Would the following look better to you?
It's obtained with what is currently on SVN trunk. Maybe it's the same
as for 1.2.2, but I don't have that compiled at the moment.
Ralf
-- function F: R^3 -> R^2
X:=[x1,x2,x3]
(9) [x1,x2,x3]
Type:
List(OrderedVariableList([x1,x2,x3]))
F := [x1*x2+x3^2,x1+x2*exp(x3)]
2 x3
(10) [x3 + x1 x2,x2 %e + x1]
Type:
List(Expression(Integer))
-- Jacobian F
DF := matrix [[D(f,x) for x in X] for f in F]
+x2 x1 2x3 +
(11) | |
| x3 x3|
+1 %e x2 %e +
Type:
Matrix(Expression(Integer))
-- function G: R^3 -> R^4
Y:=[y1,y2]
(12) [y1,y2]
Type:
List(OrderedVariableList([y1,y2]))
G := [1,y1,y1*y2,3*y1]
(13) [1,y1,y1 y2,3y1]
Type:
List(Polynomial(Integer))
-- Jacobian G
DG := matrix [[D(g,y) for y in Y] for g in G]
+0 0 +
| |
|1 0 |
(14) | |
|y2 y1|
| |
+3 0 +
Type:
Matrix(Polynomial(Integer))
-- composition GF := GoF using the following substitutions:
YX := [y=f for y in Y for f in F]
2 x3
(15) [y1= x3 + x1 x2,y2= x2 %e + x1]
Type:
List(Equation(Expression(Integer)))
GF1 := [eval(g, YX) for g in G]
2 2 2 x3 2 2 2
(16) [1,x3 + x1 x2,(x2 x3 + x1 x2 )%e + x1 x3 + x1 x2,3x3 +
3x1 x2]
Type:
List(Expression(Integer))
GF2 := [eval(G.i, YX) for i in 1..4]
2 2 2 x3 2 2 2
(17) [1,x3 + x1 x2,(x2 x3 + x1 x2 )%e + x1 x3 + x1 x2,3x3 +
3x1 x2]
Type:
List(Expression(Integer))
GF3 := [eval(G.1, YX), eval(G.2, YX), eval(G.3, YX), eval(G.4, YX) ]
2 2 2 x3 2 2 2
(18) [1,x3 + x1 x2,(x2 x3 + x1 x2 )%e + x1 x3 + x1 x2,3x3 +
3x1 x2]
Type:
List(Expression(Integer))
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