Hi,
Is it possible to define functions from Rm to Rn in Sage? And then, compose them, compute their jacobian (see also this previous post), use them for change of variables, ...
Is there something wrong with the following example for computing Jacobian ?
sage: var('x y')
sage: f(x, y) = (x^2 + y, x - sin(y))
sage: f.derivative()
[ (x, y) |--> 2*x (x, y) |--> 1]
[ (x, y) |--> 1 (x, y) |--> -cos(y)]
sage: f.derivative()(x=0, y=2)
[ 0 1]
[ 1 -cos(2)]Concerning composition, this is indeed more tricky, because:
sage: f(x, y).parent()
Vector space of dimension 2 over Symbolic RingSo, you could try:
sage: g(x, y) = (2*y, x)
sage: g(f[0], f[1])
(2*x - 2*sin(y), x^2 + y)Thanks! For Jacobian, there is something wrong: the string is ugly.
Well, you can do: sage: f.derivative()(x,y) [ 2*x 1] [ 1 -cos(y)] Or even: sage: show(f.derivative()(x,y)) Agree, i should help reviewing #14567 instead ;)
Use: g(*f) to substitute in the components of f into g.
Also, we could print the callable matrices more simply, like we print the callable vectors. Compare: f(x,y)=(3*x,y+x,sin(x)) (we print the (x,y)|--> outside of the vector). We should make a callable symbolic matrix class that prints the domain variables outside of the matrix. It would be the analog to: http://hg.sagemath.org/sage-main/src/0f8fd922eaed351e39f913f1317d319dcceb4c01/sage/modules/vector_callable_symbolic_dense.py?at=default (and shouldn't be that hard to do).
Also, you don't have to do var('x y') because f(x,y)=... automatically declares the variables x and y.
Reformulating some of my comments above as an answer so they don't get lost:
To compose, you can do:
f(x,y)=(x+2*y, x^2)
g(x,y)=(sin(x), cos(x*y))
f(*g)Note also that I didn't have to declare x and y to be variables; that is automatically done when they are used as inputs in an f(x,y)=... declaration.
As for printing of symbolic matrices, see my comment above. I would love if someone would write the necessary straightforward class to improve the printing.
Then open a ticket ;)
You mean like http://trac.sagemath.org/sage_trac/ticket/12075?
Asked: 11 years ago
Seen: 783 times
Last updated: Jun 29 '13
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