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:
if test $# -eq 0; then
echo "$0: usage: $0 order a b"
echo "example: $0 3 3 0"
exit 1
fi
order=${1-"2"}
a=${2-"0"}
b=${3-"0"}
tmp="tmp.mac"
log="tmp.log"
cat > $tmp << EOF_1
a:$a;
b:$b;
k:${order};
/* P${order} piola triangle transformation here */
y_bas : if (k=1) then 0 else x*(1-x)**(k-1);
y_haut: y_bas + (1-x);
J_bas : integrate(y**b,y,0,y_bas);
J_haut: integrate(y**b,y,0,y_haut);
I_bas : integrate(x**a * J_bas, x,0,1);
I_haut: integrate(x**a * J_haut,x,0,1);
load(f90);
res;
f90 ('exact = I_haut-I_bas);
print ("value=", bfloat(I_haut-I_bas));
EOF_1
maxima < $tmp > $log
#cat $log
exact=`grep exact $log | sed -e 's/.*exact[ ]*=[ ]*//'`
value=`grep value $log | sed -e 's/.*value=[ ]*//' -e 's/b/e/'`
echo "integral(a=$a,b=$b) = $exact = $value"
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