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## Minimal Maxima

Here is an example from the paper "Minimal Maxima" by Robert Dodier:

WebSite:maxima.sourceforge.net/docs/tutorial/en/minimal-maxima.pdf

1. 2 Solve an equation
maxima(%i2) eq_1:z+b*y+a*x = %pi

maxima(%i3) eq_2:x-5*y+z = 0

maxima(%i4) s:solve([eq_1,eq_2],[x,z])

maxima(%i5) length(s)

maxima<latex>
\mbox{\tt\red(\mathrm{\%o5}) \black}1</latex>
(%i6) [subst(s[1],eq_1),subst(s[1],eq_2)]

maxima<latex>
\mbox{\tt\red(\mathrm{\%o6}) \black}\left[ {{\left(b+5list\*a\right)list
\*y-\pi}\over{a-1}}-{{alist\*\left(\left(b+5\right)list\*y-\pi
\right)}\over{a-1}}+blist\*y=\pi , {{\left(b+5list\*a\right)list\*y-
\pi}\over{a-1}}-{{\left(b+5\right)list\*y-\pi}\over{a-1}}-5list\*y=0
\right] </latex>
(%i7) ratsimp(%)

maxima(%i8) s:solve(-1-9*D+6*C*D+(-1-3*D+4*C*D)*a+(1-2*C*D)*a^2+a^3,a)
(%i9) length(s)

maxima<latex>
\mbox{\tt\red(\mathrm{\%o9}) \black}3</latex>
maxima<latex>
\mbox{\tt\red(\mathrm{\%o9}) \black}
\mbox{{}/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/11447957390781607-25px.001.max{}}
</latex>


maxima(%i11) display2d:false
(%i12) s
(%o12) [a = (-sqrt(3)*%i/2-1/2)*(sqrt(-D
*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2
+(64*C^2+240*C-396)*D-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2+108*D
+8)
/27)
^(1/3)
+(sqrt(3)*%i/2-1/2)*(4*C^2*D^2-16*C*D+9*D+4)
/(9*(sqrt(-D*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2+(64*C^2+240*C-396)*D
-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2+108*D+8)/27)
^(1/3))-(1-2*C*D)/3,
a = (sqrt(3)*%i/2-1/2)*(sqrt(-D*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2
+(64*C^2+240*C-396)*D-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2+108*D+8)
/27)
^(1/3)
+(-sqrt(3)*%i/2-1/2)*(4*C^2*D^2-16*C*D+9*D+4)
/(9*(sqrt(-D*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2+(64*C^2+240*C-396)*D
-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2+108*D+8)/27)
^(1/3))-(1-2*C*D)/3,
a = (sqrt(-D*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2+(64*C^2+240*C-396)*D
-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2+108*D+8)/27)
^(1/3)
+(4*C^2*D^2-16*C*D+9*D+4)/(9*(sqrt(
-D
*((64*C^4-96*C^3+9*C^2)*D^3
+(-384*C^3+768*C^2-360*C+27)*D^2
+(64*C^2+240*C-396)*D-48))
/3^(3/2)
+(8*C^3*D^3+C*(27*D^2-48*D)-48*C^2*D^2
+108*D+8)
/27)
^(1/3))-(1-2*C*D)/3]
(%o12) "/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5114262280024159424-25px.002.max"


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