polynomial_product_two_variables.sagews

%typeset_mode True

var('xi, eta')

foo = 5*xi^2 + 3*xi^1 + 1
bar = 5*eta^2 + 3*eta^1 + 1

($\displaystyle \xi$, $\displaystyle \eta$)

foo

$\displaystyle 5 \, \xi^{2} + 3 \, \xi + 1$

integrate(integrate((foo * bar), xi, -1, 1), eta, -1, 1).n()

$\displaystyle 28.4444444444444$

print (foo * bar)(xi =    -1.00000000000000 , eta =    -1.00000000000000 )
print (foo * bar)(xi =    -0.71428571428571 , eta =    -0.71428571428571 )
print (foo * bar)(xi =    -0.42857142857143 , eta =    -0.42857142857143 )
print (foo * bar)(xi =    -0.14285714285714 , eta =    -0.14285714285714 )
print (foo * bar)(xi =     0.14285714285714 , eta =     0.14285714285714 )
print (foo * bar)(xi =     0.42857142857143 , eta =     0.42857142857143 )
print (foo * bar)(xi =     0.71428571428571 , eta =     0.71428571428571 )
print (foo * bar)(xi =     1.00000000000000 , eta =     1.00000000000000 )

4.00000000000000 1.21449396084962 0.481466055810080 0.601416076634741 1.81424406497291 5.79925031236988 15.6751353602663 36.0000000000000

integrate(integrate(foo * bar, xi, -1, 1), eta, -1, 1)

$\displaystyle 16$