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cliffordoptimization.mw
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cliffordoptimization.mw
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<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="13" minor="0"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"></View-Properties>
<MapleNet-Properties elisiondigitsbefore="100" labelling="true" indentamount="4" elisiontermsthreshold="10000" ansi="false" errorbreak="1" useclientjvm="true" echo="1" imaginaryunit="I" labelwidth="20" plotdriver="openviz" elisiondigitsafter="100" plotoutput="terminal" rtablesize="10" elisiontermsbefore="100" elisiondigitsthreshold="10000" typesetting="standard" plotdevice="inline" verboseproc="1" showassumed="1" errorcursor="false" longdelim="true" plotoptions="" quiet="false" elisiontermsafter="100" screenwidth="79" preplot="" prettyprint="3" displayprecision="-1" warnlevel="3" screenheight="25" latexwidth="6.0" postplot="" prompt="> " ShowLabels="true"/>
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<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
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<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
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<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
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<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="any" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="newline" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Task-table>
<Task-category name="<default>">
</Task-category>
</Task-table>
<Task>
</Task>
<Group labelreference="L3">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">restart:
with(Clifford);
B:=linalg[diag](1,1,1,1,-1);
eval(makealiases(5,"ordered"));
e0:=-1/2*e4 + 1/2*e5;
einf:=e4+e5;
gaalopinitialize := proc()
global blade;
blade[1] := 1:
blade[2] := e1:
blade[3] := e2:
blade[4] := e3:
blade[5] := einf:
blade[6] := e0:
blade[7] := e1 &w e2:
blade[8] := e1 &w e3:
blade[9] := e1 &w einf:
blade[10] := e1 &w e0:
blade[11] := e2 &w e3:
blade[12] := e2 &w einf:
blade[13] := e2 &w e0:
blade[14] := e3 &w einf:
blade[15] := e3 &w e0:
blade[16] := einf &w e0:
blade[17] := e1 &w e2 &w e3:
blade[18] := e1 &w e2 &w einf:
blade[19] := e1 &w e2 &w e0:
blade[20] := e1 &w e3 &w einf:
blade[21] := e1 &w e3 &w e0:
blade[22] := e1 &w einf &w e0:
blade[23] := e2 &w e3 &w einf:
blade[24] := e2 &w e3 &w e0:
blade[25] := e2 &w einf &w e0:
blade[26] := e3 &w einf &w e0:
blade[27] := e1 &w e2 &w e3 &w einf:
blade[28] := e1 &w e2 &w e3 &w e0:
blade[29] := e1 &w e2 &w einf &w e0:
blade[30] := e1 &w e3 &w einf &w e0:
blade[31] := e2 &w e3 &w einf &w e0:
blade[32] := e1 &w e2 &w e3 &w einf &w e0:
end:
simple:=proc(val)
local temp;
temp := val,[e4,e5];
RETURN(temp);
end:
gaalop:=proc(label::evaln)
local coefficient,val,i,j,coeffpre,test;
global coeff_list,coeff_list_size;
val := eval(label);
eval(simplify(coeff(val,e23)));
coefficient[1] := simplify(scalarpart(simplify(val)));
coefficient[2] := simplify(coeff(val,e1));
coefficient[3] := simplify(coeff(val,e2));
coefficient[4] := simplify(coeff(val,e3));
coefficient[5] := simplify((coeff(val,e4)+coeff(val,e5))/2);
coefficient[6] := simplify(coeff(val,e5)-coeff(val,e4));
coefficient[7] := simplify(coeff(val,e12));
coefficient[8] := simplify(coeff(val,e13));
coefficient[9] := simplify((coeff(val,e14)+coeff(val,e15))/2);
coefficient[10] := simplify(coeff(val,e15)-coeff(val,e14));
coefficient[11] := simplify(coeff(val,e23));
coefficient[12] := simplify((coeff(val,e24)+coeff(val,e25))/2);
coefficient[13] := simplify(coeff(val,e25)-coeff(val,e24));
coefficient[14] := simplify((coeff(val,e34)+coeff(val,e35))/2);
coefficient[15] := simplify(coeff(val,e35)-coeff(val,e34));
coefficient[16] := simplify(coeff(val,e45));
coefficient[17] := simplify(coeff(val,e123));
coefficient[18] := simplify((coeff(val,e124)+coeff(val,e125))/2);
coefficient[19] := simplify(coeff(val,e125)-coeff(val,e124));
coefficient[20] := simplify((coeff(val,e134)+coeff(val,e135))/2);
coefficient[21] := simplify((coeff(val,e135)-coeff(val,e134)));
coefficient[22] := simplify(coeff(val,e145));
coefficient[23] := simplify((coeff(val,e234)+coeff(val,e235))/2);
coefficient[24] := simplify(coeff(val,e235)-coeff(val,e234));
coefficient[25] := simplify(coeff(val,e245));
coefficient[26] := simplify(coeff(val,e345));
coefficient[27] := simplify((coeff(val,e1234)+coeff(val,e1235))/2);
coefficient[28] := simplify(coeff(val,e1235)-coeff(val,e1234));
coefficient[29] := simplify(coeff(val,e1245));
coefficient[30] := simplify(coeff(val,e1345));
coefficient[31] := simplify(coeff(val,e2345));
coefficient[32] := simplify(coeff(val,e12345));
coeff_list_size := 0;
<Font encoding="UTF-8"> printf(`gaaloparray(%s%s);\134n`,label,_opt);
</Font> for i from 1 to 32 do
if not coefficient[i]=0 then
coeff_list_size := coeff_list_size+1;
<Font encoding="UTF-8"> printf(`%s%s[%d] := %a;\134n`,label,_opt,i,coefficient[i]);
</Font> coeff_list[coeff_list_size] := i;
end if;
end do;
if coeff_list_size > 0 then
<Font encoding="UTF-8"> cliffordperformant(label);
else printf(`%s%s[1] := 0;\134n`,label,_opt);
</Font> end if;
RETURN();
end:
Gaalop:=x->gaalop(x);
cliffordperformant:=proc(y::evaln)
global coeff_list,coeff_list_size;
local ausgabe,i,k,clucalc_blades;
clucalc_blades := ["1.0","e1","e2","e3","einf","e0","(e1^e2)","(e1^e3)","(e1^einf)","(e1^e0)","(e2^e3)","(e2^einf)","(e2^e0)","(e3^einf)","(e3^e0)","(einf^e0)","(e1^e2^e3)","(e1^e2^einf)","(e1^e2^e0)","(e1^e3^einf)","(e1^e3^e0)","(e1^einf^e0)","(e2^e3^einf)","(e2^e3^e0)","(e2^einf^e0)","(e3^einf^e0)","(e1^e2^e3^einf)","(e1^e2^e3^e0)","(e1^e2^einf^e0)","(e1^e3^einf^e0)","(e2^e3^einf^e0)","(e1^e2^e3^einf^e0)"];
ausgabe := sprintf("%s := ",y);
for i from 1 to coeff_list_size do
ausgabe := sprintf("%s%s%s[%d] * blade[%d]",ausgabe,y,_opt,coeff_list[i],coeff_list[i]);
if i < coeff_list_size then
ausgabe := sprintf("%s + ",ausgabe);
else
ausgabe := sprintf("%s;",ausgabe);
end if;
end do;
parse(ausgabe,statement);
RETURN();
end:
save simple,gaalopinitialize,gaalop,cliffordperformant, "gaalop.m";</Text-field>
</Input>
<Output>
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