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<Worksheet><Version major="6" minor="0"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" linebreak="space" name="Warning"/><Layout alignment="left" linebreak="space" name="Error"/><Layout alignment="left" bullet="none" linespacing="0.0" name="Heading 1" spaceabove="8.0" spacebelow="4.0"/><Layout name="Normal"/><Layout alignment="centred" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Warning" readonly="true" size="10"/><Font background="[0,0,0]" bold="false" executable="false" family="Lucida Bright" foreground="[0,0,0]" italic="false" name="Text" opaque="false" size="12" underline="false"/><Font background="[0,0,0]" family="Monospaced" foreground="[255,0,255]" name="Error" readonly="true" size="10"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 1" opaque="false" size="18"/><Font background="[0,0,0]" family="Lucida Bright" foreground="[0,0,255]" name="2D Output" underline="false"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Line Printed Output" readonly="true" size="10"/><Font background="[0,0,0]" family="Lucida Bright" name="Page Number" underline="false"/></Styles><Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;
</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the assigned names &lt;,&gt; and &lt;|&gt; now have a global binding
</Text-field></Output><Output><Text-field layout="Warning" style="Warning">Warning, these protected names have been redefined and unprotected: *, +, ., D, Vector, diff, int, limit, series
</Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output"> </Equation></Text-field></Output><Output><Text-field layout="Warning" style="Warning">Warning, the protected name Chi has been redefined and unprotected
</Text-field></Output><Output><Text-field layout="Error" style="Error">Error, (in pack_fgb_init) external lookup of fgb_hilbert_compute: /usr/local/maple9/bin.IBM_INTEL_LINUX/libmaple.so: undefined symbol: fgb_hilbert_compute
</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output">    Gb/Maple for Unix/Windows interface package Version 0.84
    JC Faugere (Jean-Charles.Faugere@lip6.fr)
    Type ?Gb for documentation
</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output">Interface package to RS version 2.0.0 built 123 (F. Rouillier - INRIA SALSA project)
</Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNRO0xpbmtlZH5pbnRlcmZhY2V+YXZhaWxhYmxlNiI=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNROFVEWH5pbnRlcmZhY2V+YXZhaWxhYmxlNiI=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNROkFTQ0lJfmludGVyZmFjZX5hdmFpbGFibGU2Ig==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiNJJGxua0c2Ig==</Equation></Text-field></Output><Output><Text-field layout="Warning" style="Warning">Warning, the names isole, isolecoords and rur have been rebound
</Text-field></Output><Output><Text-field layout="Error" style="Error">Error, (in advance) use the command with(FGb): before !
</Text-field></Output><Output><Text-field layout="Normal" style="Line Printed Output">    RAGLib : A library of symbolic algorithms for Real Algebraic Geometry
    M. Safey El Din (Mohab.Safey@lip6.fr), University Paris 6
    Type ?RAG for documentation, Version 0.10

</Text-field></Output></Group><Section><Title><Text-field layout="Heading 1" style="Heading 1">Method 1</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eq:= -w+coeffs[1]*u+coeffs[2]*v+coeffs[3]*u^2+coeffs[4]*u*v+coeffs[5]*v^2+coeffs[6]*u^3+coeffs[7]*u^2*v+coeffs[8]*u*v^2+coeffs[9]*v^3+coeffs[10]*u^4+coeffs[11]*u^3*v+coeffs[12]*u^2*v^2+coeffs[13]*u*v^3+coeffs[14]*v^4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNlcUc2IixASSJ3R0YlISIiKiYmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRiw2IyIiIkYuSSJ1R0YlRi5GLiomJkYrNiMiIiNGLkkidkdGJUYuRi4qJiZGKzYjIiIkRi5GL0YzRi4qKCZGKzYjIiIlRi5GL0YuRjRGLkYuKiYmRis2IyIiJkYuRjRGM0YuKiYmRis2IyIiJ0YuRi9GOEYuKigmRis2IyIiKEYuRi9GM0Y0Ri5GLiooJkYrNiMiIilGLkYvRi5GNEYzRi4qJiZGKzYjIiIqRi5GNEY4Ri4qJiZGKzYjIiM1Ri5GL0Y8Ri4qKCZGKzYjIiM2Ri5GL0Y4RjRGLkYuKigmRis2IyIjN0YuRi9GM0Y0RjNGLiooJkYrNiMiIzhGLkYvRi5GNEY4Ri4qJiZGKzYjIiM5Ri5GNEY8Ri4=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" style="Text">On fait le fit dans le repere de coord [u,v,w]
puis on fait un changement de repere [u,v,w]=P*[x,y,z]
on suppose que le nouveau repere est de MOnge donc on doit avoir un truc de la forme:
f1x +f2y +f3z + 1/2( f11x^2 + f22y^2 + f33z^2 + 2f12xy + 2f13xz + 2f23yz) + 1/6(...
avec f1=f2=f12=0,  f3!=0, k1=-f11/f3, k2=-f22/f3, </Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">eq1:=simplify(subs({u=p[0][0]*x+p[0][1]*y+p[0][2]*z,v=p[1][0]*x+p[1][1]*y+p[1][2]*z,w=p[2][0]*x+p[2][1]*y+p[2][2]*z},eq)):sort(eq1,[x,y,z]):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f:=unapply(eq1,x,y,z):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">f1=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x) );
f2=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y) );
f3=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,z) );
f11=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x) );
f12=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,y) );
f13=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,z) );
f22=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,y) );
f23=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,z) );
f33=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,z,z) );
f111=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,x) );
f112=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,y) );
f122=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,y,y) );
f123=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,y,z) );
f113=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,z) );
f133=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,z,z) );
f222=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,y,y) );
f223=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,y,z) );
f233=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,z,z) );
f333=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,z,z,z) );
f1111=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,x,x) );
f1112=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,x,y) );
f1122=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,x,y,y) );
f1222=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,x,y,y,y) );
f2222=subs({x=0,y=0,z=0}, diff(f(x,y,z) ,y,y,y,y) );
g30=-(f111-3*f13*f11/f3)/f3;
g03=-(f222-3*f23*f22/f3)/f3;
g40=-(f1111+3*f113*g20+f33*g20^2+4*f13*g111)/f3;
g04=-(f2222+3*f223*g02+f33*g02^2+4*f23*g222)/f3;
</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSNmMUc2IiwoKiYmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIiIyIiIiYmSSJwR0YlNiNGLTYjIiIhRi1GLSomJkYpRjFGLSYmRjBGMkYyRi1GLSYmRjBGK0YyISIi</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSNmMkc2IiwoKiYmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIiIyIiIiYmSSJwR0YlNiNGLUYxRi1GLSomJkYpRjFGLSYmRjA2IyIiIUYxRi1GLSYmRjBGK0YxISIi</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSNmM0c2IiwoKiYmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIiIyIiIiYmSSJwR0YlNiNGLUYrRi1GLSomJkYpRjFGLSYmRjA2IyIiIUYrRi1GLSYmRjBGK0YrISIi</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMTFHNiIsKCooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiUiIiImJkkicEdGJTYjIiIhRjFGLSYmRjA2I0YtRjFGLSIiIyomJkYpNiMiIiRGLUYuRjZGNiomJkYpNiMiIiZGLUYzRjZGNg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMTJHNiIsKiooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiUiIiImJkkicEdGJTYjIiIhNiNGLUYtJiZGMEYzRjFGLUYtKigmRik2IyIiJkYtRjRGLSZGNUYzRi0iIiMqKCZGKTYjIiIkRi0mRi9GMUYtRi5GLUY7KihGKEYtRkBGLUY6Ri1GLQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMTNHNiIsKiooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiUiIiImJkkicEdGJTYjIiIhRjFGLSYmRjA2I0YtNiMiIiNGLUYtKihGKEYtJkYvRjZGLSZGNEYxRi1GLSooJkYpNiMiIiRGLUYuRi1GOUYtRjcqKCZGKTYjIiImRi1GOkYtRjNGLUY3</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMjJHNiIsKCooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiUiIiImJkkicEdGJTYjIiIhNiNGLUYtJiZGMEYzRjNGLSIiIyomJkYpNiMiIiZGLUY0RjZGNiomJkYpNiMiIiRGLUYuRjZGNg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMjNHNiIsKiooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiYiIiImJkkicEdGJTYjRi1GMUYtJkYvNiMiIiNGLUY0KigmRik2IyIiJUYtJiZGMDYjIiIhRjFGLUYyRi1GLSooJkYpNiMiIiRGLUY5Ri0mRjpGM0YtRjQqKEY2Ri1GQUYtRi5GLUYt</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRmMzNHNiIsKCooJkknY29lZmZzR0kqcHJvdGVjdGVkR0YqNiMiIiUiIiImJkkicEdGJTYjIiIhNiMiIiNGLSYmRjA2I0YtRjNGLUY0KiYmRik2IyIiJkYtRjVGNEY0KiYmRik2IyIiJEYtRi5GNEY0</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTExRzYiLCoqKCZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIoIiIiJiZJInBHRiU2IyIiIUYxIiIjJiZGMDYjRi1GMUYtIiInKigmRik2IyIiKUYtRi5GLUY0RjNGNyomJkYpNiMiIipGLUY0IiIkRjcqJiZGKTYjRjdGLUYuRkBGNw==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTEyRzYiLC4qKiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIpIiIiJiZJInBHRiU2IyIiIUYxRi0mJkYwNiNGLUYxRi0mRjRGNUYtIiIlKiomRik2IyIiKEYtRi5GLSZGL0Y1Ri1GM0YtRjcqKEYoRi1GPEYtRjMiIiNGPiooJkYpNiMiIidGLUYuRj5GPEYtRkIqKCZGKTYjIiIqRi1GM0Y+RjZGLUZCKihGOUYtRi5GPkY2Ri1GPg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTIyRzYiLC4qKCZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIpIiIiJiZJInBHRiU2IyIiIUYxRi0mJkYwNiNGLUY1IiIjRjYqKCZGKTYjIiIqRi0mRjRGMUYtRjNGNiIiJyooJkYpNiNGPEYtRi5GLSZGL0Y1RjZGPCoqJkYpNiMiIihGLUYuRi1GQEYtRjNGLSIiJSoqRihGLUZARi1GO0YtRjNGLUZFKihGQkYtRkBGNkY7Ri1GNg==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTIzRzYiLDIqKiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIpIiIiJiZJInBHRiU2IyIiITYjIiIjRi0mJkYwNiNGLUYxRi0mRjZGN0YtRjQqKiZGKTYjIiIoRi0mRi9GMUYtJkYvRjdGLSZGNkYzRi1GNCoqRjpGLUY9Ri1GLkYtRjhGLUY0KiomRik2IyIiKkYtRjVGLUY4Ri1GP0YtIiInKipGOkYtRj5GLUYuRi1GNUYtRjQqKiZGKTYjRkVGLUY9Ri1GPkYtRi5GLUZFKipGKEYtRj1GLUY4Ri1GP0YtRjQqKkYoRi1GPkYtRjVGLUY/Ri1GNA==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTEzRzYiLC4qKCZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIqIiIiJiZJInBHRiU2I0YtNiMiIiEiIiMmRi82I0Y0Ri0iIicqKiZGKTYjIiIoRi0mJkYwRjJGMkYtJkY9RjZGLUYuRi0iIiUqKiZGKTYjIiIpRi1GPEYtRi5GLUY1Ri1GPyooJkYpNiNGN0YtRjxGNEY+Ri1GNyooRjlGLUY8RjRGNUYtRjQqKEZBRi1GPkYtRi5GNEY0</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMTMzRzYiLC4qKiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIoIiIiJiZJInBHRiU2IyIiIUYxRi0mRi82IyIiI0YtJiZGMDYjRi1GNEYtIiIlKiomRik2IyIiKUYtRjNGLSZGN0YxRi1GNkYtRjkqKCZGKTYjIiInRi1GLkYtRjNGNUZCKihGO0YtRi5GLUY2RjVGNSooRihGLUYzRjVGPkYtRjUqKCZGKTYjIiIqRi1GPkYtRjZGNUZC</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMjIyRzYiLCoqKCZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIoIiIiJiZJInBHRiU2IyIiITYjRi0iIiMmJkYwRjNGM0YtIiInKigmRik2IyIiKUYtRi5GLUY1RjRGNyomJkYpNiNGN0YtRi4iIiRGNyomJkYpNiMiIipGLUY1Rj9GNw==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMjIzRzYiLC4qKiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIoIiIiJiZJInBHRiU2IyIiITYjRi1GLSZGLzYjIiIjRi0mJkYwRjNGM0YtIiIlKiomRik2IyIiKUYtRi5GLUY3Ri0mRjhGNUYtRjkqKEY7Ri1GNEYtRjdGNkY2KigmRik2IyIiKkYtRjdGNkY+Ri0iIicqKCZGKTYjRkRGLUYuRjZGNEYtRkQqKEYoRi1GLkY2Rj5GLUY2</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMjMzRzYiLC4qKiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiIoIiIiJiZJInBHRiU2IyIiITYjRi1GLSZGLzYjIiIjRi0mJkYwRjNGNUYtIiIlKiomRik2IyIiKUYtRjRGLSZGOEYzRi1GN0YtRjkqKEYoRi1GNEY2Rj5GLUY2KigmRik2IyIiJ0YtRi5GLUY0RjZGQyooRjtGLUYuRi1GN0Y2RjYqKCZGKTYjIiIqRi1GPkYtRjdGNkZD</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSVmMzMzRzYiLCoqJiZJJ2NvZWZmc0dJKnByb3RlY3RlZEdGKjYjIiInIiIiJiZJInBHRiU2IyIiITYjIiIjIiIkRiwqJiZGKTYjIiIqRi0mJkYwNiNGLUYzRjVGLCooJkYpNiMiIihGLUYuRjRGOkYtRiwqKCZGKTYjIiIpRi1GLkYtRjpGNEYs</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSZmMTExMUc2IiwsKigmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIjOCIiIiYmSSJwR0YlNiMiIiFGMUYtJiZGMDYjRi1GMSIiJCIjQyooJkYpNiMiIzZGLUYuRjZGM0YtRjcqKCZGKTYjIiM3Ri1GLiIiI0YzRkBGNyomJkYpNiMiIzlGLUYzIiIlRjcqJiZGKTYjIiM1Ri1GLkZFRjc=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSZmMTExMkc2IiwyKigmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIjOCIiIiYmSSJwR0YlNiMiIiE2I0YtRi0mJkYwRjNGMSIiJCIiJyoqRihGLSZGL0YxRi1GNCIiIyZGNUYzRi0iIz0qKCZGKTYjIiM1Ri1GOUY2Ri5GLSIjQyoqJkYpNiMiIzdGLUY5Ri1GLkYtRjRGOkZFKiomRik2IyIjNkYtRjlGOkYuRi1GNEYtRjwqKCZGKTYjIiM5Ri1GNEY2RjtGLUZBKihGR0YtRjlGNkY7Ri1GNyoqRkNGLUY5RjpGNEYtRjtGLUZF</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSZmMTEyMkc2Iiw0KiomSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIjNiIiIiYmSSJwR0YlNiMiIiFGMSIiIyZGLzYjRi1GLSYmRjBGNUY1Ri0iIzcqKiZGKTYjIiM4Ri1GLkYtJkY3RjFGLUY2RjNGOCoqRjpGLUY0Ri1GPUYzRjZGLUY4KiwmRik2I0Y4Ri1GLkYtRjRGLUY9Ri1GNkYtIiM7KipGKEYtRi5GLUY0RjNGPUYtRjgqKCZGKTYjIiM1Ri1GLkYzRjRGMyIjQyooRkBGLUY0RjNGPUYzIiIlKihGQEYtRi5GM0Y2RjNGSiooJkYpNiMiIzlGLUY9RjNGNkYzRkg=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSZmMTIyMkc2IiwyKigmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIjOCIiIiYmSSJwR0YlNiMiIiFGMUYtJiZGMDYjRi1GNSIiJCIiJyooJkYpNiMiIzVGLUYuRi0mRi9GNUY2IiNDKigmRik2IyIjOUYtJkY0RjFGLUYzRjZGPSooJkYpNiMiIzZGLUY8RjZGQkYtRjcqKkZERi1GLkYtRjwiIiNGM0YtIiM9KiomRik2IyIjN0YtRi5GLUY8Ri1GM0ZIRk0qKkZLRi1GPEZIRkJGLUYzRi1GTSoqRihGLUY8Ri1GQkYtRjNGSEZJ</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSZmMjIyMkc2IiwsKigmSSdjb2VmZnNHSSpwcm90ZWN0ZWRHRio2IyIjOCIiIiYmSSJwR0YlNiMiIiE2I0YtRi0mJkYwRjNGMyIiJCIjQyooJkYpNiMiIzZGLUYuRjZGNEYtRjcqKCZGKTYjIiM3Ri1GLiIiI0Y0RkBGNyomJkYpNiMiIzlGLUY0IiIlRjcqJiZGKTYjIiM1Ri1GLkZFRjc=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRnMzBHNiIsJComLCZJJWYxMTFHRiUiIiIqKEkkZjEzR0YlRipJJGYxMUdGJUYqSSNmM0dGJSEiIiEiJEYqRi5GL0Yv</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRnMDNHNiIsJComLCZJJWYyMjJHRiUiIiIqKEkkZjIzR0YlRipJJGYyMkdGJUYqSSNmM0dGJSEiIiEiJEYqRi5GL0Yv</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRnNDBHNiIsJComLCpJJmYxMTExR0YlIiIiKiZJJWYxMTNHRiVGKkkkZzIwR0YlRioiIiQqJkkkZjMzR0YlRipGLSIiI0YqKiZJJGYxM0dGJUYqSSVnMTExR0YlRioiIiVGKkkjZjNHRiUhIiJGNw==</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMvSSRnMDRHNiIsJComLCpJJmYyMjIyR0YlIiIiKiZJJWYyMjNHRiVGKkkkZzAyR0YlRioiIiQqJkkkZjMzR0YlRipGLSIiI0YqKiZJJGYyM0dGJUYqSSVnMjIyR0YlRioiIiVGKkkjZjNHRiUhIiJGNw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group></Section><Section><Title><Text-field layout="Heading 1" style="Heading 1">methode formelle!</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">g1:=implicitdiff(h(x,y,z),z(x,y),x);
g2:=implicitdiff(h(x,y,z),z(x,y),y);
g11:=implicitdiff(h(x,y,z),z(x,y),x,x):
g12:=implicitdiff(h(x,y,z),z(x,y),x,y):
g22:=implicitdiff(h(x,y,z),z(x,y),y,y):
g111:=implicitdiff(h(x,y,z),z(x,y),x,x,x):
g112:=implicitdiff(h(x,y,z),z(x,y),x,x,y):
g122:=implicitdiff(h(x,y,z),z(x,y),x,y,y):
g222:=implicitdiff(h(x,y,z),z(x,y),y,y,y):
g1111:=implicitdiff(h(x,y,z),z(x,y),x,x,x,x):
g1112:=implicitdiff(h(x,y,z),z(x,y),x,x,x,y):
g1122:=implicitdiff(h(x,y,z),z(x,y),x,x,y,y):
g1222:=implicitdiff(h(x,y,z),z(x,y),x,y,y,y):
g2222:=implicitdiff(h(x,y,z),z(x,y),y,y,y,y):
</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNnMUc2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIiNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJUYwLS0mRis2IyIiJEYxRjMhIiJGPA==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNnMkc2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIjNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJSIiIi0tJkYrNiMiIiRGMUYzISIiRj0=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">subs0:={D[1](h)(x,y,z)=0, D[2](h)(x,y,z)=0, D[1,2](h)(x,y,z)=0};</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZzdWJzMEc2IjwlLy0tJkkiREc2JEkqcHJvdGVjdGVkR0YtSShfc3lzbGliR0YlNiMiIiI2I0kiaEdGJTYlSSJ4R0YlSSJ5R0YlSSJ6R0YlIiIhLy0tJkYrNiRGMCIiI0YxRjNGNy8tLSZGKzYjRj1GMUYzRjc=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">g1s:=subs( subs0,g1);
g2s:=subs( subs0,g2);
g12s:=subs( subs0,g12);
g11s:=subs( subs0,g11);
g22s:=subs( subs0,g22);
g111s:=simplify(subs( subs0,g111));
g112s:=simplify(subs( subs0,g112));
g122s:=simplify(subs( subs0,g122));
g222s:=simplify(subs( subs0,g222));
g1111s:=simplify(subs( subs0,g1111));
g1112s:=simplify(subs( subs0,g1112));
g1122s:=simplify(subs( subs0,g1122));
g1222s:=simplify(subs( subs0,g1222));
g2222s:=simplify(subs( subs0,g2222));
</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRnMXNHNiIiIiE=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRnMnNHNiIiIiE=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVnMTJzRzYiIiIh</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVnMTFzRzYiLCQqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0YtSShfc3lzbGliR0YlNiQiIiJGMDYjSSJoR0YlNiVJInhHRiVJInlHRiVJInpHRiVGMC0tJkYrNiMiIiRGMUYzISIiRjw=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVnMjJzRzYiLCQqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0YtSShfc3lzbGliR0YlNiQiIiNGMDYjSSJoR0YlNiVJInhHRiVJInlHRiVJInpHRiUiIiItLSZGKzYjIiIkRjFGMyEiIkY9</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZnMTExc0c2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIkNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJSEiIywmKiYtLSZGKzYlIiIiRj5GPkYxRjNGPkYoRj5GPiomLS0mRis2JEY+RjBGMUYzRj4tLSZGKzYkRj5GPkYxRjNGPiEiJEY+ISIi</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZnMTEyc0c2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIkNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJSEiIywmKiYtLSZGKzYkIiIjRjBGMUYzIiIiLS0mRis2JEY/Rj9GMUYzRj8hIiIqJi0tJkYrNiVGP0Y/Rj5GMUYzRj9GKEY/Rj9GP0ZE</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZnMTIyc0c2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIkNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJSEiIywmKiYtLSZGKzYlIiIiIiIjRj9GMUYzRj5GKEY+Rj4qJi0tJkYrNiRGPkYwRjFGM0Y+LS0mRis2JEY/Rj9GMUYzRj4hIiJGPkZJ</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZnMjIyc0c2IiwkKiYtLSZJIkRHNiRJKnByb3RlY3RlZEdGLUkoX3N5c2xpYkdGJTYjIiIkNiNJImhHRiU2JUkieEdGJUkieUdGJUkiekdGJSEiIywmKiYtLSZGKzYlIiIjRj5GPkYxRjMiIiJGKEY/Rj8qJi0tJkYrNiRGPkYwRjFGM0Y/LS0mRis2JEY+Rj5GMUYzRj8hIiRGPyEiIg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdnMTExMXNHNiIqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0YsSShfc3lzbGliR0YlNiMiIiQ2I0kiaEdGJTYlSSJ4R0YlSSJ5R0YlSSJ6R0YlISIkLCwqJi0tJkYqNiRGL0YvRjBGMiIiIi0tJkYqNiRGPUY9RjBGMiIiI0Y2KiYtLSZGKjYmRj1GPUY9Rj1GMEYyRj1GJ0ZCISIiKigtLSZGKjYlRj1GPUYvRjBGMkY9RidGPUY+Rj0iIicqKC0tJkYqNiRGPUYvRjBGMkY9RidGPS0tJkYqNiVGPUY9Rj1GMEYyRj0iIiUqJkZQRkJGPkY9ISM3Rj0=</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdnMTExMnNHNiIqJi0tJkkiREc2JEkqcHJvdGVjdGVkR0YsSShfc3lzbGliR0YlNiMiIiQ2I0kiaEdGJTYlSSJ4R0YlSSJ5R0YlSSJ6R0YlISIkLCwqKC0tJkYqNiQiIiJGL0YwRjJGPS0tJkYqNiQiIiNGL0YwRjJGPS0tJkYqNiRGPUY9RjBGMkY9ISInKihGJ0Y9LS0mRio2JUY9RkJGL0YwRjJGPUZDRj1GLyooRjlGPUYnRj0tLSZGKjYlRj1GPUZCRjBGMkY9Ri8qKEY+Rj1GJ0Y9LS0mRio2JUY9Rj1GPUYwRjJGPUY9KiYtLSZGKjYmRj1GPUY9RkJGMEYyRj1GJ0ZCISIiRj0=</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdnMTEyMnNHNiIsJComLS0mSSJERzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IyIiJDYjSSJoR0YlNiVJInhHRiVJInlHRiVJInpHRiUhIiQsMiomLS0mRis2JiIiIkY+IiIjRj9GMUYzRj5GKEY/Rj4qKC0tJkYrNiVGPkY+RjBGMUYzRj5GKEY+LS0mRis2JEY/Rj9GMUYzRj4hIiIqKC0tJkYrNiRGPkYwRjFGM0Y+RihGPi0tJkYrNiVGPkY/Rj9GMUYzRj4hIiMqJkZLRj9GRUY+Rj8qKC0tJkYrNiVGP0Y/RjBGMUYzRj5GKEY+LS0mRis2JEY+Rj5GMUYzRj5GSSomLS0mRis2JEY/RjBGMUYzRj9GWkY+Rj8qKEZpbkY+RihGPi0tJkYrNiVGPkY+Rj9GMUYzRj5GUyooLS0mRis2JEYwRjBGMUYzRj5GRUY+RlpGPkY+Rj5GSQ==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdnMTIyMnNHNiIsJComLS0mSSJERzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IyIiJDYjSSJoR0YlNiVJInhHRiVJInlHRiVJInpHRiUhIiQsLComLS0mRis2JiIiIiIiI0Y/Rj9GMUYzRj5GKEY/Rj4qKC0tJkYrNiRGPkYwRjFGM0Y+LS0mRis2JEY/RjBGMUYzRj4tLSZGKzYkRj9GP0YxRjNGPiIiJyooRkVGPkYoRj4tLSZGKzYlRj5GP0Y/RjFGM0Y+RjcqKC0tJkYrNiVGPkY/RjBGMUYzRj5GKEY+RklGPkY3KihGQUY+RihGPi0tJkYrNiVGP0Y/Rj9GMUYzRj4hIiJGPkZnbg==</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdnMjIyMnNHNiIsJComLS0mSSJERzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IyIiJDYjSSJoR0YlNiVJInhHRiVJInlHRiVJInpHRiUhIiQsLComLS0mRis2JiIiI0Y+Rj5GPkYxRjMiIiJGKEY+Rj8qJi0tJkYrNiRGMEYwRjFGM0Y/LS0mRis2JEY+Rj5GMUYzRj5GMCooLS0mRis2JUY+Rj5GMEYxRjNGP0YoRj9GRUY/ISInKigtLSZGKzYkRj5GMEYxRjNGP0YoRj8tLSZGKzYlRj5GPkY+RjFGM0Y/ISIlKiZGUEY+RkVGPyIjN0Y/ISIi</Equation></Text-field></Output></Group></Section><Text-field/><Text-field/></Worksheet>