please look at the results of G1, G2 and G3 at the end.
I am using
FriCAS Computer Algebra System
Version: FriCAS 1.1.8
on MacBook
Another pecularity is that the system knows about the unexported
MultiVariableCalculusFunctions, but neither this domain can be loaded nor it is
available in the algebra files.
(1) -> )r loopBug?
-- function F: R^3 -> R^2
X:=[x1,x2,x3]
(1) [x1,x2,x3]
Type: List(OrderedVariableList([x1,x2,x3]))
F := [x1*x2+x3^2,x1+x2*exp(x3)]
2 x3
(2) [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 +
(3) | |
| x3 x3|
+1 %e x2 %e +
Type: Matrix(Expression(Integer))
-- function G: R^3 -> R^4
Y:=[y1,y2]
(4) [y1,y2]
Type: List(OrderedVariableList([y1,y2]))
G := [1,y1,y1*y2,3*y1]
(5) [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 |
(6) | |
|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
(7) [y1= x3 + x1 x2,y2= x2 %e + x1]
Type: List(Equation(Expression(Integer)))
GF1 := [eval(g, YX) for g in G]
(8) [1,y1,y1 y2,3y1]
Type: List(Expression(Integer))
GF2 := [eval(G.i, YX) for i in 1..4]
(9) [1,y1,y1 y2,3y1]
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
(10) [1,x3 + x1 x2,(x2 x3 + x1 x2 )%e + x1 x3 + x1 x2,3x3 + 3x1 x2]
Type: List(Expression(Integer))
Mit freundlichen Grüßen
Johannes Grabmeier
Prof. Dr. Johannes Grabmeier
Köckstraße 1, D-94469 Deggendorf
Tel. +49-(0)-991-2979584, Tel. +49-(0)-151-681-70756
Tel. +49-(0)-991-3615-141 (d), Fax: +49-(0)-3224-192688
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