+1|x<rsu trigsimplify <around*|(|1-<frac|1|4>*sin<rsup|2>
p|5>+3*x<rsup|4>+x<rsup|3>-x<rsup|2>-4>,x|)> <around*|(|2*x|)>-sin<rsup|2> <around*|\<nobracket\>|y|\<nobracket\>>-cos<
rsup|4>
<around*|\<nobracket\>|x|\<nobracket\>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|-<frac|31|18*<around*|(|x-1|)>>-<frac|479|15*<around*|(|x <\equation*>
+2|)><rsup|2>>+<frac|1742|225*<around*|(|x+2|)>>+<frac|-251*x+107|50*<around*|(| sin<rsup|2> <around*|\<nobracket\>|x|\<nobracket\>>-sin<rsup|2>
x<rsup|2>+1|)>>>> <around*|\<nobracket\>|y|\<nobracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Simplification and auto-simplification examples: Equation solving:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
simplify <around*|(|<sqrt|5+2*<sqrt|6>>+<sqrt|9-2*<sqrt|6>-4*<sqrt|5-2*<sq rt|6>>>|)> solve<around*|(|x<rsup|3>-x+1-<frac|1|2-x<rsup|2>>=0,x|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|2*<sqrt|2>+2>> <\equation*>
<around*|[|<frac|-<sqrt|5>-1|2>,-1,<frac|<sqrt|5>-1|2>,1|]>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
simplify <around*|(|cot <around*|(|atan <around*|(|<frac|12|13>|)>+acos linsolve <around*|(|<around*|[|x+y=2,x-2*y=3|]>,<around*|[|x,y|]>|)>
<around*|(|<frac|4|5>|)>|)>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|16|87>>> <\equation*>
<around*|[|<frac|7|3>,-<frac|1|3>|]>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
trigsimplify <around*|(|1-<frac|1|4>*sin<rsup|2> fsolve <around*|(|x=\<mathe\><rsup|-x>,x=0|)>
<around*|(|2*x|)>-sin<rsup|2> <around*|\<nobracket\>|y|\<nobracket\>>-cos<
rsup|4>
<around*|\<nobracket\>|x|\<nobracket\>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|sin<rsup|2> <around*|\<nobracket\>|x|\<nobracket\>>-sin<r <\equation*>
sup|2> 0.56714329041
<around*|\<nobracket\>|y|\<nobracket\>>>> </equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
trigsimplify <around*|(|<frac|<big|sum><rsub|n=1><rsup|5>sin csolve <around*|(|z<rsup|2>\<cdot\><wide|z|\<bar\>>=\<Re\>
<around*|(|n*x|)>|<big|sum><rsub|n=1><rsup|5>cos <around*|(|n*x|)>>|)> <around*|(|z|)>-8*\<mathi\>,z|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|tan <around*|(|3*x|)>>> <\equation*>
<around*|[|-2*\<mathi\>|]>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\textput>
\<gtr\>\ Solving ordinary differential equations (note that various notational
<|unfolded-io-math> formats are supported):
assume <around*|(|n,integer|)>;additionally<around*|(|n\<geqslant\>0|)> </textput>
<|unfolded-io-math>
<equation*|<math|\<bbb-Z\>,n>>
</unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<Gamma\> <around*|(|n+1|)> dsolve <around*|(|<frac|\<mathd\><rsup|2> y|\<mathd\>
x<rsup|2>>-y=2*sin <around*|\<nobracket\>|x|\<nobracket\>>,x,y|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|n!>> <\equation*>
c\<nosymbol\><rsub|0>*\<mathe\><rsup|x>+c\<nosymbol\><rsub|1>*\<mathe\><
rsup|-x>-sin
<around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
cos <around*|(|n*\<mathpi\>|)> dsolve <around*|(|<wide|x|\<ddot\>>=x,t,x|)>
<|unfolded-io-math>
<equation*|<math|<around*|(|-1|)><rsup|n>>>
</unfolded-io-math>
<\textput>
Binomial coefficients are entered using the <markup|binom> tag.
</textput>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<binom|49|7>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|85900584>> <\equation*>
c\<nosymbol\><rsub|0>*\<mathe\><rsup|t>+c\<nosymbol\><rsub|1>*\<mathe\><
rsup|-t>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
An expression with the wide bar accent is interpreted as the complex
conjugate. Additionally, the usual notation for real and imaginary
parts is supported.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
assume <around*|(|z,complex|)>;csolve dsolve <around*|(|y<rprime|''>-y=2*sin
<around*|(|z<rsup|2>\<cdot\><wide|z|\<bar\>>=\<Re\> <around*|\<nobracket\>|x|\<nobracket\>>\<wedge\>y<around*|(|0|)>=0\<wedge\
<around*|(|z|)>-8*\<mathi\>,z|)> >y<rprime|'><around*|(|0|)>=1,x,y|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|\<bbb-C\>,<around*|[|-2*\<mathi\>|]>>> <\equation*>
\<mathe\><rsup|x>-\<mathe\><rsup|-x>-sin
<around*|\<nobracket\>|x|\<nobracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
Substitution of parameters in an expression can be executed\Vbesides
using the <verbatim|subs> command\V by entering the symbol <math|\|>
(obtained by pressing <key|\|><key|Tab>) between the expression and the
sequence of equations in form <verbatim|parameter=value>.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
cos<rsup|2> <around*|\<nobracket\>|y|\<nobracket\>>+y*sin simplify <around*|(|dsolve <around*|(|y<rsup|<around*|(|3|)>>=8*y,t,y|)>|)
<around*|\<nobracket\>|x|\<nobracket\>>\|x=<frac|\<pi\>|3>,y=<frac|\<mathp >
i\>|4>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|(|<frac|<sqrt|2>|2>|)><rsup|2>+<frac|\<mathpi\>* <\equation*>
<sqrt|3>|4\<cdot\>2>>> <frac|c\<nosymbol\><rsub|0>*<around*|(|\<mathe\><rsup|t>|)><rsup|3>*tan<
rsup|2>
<\errput> <around*|(|<frac|1|2>*t*<sqrt|3>|)>+c\<nosymbol\><rsub|0>*<around*|(|\<m
// Success athe\><rsup|t>|)><rsup|3>-c\<nosymbol\><rsub|1>*tan<rsup|2>
</errput> <around*|(|<frac|1|2>*t*<sqrt|3>|)>+c\<nosymbol\><rsub|1>+2*c\<nosymbol\
><rsub|2>*tan
<around*|(|<frac|1|2>*t*<sqrt|3>|)>|\<mathe\><rsup|t>*tan<rsup|2>
<around*|(|<frac|1|2>*t*<sqrt|3>|)>+\<mathe\><rsup|t>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
The invisible addition symbol, entered with Solving inequalities in one variable:
<key|+><key|Tab><key|Tab><key|Tab><key|Tab>, translates to
<verbatim|+>.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
7\<noplus\><frac*|3|4> solve <around*|(|x-<around*|\||x-<around*|\||x<rsup|2>-3*x-2|\|>|\|>-1\<gt r\>0,x|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|31|4>>> <\equation*>
<around*|[|x\<gtr\><frac|<sqrt|13>+1|2>\<wedge\>x\<less\><frac|<sqrt|13>
+3|2>,x\<gtr\><frac|<sqrt|21>+3|2>\<wedge\>x\<less\><frac|<sqrt|29>+5|2>,<frac|<
sqrt|29>+5|2>|]>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
The invisible symbol, entered with <shortcut|\<nosymbol\>>, is
interpreted as the underscore (_). It is useful for
e.g.<nbsp>differentiating between e.g.<nbsp><verbatim|x0> and
<verbatim|x_0>, which are both typeset (and, in math input mode,
entered) as <math|x<rsub|0>>. However, in the latter case the invisible
symbol is appended to <math|x>, as in the example below. Since the
subscript of a symbol is simply appended to the symbol for input in
<name|Giac>, the concatenation yields <verbatim|x_0>. The invisible
symbol is also used for entering physical units, which begin with _,
and physical constants, which begin and end with _ in <name|Giac>.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
simplify <around*|(|x\<nosymbol\><rsub|0>-x<rsub|0>|)> domain <around*|(|<sqrt|3-<sqrt|2-<sqrt|1-x>>>,x|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|-x<rsub|0>+x\<nosymbol\><rsub|0>>> <\equation*>
x\<geqslant\>-3\<wedge\>x\<leqslant\>1
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Bold symbols may be used, which is useful for denoting matrices and Vectors and matrices (note that double symbols such as <verbatim|AA>
vectors. A bold symbol is input as a double symbol, and <verbatim|vv> are interpreted as bold symbols in <TeXmacs> and vice
e.g.<nbsp><math|\<b-up-G\>> corresponds to <verbatim|GG> in versa):
<name|Giac>. Note that indices in <name|Giac> are 0-based by default.
For 1-based indices, switch to Maple mode.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<b-up-A\>\<assign\>matrix <around*|(|4,4,<around*|(|j,k|)>\<mapsto\>k+j<r sup|k+1>|)> \<b-up-A\>\<assign\>hilbert <around*|(|3|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<matrix|<tformat|<table|<row|<cell|0>|<cell|1>|<cell|2>|< <\equation*>
cell|3>>|<row|<cell|1>|<cell|2>|<cell|3>|<cell|4>>|<row|<cell|2>|<cell|5>|<cell| <matrix|<tformat|<table|<row|<cell|1>|<cell|<frac|1|2>>|<cell|<frac|1|3>
10>|<cell|19>>|<row|<cell|3>|<cell|10>|<cell|29>|<cell|84>>>>>>> >>|<row|<cell|<frac|1|2>>|<cell|<frac|1|3>>|<cell|<frac|1|4>>>|<row|<cell|<frac|
1|3>>|<cell|<frac|1|4>>|<cell|<frac|1|5>>>>>>
<\errput> </equation*>
// Success
</errput>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
det <around*|(|\<b-up-A\>|)> det <around*|(|\<b-up-A\>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|-24>> <\equation*>
<frac|1|2160>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<b-up-A\><rsup|-1> \<b-up-v\>\<assign\><around*|[|1,2,3|]>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<matrix|<tformat|<table|<row|<cell|-<frac|17|6>>|<cell|-< <\equation*>
frac|3|2>>|<cell|<frac|3|2>>|<cell|-<frac|1|6>>>|<row|<cell|<frac|17|6>>|<cell|< <around*|[|1,2,3|]>
frac|23|4>>|<cell|-<frac|7|2>>|<cell|<frac|5|12>>>|<row|<cell|-<frac|7|6>>|<cell </equation*>
|-4>|<cell|<frac|5|2>>|<cell|-<frac|1|3>>>|<row|<cell|<frac|1|6>>|<cell|<frac|3|
4>>|<cell|-<frac|1|2>>|<cell|<frac|1|12>>>>>>>>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<b-up-v\>\<assign\><around*|[|-1,3,7|]>
<|unfolded-io-math>
<equation*|<math|<around*|[|-1,3,7|]>>>
</unfolded-io-math>
<\textput>
The expression below is computed as <math|\<ell\><rsup|2>>-norm of
<math|\<b-up-v\>>.
</textput>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<around*|\<\|\|\>|\<b-up-v\>|\<\|\|\>> <around*|\<\|\|\>|\<b-up-v\>|\<\|\|\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<sqrt|59>>> <\equation*>
<sqrt|14>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
If <math|A> is a matrix, then its element <math|a<rsub|i\<nocomma\>j>> If <math|A> is a matrix, then its element <math|a<rsub|i\<nocomma\>j>>
can be fetched using the common notation, as below. Note that the can be obtained by using the usual notation. Note that the indices in
indices in the subscript must be enclosed within invisible parentheses the subscript must be enclosed within invisible parentheses and
and separated by (invisible) comma. separated by (invisible) comma.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<b-up-A\><rsub|<around*|\<nobracket\>|3\<nocomma\>2|\<nobracket\>>> \<b-up-A\><rsub|<around*|\<nobracket\>|2\<nocomma\>1|\<nobracket\>>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|29>> <\equation*>
<frac|1|4>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
\<b-up-v\><rsub|<around*|\<nobracket\>|1|\<nobracket\>>>+\<b-up-v\><rsub|< around*|\<nobracket\>|2|\<nobracket\>>> \<b-up-v\><rsub|<around*|\<nobracket\>|1|\<nobracket\>>>+\<b-up-v\><rsub|< around*|\<nobracket\>|2|\<nobracket\>>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|10>> <\equation*>
5
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Limits are entered like in the examples below. Note that the body of a Finite sequences, lists, and sets can be generated as in the examples
limit must be parenthesed (use invisible parentheses when appropriate) below. The symbol <math|\<barsuchthat\>> is entered by pressing
and prepended by the function application symbol. <key|\|><key|Tab><key|Tab><key|Tab><key|Tab> and it corresponds to the
<verbatim|$> operator in Giac, which has a very high priority.
Therefore the compound expressions on both sides of
<math|\<barsuchthat\>> should be surrounded by hidden parentheses.
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
lim<rsub|x\<rightarrow\>0> <around*|\<nobracket\>|<frac|1-<frac|1|2>*x<rsu euler <around*|(|k|)>\<barsuchthat\><around*|\<nobracket\>|k=1\<ldots\>20|
p|2>-cos \<nobracket\>>
<around*|(|<frac|x|1-x<rsup|2>>|)>|x<rsup|4>>|\<nobracket\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|23|24>>> <\equation*>
1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
lim<rsub|x\<rightarrow\>0<rsup|+>> <around*|\<nobracket\>|\<mathe\><rsup|- 1/x>|\<nobracket\>> <around*|[|ithprime <around*|(|j|)>\<barsuchthat\><around*|\<nobracket\>|j =1\<ldots\>20|\<nobracket\>>|]>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|0>> <\equation*>
<around*|[|2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71|]>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
lim<rsub|x\<rightarrow\>1<rsup|->> <around*|\<nobracket\>|sin A\<assign\><around*|{|k<rsup|2>\<barsuchthat\><around*|\<nobracket\>|k=1\<
<around*|(|\<pi\>*x|)><rsup|1/ln <around*|(|1-x|)>>|\<nobracket\>> ldots\>10|\<nobracket\>>|}>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|\<mathe\>>> <\equation*>
<around*|{|1,4,9,16,25,36,49,64,81,100|}>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
lim<rsub|n\<rightarrow\>+\<infty\>> B\<assign\><around*|{|<around*|\<nobracket\>|1+8*k|\<nobracket\>>\<barsuch
<around*|(|<sqrt|n<rsup|3>-2*n<rsup|2>+n-1|3>-n|)> that\><around*|\<nobracket\>|k=1\<ldots\>10|\<nobracket\>>|}>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|-<frac|2|3>>> <\equation*>
<around*|{|9,17,25,33,41,49,57,65,73,81|}>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
<paragraph|Example.>It can be shown that be shown that the series
<math|<big|sum><rsub|n=0><rsup|\<infty\>>s <around*|(|n|)>>, where
<math|s> is defined below, converges to <math|<frac|1|\<mathpi\>>>
(J.<nbsp>M.<nbsp>Borwein et al., 1989). We prove the convergence using
the criterion of D'Alembert and compute the number of significant
digits in the approximation of <math|\<mathpi\>> using the first 11
terms.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
s<around*|(|n|)>\<assign\><binom|2*n|n><rsup|3>*<frac|42*n+5|2<rsup|12*n+4 >> C\<assign\><around*|{|9,18,27|}>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|n\<mapsto\><binom|2*n|n><rsup|3>*<frac|42*n+5|2<rsup|12*n <\equation*>
+4>>>> <around*|{|9,18,27|}>
</equation*>
<\errput>
// Parsing s
// Success
// compiling s
</errput>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
The following limit is smaller than 1, hence the series converges. Set operations:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
simplify <around*|(|lim<rsub|n\<rightarrow\>+\<infty\>> <around*|(|A\<cap\> B|)>\<cup\> C
<around*|\<nobracket\>|<around*|\||<frac|s<around*|(|n+1|)>|s<around*|(|n|
)>>|\|>|\<nobracket\>>|)>
<|unfolded-io-math>
<equation*|<math|<frac|1|64>>>
</unfolded-io-math>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
p\<assign\><around*|(|<big|sum><rsub|n=0><rsup|10>s
<around*|(|n|)>|)><rsup|-1>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<frac|332306998946228968225951765070086144|10577660301265 <\equation*>
1189498293061907704445>>> <around*|{|9,25,49,81,18,27|}>
</equation*>
<\errput>
Warning: solving in n equation 16*(2^n)^12*(n!)^6=0
Unable to isolate function factorial
</errput>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
simplify <around*|(|1+<around*|\<lfloor\>|-log<rsub|10> A\<setminus\>B
<around*|(|2*<around*|\||\<mathpi\>-p|\|>|)>|\<rfloor\>>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|20>> <\equation*>
<around*|{|1,4,16,36,64,100|}>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
The symbol <math|\<varepsilon\>> stands for <verbatim|epsilon()> in Using the notation <math|a\<in\>A> we get the 1-based index of the
<name|Giac>, which is set to <math|10<rsup|-12>> by default. element <math|a> in the set <math|A>, or 0 if <math|a\<nin\>A>:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
125.483*\<varepsilon\> 19\<in\> A
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|1.25483\<times\>10<rsup|-10>>> <\equation*>
0
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
Finite sequences, lists, and sets can be generated as in the examples
below. The symbol <math|\<barsuchthat\>> is entered by pressing
<key|\|><key|Tab><key|Tab><key|Tab><key|Tab>. Note that
<math|\<barsuchthat\>> corresponds to the <verbatim|$> operator in
Giac, which has a very high priority. Therefore the compound
expressions on both sides of <math|\<barsuchthat\>> should be
surrounded by hidden parentheses, as in the examples below.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
euler <around*|(|k|)>\<barsuchthat\><around*|\<nobracket\>|k=1\<ldots\>20| \<nobracket\>> 57\<in\> B
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8>> <\equation*>
7
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\textput>
\<gtr\>\ Binomial coefficients are entered using the <markup|binom> tag:
<|unfolded-io-math> </textput>
<around*|[|ithprime <around*|(|j|)>\<barsuchthat\><around*|\<nobracket\>|j
=1\<ldots\>20|\<nobracket\>>|]>
<|unfolded-io-math>
<equation*|<math|<around*|[|2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59
,61,67,71|]>>>
</unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
A\<assign\><around*|{|k<rsup|2>\<barsuchthat\><around*|\<nobracket\>|k=1\< ldots\>10|\<nobracket\>>|}> <binom|49|6>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|{|1,4,9,16,25,36,49,64,81,100|}>>> <\equation*>
13983816
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
B\<assign\><around*|{|<around*|\<nobracket\>|1+8*k|\<nobracket\>>\<barsuch assume <around*|(|n,integer|)>;additionally
that\><around*|\<nobracket\>|k=1\<ldots\>10|\<nobracket\>>|}> <around*|(|n\<geqslant\>2|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|{|9,17,25,33,41,49,57,65,73,81|}>>> <\equation*>
\<bbb-Z\>,n
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
C\<assign\><around*|{|9,18,27|}> <binom|n|2>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|{|9,18,27|}>>> <\equation*>
<frac|n!|2\<cdot\><around*|(|n-2|)>!>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Set operations are entered in the usual way. Composition of functions:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
A\<setminus\>B <around*|(|cos\<circ\>sin|)><around*|(|\<mathpi\>|)>
<|unfolded-io-math>
<equation*|<math|<around*|{|1,4,16,36,64,100|}>>>
</unfolded-io-math>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
<around*|(|A\<cap\>B|)>\<cup\>C
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|{|9,25,49,81,18,27|}>>> <\equation*>
1
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
Using the notation <math|a\<in\>A> we get the 1-based index of the
element <math|a> in the set <math|A>, or 0 if <math|a\<nin\>A>.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
19\<in\>A,57\<in\>B f\<assign\>x\<mapsto\>x<rsup|2>+1
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|0,7>> <\equation*>
</unfolded-io-math> x\<mapsto\>x<rsup|2>+1
</equation*>
<\textput> <\errput>
The usual notation for composition of functions is supported. // Success
</textput>
<\unfolded-io-math> // End defining f
\<gtr\>\ </errput>
<|unfolded-io-math>
<around*|(|cos\<circ\>sin|)><around*|(|\<mathpi\>|)>
<|unfolded-io-math>
<equation*|<math|1>>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
f\<assign\>x\<mapsto\>x<rsup|2>+1;g\<assign\>y\<mapsto\>y-1 g\<assign\>y\<mapsto\>y-1
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|x\<mapsto\>x<rsup|2>+1,y\<mapsto\>y-1>> <\equation*>
y\<mapsto\>y-1
</equation*>
<\errput> <\errput>
// Success // Success
// End defining f
// Success
// End defining g // End defining g
</errput> </errput>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<around*|(|f\<circ\>g|)><around*|(|t|)> <around*|(|f\<circ\>g|)><around*|(|u|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|(|t-1|)><rsup|2>+1>> <\equation*>
<around*|(|u-1|)><rsup|2>+1
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
<around*|(|g\<circ\>f|)><around*|(|t|)> <around*|(|g\<circ\>f|)><around*|(|v|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|t<rsup|2>>> <\equation*>
v<rsup|2>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Conditionals are entered like in the examples below. Conditionals:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
1\<longequal\>2 1\<longequal\>2
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|false>> <\equation*>
false
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
1\<neq\>0 1\<neq\>2
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|true>> <\equation*>
true
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
assume <around*|(|h\<geqslant\>0|)> 1\<less\>2
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|h>> <\equation*>
true
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
h\<less\>h+1 1\<geqslant\>2
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|true>> <\equation*>
</unfolded-io-math> false
</equation*>
<\unfolded-io-math>
\<gtr\>\
<|unfolded-io-math>
sin <around*|(|h|)>-h\<leqslant\>2
<|unfolded-io-math>
<equation*|<math|true>>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Polynomials may be entered as lists of coefficients with double-struck Polynomials may be entered as lists of coefficients with double-struck
brackets. brackets:
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
p\<assign\><around*|\<llbracket\>|-1,3,2|\<rrbracket\>>;q\<assign\><around *|\<llbracket\>|2,0,-2,1|\<rrbracket\>> p\<assign\><around*|\<llbracket\>|-1,3,2|\<rrbracket\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|\<llbracket\>|-1,3,2|\<rrbracket\>>,<around*|\<l <\equation*>
lbracket\>|2,0,-2,1|\<rrbracket\>>>> <around*|\<llbracket\>|-1,3,2|\<rrbracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
p\<cdot\>q expand <around*|(|poly2symb <around*|(|p,x|)>|)>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|\<llbracket\>|-2,6,6,-7,-1,2|\<rrbracket\>>>> <\equation*>
-x<rsup|2>+3*x+2
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
expand <around*|(|poly2symb <around*|(|p+q,x|)>|)> q\<assign\><around*|\<llbracket\>|2,0,-2,1|\<rrbracket\>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|2*x<rsup|3>-x<rsup|2>+x+3>> <\equation*>
<around*|\<llbracket\>|2,0,-2,1|\<rrbracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput>
Periodic functions can be defined, as demonstrated below.
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
h\<assign\>periodic <around*|(|<around*|(|1-x<rsup|4>|)>*\<mathe\><rsup|1- x<rsup|3>>,x=-1\<ldots\>1|)> p\<cdot\>q
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|<around*|(|1-<around*|(|x-2*<around*|\<lfloor\>|<frac|x+1 <\equation*>
|2>|\<rfloor\>>|)><rsup|4>|)>*\<mathe\><rsup|1-<around*|(|x-2*<around*|\<lfloor\ <around*|\<llbracket\>|-2,6,6,-7,-1,2|\<rrbracket\>>
>|<frac|x+1|2>|\<rfloor\>>|)><rsup|3>>>> </equation*>
</unfolded-io-math> </unfolded-io-math>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
plot <around*|(|h,x=-5\<ldots\>5|)> p+q
<|unfolded-io-math> <|unfolded-io-math>
<image|giac-demo.en-image-10.pdf|0.7par|||> <\equation*>
<around*|\<llbracket\>|2,-1,1,3|\<rrbracket\>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
<\textput> <\textput>
Piecewise functions can be entered by using the <markup|choice> tag, as Piecewise functions can be entered by using the <markup|choice> tag
in the example below. Note that any textual condition (a <markup|text> (note that any textual condition, i.e.<nbsp>a <markup|text> tag, is
tag) is interpreted as \Potherwise\Q, no matter of its contents. interpreted as \Potherwise\Q, no matter of its contents):
</textput> </textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
f <around*|(|x|)>\<assign\><choice|<tformat|<table|<row|<cell|0,>|<cell|x\ <less\>0>>|<row|<cell|x,>|<cell|x\<less\>1>>|<row|<cell|1,>|<cell|x\<less\>3>>|< row|<cell|\<mathe\><rsup|3-x>,>|<cell|<text|in f <around*|(|x|)>\<assign\><choice|<tformat|<table|<row|<cell|0,>|<cell|x\ <less\>0>>|<row|<cell|x,>|<cell|x\<less\>1>>|<row|<cell|1,>|<cell|x\<less\>3>>|< row|<cell|\<mathe\><rsup|3-x>,>|<cell|<text|in
all other cases>>>>>> all other cases>>>>>>
<|unfolded-io-math> <|unfolded-io-math>
<equation*|<math|x\<mapsto\><choice|<tformat|<table|<row|<cell|0,>|<cell|x <\equation*>
\<less\>0>>|<row|<cell|x,>|<cell|x\<less\>1>>|<row|<cell|1,>|<cell|x\<less\>3>>| x\<mapsto\><choice|<tformat|<table|<row|<cell|0,>|<cell|x\<less\>0>>|<ro
<row|<cell|\<mathe\><rsup|3-x>,>|<cell|<text|otherwise>>>>>>>> w|<cell|x,>|<cell|x\<less\>1>>|<row|<cell|1,>|<cell|x\<less\>3>>|<row|<cell|\<ma
the\><rsup|3-x>,>|<cell|<text|otherwise>>>>>>
</equation*>
<\errput> <\errput>
// Parsing f // Parsing f
// Success // Success
// compiling f // compiling f
</errput> </errput>
</unfolded-io-math> </unfolded-io-math>
<\textput>
Periodic functions can be entered as well:
</textput>
<\unfolded-io-math> <\unfolded-io-math>
\<gtr\>\ \<gtr\>\
<|unfolded-io-math> <|unfolded-io-math>
plot <around*|(|f <around*|(|x|)>,x=-1\<ldots\>6|)> h\<assign\>periodic <around*|(|<around*|(|1-x<rsup|4>|)>*\<mathe\><rsup|1- x<rsup|3>>,x=-1\<ldots\>1|)>
<|unfolded-io-math> <|unfolded-io-math>
<image|giac-demo.en-image-11.pdf|0.7par|||> <\equation*>
<around*|(|1-<around*|(|x-2*<around*|\<lfloor\>|<frac|x+1|2>|\<rfloor\>>
|)><rsup|4>|)>*\<mathe\><rsup|1-<around*|(|x-2*<around*|\<lfloor\>|<frac|x+1|2>|
\<rfloor\>>|)><rsup|3>>
</equation*>
</unfolded-io-math> </unfolded-io-math>
</session> </session>
\;
<tmdoc-copyright|2021|Luka Marohnió>
<tmdoc-license|Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License, Version 1.1
or any later version published by the Free Software Foundation; with no
Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
Texts. A copy of the license is included in the section entitled "GNU Free
Documentation License".>
</body> </body>
<\initial> <initial|<\collection>
<\collection> </collection>>
<associate|page-medium|paper>
</collection>
</initial>
 End of changes. 195 change blocks. 
661 lines changed or deleted 434 lines changed or added

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